(%i1) batch("diffeq.max") read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max (%i2) load("stringproc") (%o2) /usr/share/maxima/5.31.3/share/stringproc/stringproc.mac (%i3) alias(convfloat,float) (%o3) [convfloat] (%i4) alias(int_trunc,truncate) (%o4) [truncate] (%i5) alias(elapsed_time_seconds,elapsed_real_time) (%o5) [elapsed_time_seconds] (%i6) alias(ln,log) (%o6) [log] (%i7) alias(arcsin,asin) (%o7) [asin] (%i8) alias(arccos,acos) (%o8) [acos] (%i9) alias(arctan,atan) (%o9) [atan] (%i10) alias(float_abs,abs) (%o10) [mabs] (%i11) keepfloat:true (%o11) true (%i12) mode_declare(display_poles(),fixnum) (%o12) [display_poles()] (%i13) mode_declare(est_size_answer(),convfloat) (%o13) [est_size_answer()] (%i14) mode_declare(test_suggested_h(),convfloat) (%o14) [test_suggested_h()] (%i15) mode_declare(reached_interval(),boolean) (%o15) [reached_interval()] (%i16) mode_declare(display_alot([iter],fixnum),fixnum) (%o16) [display_alot([iter], fixnum)] (%i17) mode_declare(adjust_for_pole([h_param],convfloat),convfloat) (%o17) [adjust_for_pole([h_param], convfloat)] (%i18) mode_declare(prog_report([x_start],convfloat,[x_end],convfloat),fixnum) (%o18) [prog_report([x_start], convfloat, [x_end], convfloat)] (%i19) mode_declare(check_for_pole(),fixnum) (%o19) [check_for_pole()] (%i20) mode_declare(atomall(),fixnum) (%o20) [atomall()] (%i21) mode_declare(log10([x],convfloat),convfloat) (%o21) [log10([x], convfloat)] (%i22) mode_declare(logitem_timestr([fd],fixnum,[secs_in],number),fixnum) (%o22) [logitem_timestr([fd], fixnum, [secs_in], number)] (%i23) mode_declare(omniout_timestr(secs_in,number),fixnum) (%o23) [omniout_timestr(secs_in, number)] (%i24) mode_declare(zero_ats_ar(ar,array([MAX_TERMS],convfloat)),fixnum) (%o24) [zero_ats_ar(ar, array([MAX_TERMS], convfloat))] (%i25) mode_declare(ats([mmm_ats],fixnum,[arr_a], completearray([MAX_TERMS],convfloat),[arr_b], completearray([MAX_TERMS],convfloat),[jjj_ats], fixnum),convfloat) (%o25) [ats([mmm_ats], fixnum, [arr_a], completearray([MAX_TERMS], convfloat), [arr_b], completearray([MAX_TERMS], convfloat), [jjj_ats], fixnum)] (%i26) mode_declare(att([mmm_att],fixnum,[arr_a], completearray([MAX_TERMS],convfloat),[arr_b], completearray([MAX_TERMS],convfloat),[jjj_att], fixnum),convfloat) (%o26) [att([mmm_att], fixnum, [arr_a], completearray([MAX_TERMS], convfloat), [arr_b], completearray([MAX_TERMS], convfloat), [jjj_att], fixnum)] (%i27) mode_declare(logitem_ditto([file],fixnum),fixnum) (%o27) [logitem_ditto([file], fixnum)] (%i28) mode_declare(logitem_integer([file],fixnum,[n],fixnum),fixnum) (%o28) [logitem_integer([file], fixnum, [n], fixnum)] (%i29) mode_declare(logitem_good_digits([file],fixnum,[relerror],convfloat),fixnum) (%o29) [logitem_good_digits([file], fixnum, [relerror], convfloat)] (%i30) mode_declare(logitem_number([file],fixnum,[x],number),fixnum) (%o30) [logitem_number([file], fixnum, [x], number)] (%i31) mode_declare(logitem_pole([file],fixnum,[pole],fixnum),fixnum) (%o31) [logitem_pole([file], fixnum, [pole], fixnum)] (%i32) mode_declare(logstart([file],fixnum),fixnum) (%o32) [logstart([file], fixnum)] (%i33) mode_declare(logend([file],fixnum),fixnum) (%o33) [logend([file], fixnum)] (%i34) mode_declare(chk_data(),fixnum) (%o34) [chk_data()] (%i35) mode_declare(comp_expect_sec([t_end2],convfloat,[t_start2],convfloat, [t2],convfloat,[clock_sec2],convfloat), convfloat) (%o35) [comp_expect_sec([t_end2], convfloat, [t_start2], convfloat, [t2], convfloat, [clock_sec2], convfloat)] (%i36) mode_declare(comp_percent([t_end2],convfloat,[start2],convfloat,[t2], convfloat),convfloat) (%o36) [comp_percent([t_end2], convfloat, [start2], convfloat, [t2], convfloat)] (%i37) mode_declare(comp_rad_from_ratio([term1],convfloat,[term2],convfloat, [last_no],fixnum),convfloat) (%o37) [comp_rad_from_ratio([term1], convfloat, [term2], convfloat, [last_no], fixnum)] (%i38) mode_declare(comp_ord_from_ratio([term1],convfloat,[term2],convfloat, [last_no],fixnum),convfloat) (%o38) [comp_ord_from_ratio([term1], convfloat, [term2], convfloat, [last_no], fixnum)] (%i39) mode_declare(comp_rad_from_three_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [last_no],fixnum),convfloat) (%o39) [comp_rad_from_three_terms([term1], convfloat, [term2], convfloat, [term3], convfloat, [last_no], fixnum)] (%i40) mode_declare(comp_ord_from_three_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [last_no],fixnum),convfloat) (%o40) [comp_ord_from_three_terms([term1], convfloat, [term2], convfloat, [term3], convfloat, [last_no], fixnum)] (%i41) mode_declare(comp_rad_from_six_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [term4],convfloat,[term5], convfloat,[term6],convfloat, [last_no],fixnum),convfloat) (%o41) [comp_rad_from_six_terms([term1], convfloat, [term2], convfloat, [term3], convfloat, [term4], convfloat, [term5], convfloat, [term6], convfloat, [last_no], fixnum)] (%i42) mode_declare(comp_ord_from_six_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [term4],convfloat,[term5], convfloat,[term6],convfloat, [last_no],fixnum),convfloat) (%o42) [comp_ord_from_six_terms([term1], convfloat, [term2], convfloat, [term3], convfloat, [term4], convfloat, [term5], convfloat, [term6], convfloat, [last_no], fixnum)] (%i43) mode_declare(factorial_2([nnn],fixnum),fixnum) (%o43) [factorial_2([nnn], fixnum)] (%i44) mode_declare(factorial_1([nnn],fixnum),fixnum) (%o44) [factorial_1([nnn], fixnum)] (%i45) mode_declare(factorial_3([mmm],fixnum,[nnn],fixnum),fixnum) (%o45) [factorial_3([mmm], fixnum, [nnn], fixnum)] (%i46) mode_declare(convfloat([mmm],fixnum),convfloat) (%o46) [convfloat([mmm], fixnum)] (%i47) mode_declare(elaped_time_seconds(),convfloat) (%o47) [elaped_time_seconds()] (%i48) mode_declare(Si([x],convfloat),convfloat) (%o48) [Si([x], convfloat)] (%i49) mode_declare(Ci([x],convfloat),convfloat) (%o49) [Ci([x], convfloat)] (%i50) mode_declare(estimated_needed_step_error([x_start],convfloat,[x_end], convfloat,[estimated_h], convfloat,[estimated_answer], convfloat),convfloat) (%o50) [estimated_needed_step_error([x_start], convfloat, [x_end], convfloat, [estimated_h], convfloat, [estimated_answer], convfloat)] (%i51) mode_declare(my_check_sign([x0],convfloat,[xf],convfloat),convfloat) (%o51) [my_check_sign([x0], convfloat, [xf], convfloat)] (%i52) mode_declare(main_prog(),fixnum) (%o52) [main_prog()] (%i53) define_variable(MAX_TERMS,30,fixnum) (%o53) 30 (%i54) define_variable(glob_iolevel,5,fixnum) (%o54) 5 (%i55) define_variable(glob_yes_pole,4,fixnum) (%o55) 4 (%i56) define_variable(glob_no_pole,3,fixnum) (%o56) 3 (%i57) define_variable(glob_not_given,0,fixnum) (%o57) 0 (%i58) define_variable(glob_no_sing_tests,4,fixnum) (%o58) 4 (%i59) define_variable(glob_ratio_test,1,fixnum) (%o59) 1 (%i60) define_variable(glob_three_term_test,2,fixnum) (%o60) 2 (%i61) define_variable(glob_six_term_test,3,fixnum) (%o61) 3 (%i62) define_variable(glob_log_10,log(10.0),convfloat) (%o62) 2.302585092994046 (%i63) define_variable(ALWAYS,1,fixnum) (%o63) 1 (%i64) define_variable(INFO,2,fixnum) (%o64) 2 (%i65) define_variable(DEBUGL,3,fixnum) (%o65) 3 (%i66) define_variable(DEBUGMASSIVE,4,fixnum) (%o66) 4 (%i67) define_variable(MAX_UNCHANGED,10,fixnum) (%o67) 10 (%i68) define_variable(glob_check_sign,1.0,convfloat) (%o68) 1.0 (%i69) define_variable(glob_desired_digits_correct,8.0,convfloat) (%o69) 8.0 (%i70) define_variable(glob_max_estimated_step_error,0.0,convfloat) (%o70) 0.0 (%i71) define_variable(glob_ratio_of_radius,0.1,convfloat) (%o71) 0.1 (%i72) define_variable(glob_percent_done,0.0,convfloat) (%o72) 0.0 (%i73) define_variable(glob_subiter_method,3,fixnum) (%o73) 3 (%i74) define_variable(glob_total_exp_sec,0.1,convfloat) (%o74) 0.1 (%i75) define_variable(glob_optimal_expect_sec,0.1,convfloat) (%o75) 0.1 (%i76) define_variable(glob_estimated_size_answer,100.0,convfloat) (%o76) 100.0 (%i77) define_variable(glob_html_log,true,boolean) (%o77) true (%i78) define_variable(glob_good_digits,0,fixnum) (%o78) 0 (%i79) define_variable(glob_max_opt_iter,10,fixnum) (%o79) 10 (%i80) define_variable(glob_dump,false,boolean) (%o80) false (%i81) define_variable(glob_djd_debug,true,boolean) (%o81) true (%i82) define_variable(glob_display_flag,true,boolean) (%o82) true (%i83) define_variable(glob_djd_debug2,true,boolean) (%o83) true (%i84) define_variable(glob_sec_in_minute,60,fixnum) (%o84) 60 (%i85) define_variable(glob_min_in_hour,60.0,convfloat) (%o85) 60.0 (%i86) define_variable(glob_hours_in_day,24.0,convfloat) (%o86) 24.0 (%i87) define_variable(glob_days_in_year,365,fixnum) (%o87) 365 (%i88) define_variable(glob_sec_in_hour,3600,fixnum) (%o88) 3600 (%i89) define_variable(glob_sec_in_day,86400,fixnum) (%o89) 86400 (%i90) define_variable(glob_sec_in_year,31536000,fixnum) (%o90) 31536000 (%i91) define_variable(glob_almost_1,0.999,convfloat) (%o91) 0.999 (%i92) define_variable(glob_clock_sec,0.0,convfloat) (%o92) 0.0 (%i93) define_variable(glob_clock_start_sec,0.0,convfloat) (%o93) 0.0 (%i94) define_variable(glob_not_yet_finished,true,boolean) (%o94) true (%i95) define_variable(glob_initial_pass,true,boolean) (%o95) true (%i96) define_variable(glob_not_yet_start_msg,true,boolean) (%o96) true (%i97) define_variable(glob_reached_optimal_h,false,boolean) (%o97) false (%i98) define_variable(glob_optimal_done,false,boolean) (%o98) false (%i99) define_variable(glob_disp_incr,0.1,convfloat) (%o99) 0.1 (%i100) define_variable(glob_h,0.1,convfloat) (%o100) 0.1 (%i101) define_variable(glob_diff_rc_fm,0.1,convfloat) (%o101) 0.1 (%i102) define_variable(glob_diff_rc_fmm1,0.1,convfloat) (%o102) 0.1 (%i103) define_variable(glob_diff_rc_fmm2,0.1,convfloat) (%o103) 0.1 (%i104) define_variable(glob_diff_ord_fm,0.1,convfloat) (%o104) 0.1 (%i105) define_variable(glob_diff_ord_fmm1,0.1,convfloat) (%o105) 0.1 (%i106) define_variable(glob_diff_ord_fmm2,0.1,convfloat) (%o106) 0.1 (%i107) define_variable(glob_six_term_ord_save,0.1,convfloat) (%o107) 0.1 (%i108) define_variable(glob_guess_error_rc,0.1,convfloat) (%o108) 0.1 (%i109) define_variable(glob_guess_error_ord,0.1,convfloat) (%o109) 0.1 (%i110) define_variable(glob_max_h,0.1,convfloat) (%o110) 0.1 (%i111) define_variable(glob_min_h,1.0E-6,convfloat) (%o111) 1.0E-6 (%i112) define_variable(glob_type_given_pole,0,fixnum) (%o112) 0 (%i113) define_variable(glob_large_float,1.0E+100,convfloat) (%o113) 1.0E+100 (%i114) define_variable(glob_larger_float,1.1E+100,convfloat) (%o114) 1.1E+100 (%i115) define_variable(glob_least_given_sing,9.9E+100,convfloat) (%o115) 9.9E+100 (%i116) define_variable(glob_least_ratio_sing,9.9E+100,convfloat) (%o116) 9.9E+100 (%i117) define_variable(glob_least_3_sing,9.9E+100,convfloat) (%o117) 9.9E+100 (%i118) define_variable(glob_least_6_sing,9.9E+100,convfloat) (%o118) 9.9E+100 (%i119) define_variable(glob_last_good_h,0.1,convfloat) (%o119) 0.1 (%i120) define_variable(glob_look_poles,false,boolean) (%o120) false (%i121) define_variable(glob_neg_h,false,boolean) (%o121) false (%i122) define_variable(glob_display_interval,0.0,convfloat) (%o122) 0.0 (%i123) define_variable(glob_next_display,0.0,convfloat) (%o123) 0.0 (%i124) define_variable(glob_dump_analytic,false,boolean) (%o124) false (%i125) define_variable(glob_abserr,1.0E-11,convfloat) (%o125) 1.0E-11 (%i126) define_variable(glob_relerr,1.0E-11,convfloat) (%o126) 1.0E-11 (%i127) define_variable(glob_min_pole_est,1.0E+9,convfloat) (%o127) 1.0E+9 (%i128) define_variable(glob_max_hours,0.0,convfloat) (%o128) 0.0 (%i129) define_variable(glob_max_iter,1000,fixnum) (%o129) 1000 (%i130) define_variable(glob_max_rel_trunc_err,1.0E-11,convfloat) (%o130) 1.0E-11 (%i131) define_variable(glob_max_trunc_err,1.0E-11,convfloat) (%o131) 1.0E-11 (%i132) define_variable(glob_no_eqs,0,fixnum) (%o132) 0 (%i133) define_variable(glob_optimal_clock_start_sec,0.0,convfloat) (%o133) 0.0 (%i134) define_variable(glob_optimal_start,0.0,convfloat) (%o134) 0.0 (%i135) define_variable(glob_upper_ratio_limit,1.0001,convfloat) (%o135) 1.0001 (%i136) define_variable(glob_lower_ratio_limit,0.9999,convfloat) (%o136) 0.9999 (%i137) define_variable(glob_small_float,0.0,convfloat) (%o137) 0.0 (%i138) define_variable(glob_smallish_float,0.0,convfloat) (%o138) 0.0 (%i139) define_variable(glob_unchanged_h_cnt,0,fixnum) (%o139) 0 (%i140) define_variable(glob_warned,false,boolean) (%o140) false (%i141) define_variable(glob_warned2,false,boolean) (%o141) false (%i142) define_variable(glob_max_sec,10000.0,convfloat) (%o142) 10000.0 (%i143) define_variable(glob_orig_start_sec,0.0,convfloat) (%o143) 0.0 (%i144) define_variable(glob_start,0,fixnum) (%o144) 0 (%i145) define_variable(glob_curr_iter_when_opt,0,fixnum) (%o145) 0 (%i146) define_variable(glob_current_iter,0,fixnum) (%o146) 0 (%i147) define_variable(glob_iter,0,fixnum) (%o147) 0 (%i148) define_variable(glob_normmax,0.0,convfloat) (%o148) 0.0 (%i149) define_variable(glob_max_minutes,0.0,convfloat) (%o149) 0.0 (%i150) array(array_y_init,MAX_TERMS) (%o150) array_y_init (%i151) array(array_norms,MAX_TERMS) (%o151) array_norms (%i152) array(array_fact_1,MAX_TERMS) (%o152) array_fact_1 (%i153) array(array_1st_rel_error,2) (%o153) array_1st_rel_error (%i154) array(array_last_rel_error,2) (%o154) array_last_rel_error (%i155) array(array_type_pole,2) (%o155) array_type_pole (%i156) array(array_type_real_pole,2) (%o156) array_type_real_pole (%i157) array(array_type_complex_pole,2) (%o157) array_type_complex_pole (%i158) array(array_y,MAX_TERMS) (%o158) array_y (%i159) array(array_x,MAX_TERMS) (%o159) array_x (%i160) array(array_tmp0,MAX_TERMS) (%o160) array_tmp0 (%i161) array(array_tmp1,MAX_TERMS) (%o161) array_tmp1 (%i162) array(array_tmp2_g,MAX_TERMS) (%o162) array_tmp2_g (%i163) array(array_tmp2,MAX_TERMS) (%o163) array_tmp2 (%i164) array(array_tmp3,MAX_TERMS) (%o164) array_tmp3 (%i165) array(array_m1,MAX_TERMS) (%o165) array_m1 (%i166) array(array_y_higher,2,MAX_TERMS) (%o166) array_y_higher (%i167) array(array_y_higher_work,2,MAX_TERMS) (%o167) array_y_higher_work (%i168) array(array_y_higher_work2,2,MAX_TERMS) (%o168) array_y_higher_work2 (%i169) array(array_y_set_initial,2,MAX_TERMS) (%o169) array_y_set_initial (%i170) array(array_given_rad_poles,2,3) (%o170) array_given_rad_poles (%i171) array(array_given_ord_poles,2,3) (%o171) array_given_ord_poles (%i172) array(array_rad_test_poles,2,3) (%o172) array_rad_test_poles (%i173) array(array_ord_test_poles,2,3) (%o173) array_ord_test_poles (%i174) array(array_fact_2,MAX_TERMS,MAX_TERMS) (%o174) array_fact_2 (%i175) omniout_str(iolevel,str):=if glob_iolevel >= iolevel then printf(true,"~a~%",string(str)) (%o175) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%i176) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel then printf(true,"~a",string(str)) (%o176) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%i177) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel then printf(true,"~a = ~a~%",string(label), string(str)) (%o177) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%i178) omniout_float(iolevel,prelabel,prelen,value,vallen,postlabel):=if glob_iolevel >= iolevel then (if vallen = 4 then printf(true,"~a = ~g ~s ~%",prelabel, value,postlabel) else printf(true,"~a = ~g ~s ~%",prelabel, value,postlabel)) (%o178) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (if vallen = 4 then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel) else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)) (%i179) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if glob_iolevel >= iolevel then (printf(true,"~a = ~d ~a~%",prelabel,value, postlabel),newline()) (%o179) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%i180) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen, postlabel):=if glob_iolevel >= iolevel then (sprint(prelabel,"[",elemnt,"]=",value, postlabel),newline()) (%o180) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%i181) logitem_time(fd,secs_in):=( block(mode_declare( [[days_int,hours_int,minutes_int,sec_int, years_int],fixnum,[secs,secs_temp],convfloat]), secs:secs_in,printf(fd,"~%"), if secs >= 0 then (years_int :truncate(secs/glob_sec_in_year), sec_temp :mod(truncate(secs), truncate(glob_sec_in_year)), days_int :truncate(sec_temp/glob_sec_in_day), sec_temp :mod(sec_temp, truncate(glob_sec_in_day)), hours_int :truncate(sec_temp/glob_sec_in_hour), sec_temp :mod(sec_temp, truncate(glob_sec_in_hour)), minutes_int :truncate(sec_temp/glob_sec_in_minute), sec_int :mod(sec_temp, truncate(glob_sec_in_minute)), if truncate(years_int) > 0.1 then printf(fd, "~d Years ~f Days ~f Hours ~f Minutes ~f Seconds~%", years_int,days_int, hours_int,minutes_int, sec_int) elseif days_int > 0.1 then printf(fd, "~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,hours_int, minutes_int,sec_int) elseif hours_int > 0.1 then printf(fd, "~d Hours ~d Minutes ~d Seconds~%", hours_int,minutes_int, sec_int) elseif minutes_int > 0.1 then printf(fd, "~d Minutes ~d Seconds~%", minutes_int,sec_int) else printf(fd,"~d Seconds~%", sec_int)) else printf(fd," 0.0 Seconds~%"), printf(fd,"~%")),0) (%o181) logitem_time(fd, secs_in) := (block(mode_declare([[days_int, hours_int, minutes_int, sec_int, years_int], fixnum, [secs, secs_temp], convfloat]), secs : secs_in, printf(fd, "~%"), secs if secs >= 0 then (years_int : truncate(----------------), glob_sec_in_year sec_temp : mod(truncate(secs), truncate(glob_sec_in_year)), sec_temp days_int : truncate(---------------), sec_temp : glob_sec_in_day mod(sec_temp, truncate(glob_sec_in_day)), sec_temp hours_int : truncate(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, truncate(glob_sec_in_hour)), sec_temp minutes_int : truncate(------------------), glob_sec_in_minute sec_int : mod(sec_temp, truncate(glob_sec_in_minute)), if truncate(years_int) > 0.1 then printf(fd, "~d Years ~f Days ~f Hours ~f Minutes ~f Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0.1 then printf(fd, "~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0.1 then printf(fd, "~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0.1 then printf(fd, "~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(fd, "~d Seconds~%", sec_int)) else printf(fd, " 0.0 Seconds~%"), printf(fd, "~%")), 0) (%i182) omniout_timestr(secs_in):=( block(mode_declare( [[days_int,hours_int,minutes_int,sec_int, years_int],fixnum,[secs,secs_temp], convfloat]),secs:secs_in, if secs >= 0 then ( years_int:truncate(secs/glob_sec_in_year), sec_temp :mod(truncate(secs), truncate(glob_sec_in_year)), days_int:truncate(sec_temp/glob_sec_in_day), sec_temp :mod(sec_temp,truncate(glob_sec_in_day)), hours_int :truncate(sec_temp/glob_sec_in_hour), sec_temp :mod(sec_temp,truncate(glob_sec_in_hour)), minutes_int :truncate(sec_temp/glob_sec_in_minute), sec_int :mod(sec_temp, truncate(glob_sec_in_minute)), if years_int > 0 then printf(true, "= ~f Years ~f Days ~f Hours ~f Minutes ~f Seconds~%", years_int,days_int, hours_int,minutes_int, sec_int) elseif days_int > 0.1 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,hours_int, minutes_int,sec_int) elseif hours_int > 0.1 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,minutes_int, sec_int) elseif minutes_int > 0.1 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int,sec_int) else printf(true,"= ~d Seconds~%", sec_int)) else printf(true,"= 0.0 Seconds~%")),0) (%o182) omniout_timestr(secs_in) := (block(mode_declare([[days_int, hours_int, minutes_int, sec_int, years_int], fixnum, [secs, secs_temp], convfloat]), secs secs : secs_in, if secs >= 0 then (years_int : truncate(----------------), glob_sec_in_year sec_temp : mod(truncate(secs), truncate(glob_sec_in_year)), sec_temp days_int : truncate(---------------), sec_temp : glob_sec_in_day mod(sec_temp, truncate(glob_sec_in_day)), sec_temp hours_int : truncate(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, truncate(glob_sec_in_hour)), sec_temp minutes_int : truncate(------------------), glob_sec_in_minute sec_int : mod(sec_temp, truncate(glob_sec_in_minute)), if years_int > 0 then printf(true, "= ~f Years ~f Days ~f Hours ~f Minutes ~f Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0.1 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0.1 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0.1 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, "= 0.0 Seconds~%")), 0) (%i183) zero_ats_ar(arr_a):=( block(modedcclare([iii],fixnum),iii:1, while iii <= MAX_TERMS do (arr_a[iii]:0.0,iii:1+iii)),0) (%o183) zero_ats_ar(arr_a) := (block(modedcclare([iii], fixnum), iii : 1, while iii <= MAX_TERMS do (arr_a : 0.0, iii : 1 + iii)), 0) iii (%i184) ats(mmm_ats,arr_a,arr_b,jjj_ats):=block( mode_declare([[iii_ats,lll_ats,ma_ats],fixnum,[ret_ats], convfloat]),ret_ats:0.0, if jjj_ats <= mmm_ats then (ma_ats:1+mmm_ats,iii_ats:jjj_ats, while iii_ats <= mmm_ats do (lll_ats:ma_ats-iii_ats, if lll_ats <= MAX_TERMS and iii_ats <= MAX_TERMS then ret_ats :arr_a[iii_ats]*arr_b[lll_ats]+ret_ats, iii_ats:1+iii_ats)),ret_ats) (%o184) ats(mmm_ats, arr_a, arr_b, jjj_ats) := block(mode_declare([[iii_ats, lll_ats, ma_ats], fixnum, [ret_ats], convfloat]), ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats, if (lll_ats <= MAX_TERMS) and (iii_ats <= MAX_TERMS) then ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%i185) att(mmm_att,arr_aa,arr_bb,jjj_att):=block( mode_declare([[al_att,iii_att,lll_att,ma_att],convfloat,[ret_att], fixnum]),ret_att:0.0, if jjj_att < mmm_att then (ma_att:2+mmm_att,iii_att:jjj_att, while iii_att < mmm_att and iii_att <= MAX_TERMS do (lll_att:ma_att-iii_att,al_att:lll_att-1, if lll_att <= MAX_TERMS and iii_att <= MAX_TERMS then ret_att :arr_aa[iii_att]*arr_bb[lll_att]*al_att +ret_att,iii_att:1+iii_att), ret_att:ret_att/mmm_att),ret_att) (%o185) att(mmm_att, arr_aa, arr_bb, jjj_att) := block(mode_declare([[al_att, iii_att, lll_att, ma_att], convfloat, [ret_att], fixnum]), ret_att : 0.0, if jjj_att < mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att, while (iii_att < mmm_att) and (iii_att <= MAX_TERMS) do (lll_att : ma_att - iii_att, al_att : lll_att - 1, if (lll_att <= MAX_TERMS) and (iii_att <= MAX_TERMS) then ret_att : arr_aa arr_bb al_att + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : -------), ret_att) mmm_att (%i186) logditto(file):=(printf(file,""),printf(file,"ditto"), printf(file,""),0) (%o186) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, ""), 0) (%i187) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n), printf(file,""),0) (%o187) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, ""), 0) (%i188) logitem_str(file,str):=(printf(file,""),printf(file,str), printf(file,""),0) (%o188) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, ""), 0) (%i189) logitem_good_digits(file,rel_error):=( block(mode_declare([[good_digits],fixnum]), printf(file,""), if rel_error # -1.0 then (if rel_error > +1.0E-34 then ( good_digits :3-floor(log10(rel_error)), printf(file,"~d",good_digits)) else (good_digits:16, printf(file,"~d", good_digits))) else printf(file,"Unknown"), printf(file,"")),0) (%o189) logitem_good_digits(file, rel_error) := (block(mode_declare([[good_digits], fixnum]), printf(file, ""), if rel_error # - 1.0 then (if rel_error > + 1.0E-34 then (good_digits : 3 - floor(log10(rel_error)), printf(file, "~d", good_digits)) else (good_digits : 16, printf(file, "~d", good_digits))) else printf(file, "Unknown"), printf(file, "")), 0) (%i190) log_revs(file,revs):=printf(file,revs) (%o190) log_revs(file, revs) := printf(file, revs) (%i191) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x), printf(file,""),0) (%o191) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, ""), 0) (%i192) logitem_pole(file,pole):=(printf(file,""), if pole = 0 then printf(file,"NA") elseif pole = 1 then printf(file,"Real") elseif pole = 2 then printf(file,"Complex") elseif pole = 4 then printf(file,"Yes") else printf(file,"No"), printf(file,""),0) (%o192) logitem_pole(file, pole) := (printf(file, ""), if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real") elseif pole = 2 then printf(file, "Complex") elseif pole = 4 then printf(file, "Yes") else printf(file, "No"), printf(file, ""), 0) (%i193) logstart(file):=(printf(file,""),0) (%o193) logstart(file) := (printf(file, ""), 0) (%i194) logend(file):=(printf(file,"~%"),0) (%o194) logend(file) := (printf(file, "~%"), 0) (%i195) chk_data():=( block(mode_declare([[errflag],boolean]),errflag:false, if glob_max_iter < 2 then (omniout_str(ALWAYS,"Illegal max_iter"), errflag:true),if errflag then quit()),0) (%o195) chk_data() := (block(mode_declare([[errflag], boolean]), errflag : false, if glob_max_iter < 2 then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true), if errflag then quit()), 0) (%i196) comp_expect_sec(t_end2,t_start2,t2,clock_sec2):=block( mode_declare([[ms2,rrr,sec_left,sub1,sub2], convfloat]),ms2:clock_sec2, sub1:t_end2-t_start2,sub2:t2-t_start2, if sub1 = 0.0 then sec_left:0.0 else (if sub2 > 0.0 then (rrr:sub1/sub2, sec_left:rrr*ms2-ms2) else sec_left:0.0),sec_left) (%o196) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) := block(mode_declare([[ms2, rrr, sec_left, sub1, sub2], convfloat]), ms2 : clock_sec2, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0 sub1 then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left) sub2 (%i197) comp_percent(t_end2,t_start2,t2):=block( mode_declare([[rrr,sub1,sub2],convfloat]), sub1:t_end2-t_start2,sub2:t2-t_start2, if sub2 > glob_small_float then rrr:100.0*sub2/sub1 else rrr:0.0,rrr) (%o197) comp_percent(t_end2, t_start2, t2) := block(mode_declare([[rrr, sub1, sub2], convfloat]), sub1 : t_end2 - t_start2, 100.0 sub2 sub2 : t2 - t_start2, if sub2 > glob_small_float then rrr : ---------- sub1 else rrr : 0.0, rrr) (%i198) comp_rad_from_ratio(term1,term2,last_no):=( if term2 > 0.0 then ret:abs(term1*glob_h/term2) else ret:glob_larger_float,ret) (%o198) comp_rad_from_ratio(term1, term2, last_no) := !term1 glob_h! (if term2 > 0.0 then ret : !------------! else ret : glob_larger_float, ret) ! term2 ! (%i199) comp_ord_from_ratio(term1,term2,last_no):=( if term2 > 0.0 then ret :abs(term2)*convfloat(last_no) *log(abs(term1*glob_h/term2)) /log(convfloat(last_no)) +1.0 else ret:glob_larger_float,ret) (%o199) comp_ord_from_ratio(term1, term2, last_no) := !term1 glob_h! mabs(term2) convfloat(last_no) log(!------------!) ! term2 ! (if term2 > 0.0 then ret : -------------------------------------------------- log(convfloat(last_no)) + 1.0 else ret : glob_larger_float, ret) (%i200) comp_rad_from_three_terms(term1,term2,term3,last_no):=( temp:abs( term1*term3 -term1*term3*convfloat(last_no) -2.0*term2*term2 +term2*term2*convfloat(last_no)), if temp > 0.0 then ret:abs(term2*glob_h*term1/temp) else ret:glob_larger_float,ret) (%o200) comp_rad_from_three_terms(term1, term2, term3, last_no) := (temp : mabs(term1 term3 - term1 term3 convfloat(last_no) - 2.0 term2 term2 + term2 term2 convfloat(last_no)), if temp > 0.0 !term2 glob_h term1! then ret : !------------------! else ret : glob_larger_float, ret) ! temp ! (%i201) comp_ord_from_three_terms(term1,term2,term3,last_no):=( ret:abs( (-term1*term3*convfloat(last_no*last_no) +term2*term2*convfloat(last_no*last_no) +4.0*term2*term2 -4.0*term2*term2*convfloat(last_no) -3.0*term1*term3 +4.0*term1*term3*convfloat(last_no)) /(term1*term3 -term1*term3*convfloat(last_no) -2.0*term2*term2 +term2*term2*convfloat(last_no))),ret) (%o201) comp_ord_from_three_terms(term1, term2, term3, last_no) := (ret : mabs((- term1 term3 convfloat(last_no last_no) + term2 term2 convfloat(last_no last_no) + 4.0 term2 term2 - 4.0 term2 term2 convfloat(last_no) - 3.0 term1 term3 + 4.0 term1 term3 convfloat(last_no))/(term1 term3 - term1 term3 convfloat(last_no) - 2.0 term2 term2 + term2 term2 convfloat(last_no))), ret) (%i202) comp_rad_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):= ( if term5 # 0.0 and term4 # 0.0 and term3 # 0.0 and term2 # 0.0 and term1 # 0.0 then (rm0:term6/term5,rm1:term5/term4, rm2:term4/term3,rm3:term3/term2, rm4:term2/term1, nr1 :convfloat(last_no-3)*rm2 -2.0*convfloat(last_no-2)*rm1 +convfloat(last_no-1)*rm0, nr2 :convfloat(last_no-4)*rm3 -2.0*convfloat(last_no-3)*rm2 +convfloat(last_no-2)*rm1, dr1:(-1.0)/rm3+2.0/rm2+(-1.0)/rm1, dr2:(-1.0)/rm4+2.0/rm3+(-1.0)/rm2, ds1:5.0/rm3-8.0/rm2+3.0/rm1, ds2:5.0/rm4-8.0/rm3+3.0/rm2, if abs(nr1*dr2-nr2*dr1) = 0.0 or abs(dr1) = 0.0 then (rad_c:glob_larger_float, ord_no:glob_larger_float) else (if abs(nr1*dr2-nr2*dr1) # 0.0 then ( rcs :(dr1*dr2-ds2*dr1+ds1*dr2) /(nr1*dr2-nr2*dr1), ord_no :(rcs*nr1-ds1)/(2.0*dr1) -convfloat(last_no)/2.0, if abs(rcs) # 0.0 then (if rcs > 0.0 then rad_c :sqrt(rcs) *abs(glob_h) else ( rad_c :glob_larger_float, ord_no :glob_larger_float)) else ( rad_c:glob_larger_float, ord_no:glob_larger_float)) else (rad_c:glob_larger_float, ord_no:glob_larger_float))) else (rad_c:glob_larger_float, ord_no:glob_larger_float), glob_six_term_ord_save:ord_no,rad_c) (%o202) comp_rad_from_six_terms(term1, term2, term3, term4, term5, term6, last_no) := (if (term5 # 0.0) and (term4 # 0.0) and (term3 # 0.0) term6 term5 and (term2 # 0.0) and (term1 # 0.0) then (rm0 : -----, rm1 : -----, term5 term4 term4 term3 term2 rm2 : -----, rm3 : -----, rm4 : -----, term3 term2 term1 nr1 : convfloat(last_no - 3) rm2 - 2.0 convfloat(last_no - 2) rm1 + convfloat(last_no - 1) rm0, nr2 : convfloat(last_no - 4) rm3 - 2.0 convfloat(last_no - 3) rm2 + convfloat(last_no - 2) rm1, - 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0 dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---, rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1 5.0 8.0 3.0 ds2 : --- - --- + ---, if (mabs(nr1 dr2 - nr2 dr1) = 0.0) or (mabs(dr1) = 0.0) rm4 rm3 rm2 then (rad_c : glob_larger_float, ord_no : glob_larger_float) else (if mabs(nr1 dr2 - nr2 dr1) # 0.0 dr1 dr2 - ds2 dr1 + ds1 dr2 then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(last_no) ord_no : ------------- - ------------------, 2.0 dr1 2.0 if mabs(rcs) # 0.0 then (if rcs > 0.0 then rad_c : sqrt(rcs) mabs(glob_h) else (rad_c : glob_larger_float, ord_no : glob_larger_float)) else (rad_c : glob_larger_float, ord_no : glob_larger_float)) else (rad_c : glob_larger_float, ord_no : glob_larger_float))) else (rad_c : glob_larger_float, ord_no : glob_larger_float), glob_six_term_ord_save : ord_no, rad_c) (%i203) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save (%o203) comp_ord_from_six_terms(term1, term2, term3, term4, term5, term6, last_no) := glob_six_term_ord_save (%i204) factorial_2(nnn):=nnn! (%o204) factorial_2(nnn) := nnn! (%i205) factorial_1(nnn):=block(mode_declare([[ret],convfloat]), if nnn <= MAX_TERMS then (if array_fact_1[nnn] = 0 then (ret:factorial_2(nnn), array_fact_1[nnn]:ret) else ret:array_fact_1[nnn]) else ret:factorial_2(nnn),ret) (%o205) factorial_1(nnn) := block(mode_declare([[ret], convfloat]), if nnn <= MAX_TERMS then (if array_fact_1 = 0 nnn then (ret : factorial_2(nnn), array_fact_1 : ret) nnn else ret : array_fact_1 ) else ret : factorial_2(nnn), ret) nnn (%i206) factorial_3(mmm,nnn):=block(mode_declare([[ret],convfloat]), if nnn <= MAX_TERMS and mmm <= MAX_TERMS then (if array_fact_2[mmm,nnn] = 0 then (ret:factorial_1(mmm)/factorial_1(nnn), array_fact_2[mmm,nnn]:ret) else ret:array_fact_2[mmm,nnn]) else ret:factorial_2(mmm)/factorial_2(nnn),ret) (%o206) factorial_3(mmm, nnn) := block(mode_declare([[ret], convfloat]), if (nnn <= MAX_TERMS) and (mmm <= MAX_TERMS) factorial_1(mmm) then (if array_fact_2 = 0 then (ret : ----------------, mmm, nnn factorial_1(nnn) array_fact_2 : ret) else ret : array_fact_2 ) mmm, nnn mmm, nnn factorial_2(mmm) else ret : ----------------, ret) factorial_2(nnn) (%i207) log10(x):=log(x)/glob_log_10 log(x) (%o207) log10(x) := ----------- glob_log_10 (%i208) expt(x,y):=(if x <= 0.0 and y < 0.0 then print("expt error x = ",x,"y = ",y),x^y) (%o208) expt(x, y) := (if (x <= 0.0) and (y < 0.0) y then print("expt error x = ", x, "y = ", y), x ) (%i209) estimated_needed_step_error(x_start,x_end,estimated_h, estimated_answer):=block( [desired_abs_gbl_error,range, estimated_steps,step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32,""), desired_abs_gbl_error :expt(10.0,-glob_desired_digits_correct) *abs(estimated_answer), omniout_float(ALWAYS,"estimated_h",32, estimated_h,32,""), omniout_float(ALWAYS,"estimated_answer", 32,estimated_answer,32,""), omniout_float(ALWAYS, "desired_abs_gbl_error",32, desired_abs_gbl_error,32, ""),range:x_end-x_start, omniout_float(ALWAYS,"range",32,range,32, ""), estimated_steps:range/estimated_h, omniout_float(ALWAYS,"estimated_steps",32, estimated_steps,32,""), step_error :abs( desired_abs_gbl_error/estimated_steps), omniout_float(ALWAYS,"step_error",32, step_error,32,""), step_error) (%o209) estimated_needed_step_error(x_start, x_end, estimated_h, estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps, step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""), desired_abs_gbl_error : expt(10.0, - glob_desired_digits_correct) mabs(estimated_answer), omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, ""), omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, ""), omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""), range : x_end - x_start, omniout_float(ALWAYS, "range", 32, range, 32, range ""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps", estimated_h !desired_abs_gbl_error! 32, estimated_steps, 32, ""), step_error : !---------------------!, ! estimated_steps ! omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error) (%i210) exact_soln_y(x):=block(x+cos(x)+2.0) (%o210) exact_soln_y(x) := block(x + cos(x) + 2.0) (%i211) display_poles():=( block(mode_declare([[rad_given],convfloat]), if glob_type_given_pole = 4 then (rad_given :sqrt( array_given_rad_poles[1,2] *array_given_rad_poles[1,2] +(array_x[1] -array_given_rad_poles[1,1]) *(array_x[1] -array_given_rad_poles[1,1])), if rad_given < glob_least_given_sing then glob_least_given_sing :rad_given, omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4,rad_given,4," "), omniout_float(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles[ 1,1],4," ")) elseif glob_type_given_pole = 3 then omniout_str(ALWAYS, "NO POLE (given) for Equation 1") else omniout_str(ALWAYS, "NO INFO (given) for Equation 1"), if array_rad_test_poles[1,1] < glob_large_float then (omniout_float(ALWAYS, "Radius of convergence (ratio test) for eq 1 ", 4, array_rad_test_poles[1,1], 4," "), if array_rad_test_poles[1,1] < glob_least_ratio_sing then glob_least_ratio_sing :array_rad_test_poles[1,1], omniout_float(ALWAYS, "Order of pole (ratio test) ", 4, array_ord_test_poles[1,1], 4," ")) else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1"), if array_rad_test_poles[1,2] > 0.0 and array_rad_test_poles[1,2] < glob_large_float then (omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 1 ", 4, array_rad_test_poles[1,2], 4," "), if array_rad_test_poles[1,2] < glob_least_3_sing then glob_least_3_sing :array_rad_test_poles[1,2], omniout_float(ALWAYS, "Order of pole (three term test) ", 4, array_ord_test_poles[1,2], 4," ")) else omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 1"), if array_rad_test_poles[1,3] > 0.0 and array_rad_test_poles[1,3] < glob_large_float then (omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 1 ", 4, array_rad_test_poles[1,3], 4," "), if array_rad_test_poles[1,3] < glob_least_6_sing then glob_least_6_sing :array_rad_test_poles[1,3], omniout_float(ALWAYS, "Order of pole (six term test) ", 4, array_ord_test_poles[1,3], 4," ")) else omniout_str(ALWAYS, "NO COMPLEX POLE (six term test) for Equation 1")), 0) (%o211) display_poles() := (block(mode_declare([[rad_given], convfloat]), if glob_type_given_pole = 4 then (rad_given : sqrt(array_given_rad_poles array_given_rad_poles 1, 2 1, 2 + (array_x - array_given_rad_poles ) 1 1, 1 (array_x - array_given_rad_poles )), 1 1, 1 if rad_given < glob_least_given_sing then glob_least_given_sing : rad_given, omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4, rad_given, 4, " "), omniout_float(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles , 4, " ")) elseif glob_type_given_pole = 3 1, 1 then omniout_str(ALWAYS, "NO POLE (given) for Equation 1") else omniout_str(ALWAYS, "NO INFO (given) for Equation 1"), if array_rad_test_poles < glob_large_float then (omniout_float(ALWAYS, "Ra\ 1, 1 dius of convergence (ratio test) for eq 1 ", 4, array_rad_test_poles , 4, " "), if array_rad_test_poles < 1, 1 1, 1 glob_least_ratio_sing then glob_least_ratio_sing : array_rad_test_poles , 1, 1 omniout_float(ALWAYS, "Order of pole (ratio test) ", 4, array_ord_test_poles , 4, " ")) else omniout_str(ALWAYS, 1, 1 "NO POLE (ratio test) for Equation 1"), if (array_rad_test_poles > 0.0) and (array_rad_test_poles < glob_large_float) 1, 2 1, 2 then (omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 1 ", 4, array_rad_test_poles , 4, " "), if array_rad_test_poles < 1, 2 1, 2 glob_least_3_sing then glob_least_3_sing : array_rad_test_poles , 1, 2 omniout_float(ALWAYS, "Order of pole (three term test) ", 4, array_ord_test_poles , 4, " ")) else omniout_str(ALWAYS, 1, 2 "NO REAL POLE (three term test) for Equation 1"), if (array_rad_test_poles > 0.0) and (array_rad_test_poles < 1, 3 1, 3 glob_large_float) then (omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 1 ", 4, array_rad_test_poles , 4, " "), if array_rad_test_poles < 1, 3 1, 3 glob_least_6_sing then glob_least_6_sing : array_rad_test_poles , 1, 3 omniout_float(ALWAYS, "Order of pole (six term test) ", 4, array_ord_test_poles , 4, " ")) else omniout_str(ALWAYS, 1, 3 "NO COMPLEX POLE (six term test) for Equation 1")), 0) (%i212) my_check_sign(x0,xf):=block([ret],if xf > x0 then ret:1.0 else ret:-1.0,ret) (%o212) my_check_sign(x0, xf) := block([ret], if xf > x0 then ret : 1.0 else ret : - 1.0, ret) (%i213) est_size_answer():=block([min_size], min_size:glob_estimated_size_answer, if abs(array_y[1]) < min_size then (min_size:abs(array_y[1]), omniout_float(ALWAYS,"min_size",32,min_size, 32,"")), if min_size < 1.0 then (min_size:1.0, omniout_float(ALWAYS,"min_size",32,min_size, 32,"")),min_size) (%o213) est_size_answer() := block([min_size], min_size : glob_estimated_size_answer, if !array_y ! < min_size then (min_size : !array_y !, ! 1! ! 1! omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), if min_size < 1.0 then (min_size : 1.0, omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size) (%i214) test_suggested_h():=block( [max_estimated_step_error,hn_div_ho,hn_div_ho_2, hn_div_ho_3,no_terms,est_tmp], max_estimated_step_error:0.0,no_terms:MAX_TERMS, hn_div_ho:0.5,hn_div_ho_2:0.25,hn_div_ho_3:0.125, omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""), omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32, ""), omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32, ""), est_tmp:abs(array_y[no_terms]*hn_div_ho_3 +array_y[no_terms-1]*hn_div_ho_2 +array_y[no_terms-2]*hn_div_ho +array_y[no_terms-3]), if est_tmp >= max_estimated_step_error then max_estimated_step_error:est_tmp, omniout_float(ALWAYS,"max_estimated_step_error",32, max_estimated_step_error,32,""), max_estimated_step_error) (%o214) test_suggested_h() := block([max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp], max_estimated_step_error : 0.0, no_terms : MAX_TERMS, hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125, omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""), omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""), omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""), est_tmp : mabs(array_y hn_div_ho_3 + array_y hn_div_ho_2 no_terms no_terms - 1 + array_y hn_div_ho + array_y ), no_terms - 2 no_terms - 3 if est_tmp >= max_estimated_step_error then max_estimated_step_error : est_tmp, omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""), max_estimated_step_error) (%i215) reached_interval():=block(mode_declare([[ret],boolean]), if glob_check_sign*array_x[1] >= glob_check_sign*glob_next_display then ret:true else ret:false,return(ret)) (%o215) reached_interval() := block(mode_declare([[ret], boolean]), if glob_check_sign array_x >= glob_check_sign glob_next_display 1 then ret : true else ret : false, return(ret)) (%i216) display_alot(iter):=( block(mode_declare( [[abserr],convfloat,[analytic_val_y],convfloat, [ind_var],convfloat,[numeric_val],convfloat, [relerr],convfloat,[term_no],fixnum]), if reached_interval() then (if iter >= 0 then (ind_var:array_x[1], omniout_float(ALWAYS, "x[1] ", 33,ind_var,20, " "), analytic_val_y :exact_soln_y(ind_var), omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20," "), term_no:1, numeric_val:array_y[term_no], abserr :abs( numeric_val-analytic_val_y), omniout_float(ALWAYS, "y[1] (numeric) ", 33,numeric_val, 20," "), if abs(analytic_val_y) # 0.0 then ( relerr :abserr*100.0 /abs(analytic_val_y), if relerr > 1.0E-34 then glob_good_digits :3-floor(log10(relerr)) else glob_good_digits :16) else (relerr:-1.0, glob_good_digits:-1), if glob_iter = 1 then array_1st_rel_error[1] :relerr else array_last_rel_error[ 1] :relerr, omniout_float(ALWAYS, "absolute error ", 4,abserr,20," "), omniout_float(ALWAYS, "relative error ", 4,relerr,20,"%"), omniout_int(INFO, "Correct digits ", 32, glob_good_digits,4, " "), omniout_float(ALWAYS, "h ", 4,glob_h,20, " ")))),0) (%o216) display_alot(iter) := (block(mode_declare([[abserr], convfloat, [analytic_val_y], convfloat, [ind_var], convfloat, [numeric_val], convfloat, [relerr], convfloat, [term_no], fixnum]), if reached_interval() then (if iter >= 0 then (ind_var : array_x , omniout_float(ALWAYS, 1 "x[1] ", 33, ind_var, 20, " "), analytic_val_y : exact_soln_y(ind_var), omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_y , term_no abserr : mabs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "), if mabs(analytic_val_y) # 0.0 abserr 100.0 then (relerr : --------------------, if relerr > 1.0E-34 mabs(analytic_val_y) then glob_good_digits : 3 - floor(log10(relerr)) else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1), if glob_iter = 1 then array_1st_rel_error : relerr 1 else array_last_rel_error : relerr, omniout_float(ALWAYS, 1 "absolute error ", 4, abserr, 20, " "), omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"), omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "), omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ")))), 0) (%i217) adjust_for_pole(h_param):=( block(mode_declare( [[hnew],convfloat,[sz2],convfloat,[tmp], convfloat]),hnew:h_param, glob_normmax:glob_small_float, if abs(array_y_higher[1,1]) > glob_small_float then (tmp:abs(array_y_higher[1,1]), if tmp < glob_normmax then glob_normmax:tmp), if glob_look_poles and glob_min_pole_est > glob_small_float and glob_min_pole_est < glob_large_float then (sz2:glob_min_pole_est/10.0, if sz2 < hnew then ( omniout_float(INFO, "glob_h adjusted to ", 20,h_param,12, "due to singularity."), omniout_str(INFO, "Reached Optimal"), return(hnew))), if not glob_reached_optimal_h then (glob_reached_optimal_h:true, glob_curr_iter_when_opt :glob_current_iter, glob_optimal_clock_start_sec :elapsed_time_seconds(), glob_optimal_start:array_x[1]), hnew:sz2),hnew) (%o217) adjust_for_pole(h_param) := (block(mode_declare([[hnew], convfloat, [sz2], convfloat, [tmp], convfloat]), hnew : h_param, glob_normmax : glob_small_float, if !array_y_higher ! > glob_small_float ! 1, 1! then (tmp : !array_y_higher !, if tmp < glob_normmax ! 1, 1! then glob_normmax : tmp), if glob_look_poles and (glob_min_pole_est > glob_small_float) and (glob_min_pole_est < glob_large_float) glob_min_pole_est then (sz2 : -----------------, if sz2 < hnew 10.0 then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."), omniout_str(INFO, "Reached Optimal"), return(hnew))), if not glob_reached_optimal_h then (glob_reached_optimal_h : true, glob_curr_iter_when_opt : glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(), glob_optimal_start : array_x ), hnew : sz2), hnew) 1 (%i218) prog_report(x_start,x_end):=( block(mode_declare([[clock_sec],convfloat,[opt_clock_sec], convfloat,[clock_sec1],convfloat, [expect_sec],convfloat,[left_sec], convfloat,[percent_done],convfloat, [total_clock_sec],convfloat]), clock_sec1:elapsed_time_seconds(), total_clock_sec:clock_sec1-glob_orig_start_sec, glob_clock_sec:clock_sec1-glob_clock_start_sec, left_sec:-clock_sec1+glob_orig_start_sec +glob_max_sec, expect_sec:comp_expect_sec(x_end,x_start, glob_h+array_x[1], clock_sec1 -glob_orig_start_sec), opt_clock_sec:clock_sec1 -glob_optimal_clock_start_sec, glob_optimal_expect_sec :comp_expect_sec(x_end,x_start,glob_h+array_x[1], opt_clock_sec), glob_total_exp_sec :total_clock_sec+glob_optimal_expect_sec, percent_done:comp_percent(x_end,x_start, glob_h+array_x[1]), glob_percent_done:percent_done, omniout_str_noeol(INFO, "Total Elapsed Time "), omniout_timestr(total_clock_sec), omniout_str_noeol(INFO, "Elapsed Time(since restart) "), omniout_timestr(glob_clock_sec), if percent_done < 100.0 then (omniout_str_noeol(INFO, "Expected Time Remaining "), omniout_timestr(expect_sec), omniout_str_noeol(INFO, "Optimized Time Remaining "), omniout_timestr(glob_optimal_expect_sec), omniout_str_noeol(INFO, "Expected Total Time "), omniout_timestr(glob_total_exp_sec)), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(left_sec), omniout_float(INFO, "Percent Done ",33, percent_done,4,"%")),0) (%o218) prog_report(x_start, x_end) := (block(mode_declare([[clock_sec], convfloat, [opt_clock_sec], convfloat, [clock_sec1], convfloat, [expect_sec], convfloat, [left_sec], convfloat, [percent_done], convfloat, [total_clock_sec], convfloat]), clock_sec1 : elapsed_time_seconds(), total_clock_sec : clock_sec1 - glob_orig_start_sec, glob_clock_sec : clock_sec1 - glob_clock_start_sec, left_sec : - clock_sec1 + glob_orig_start_sec + glob_max_sec, expect_sec : comp_expect_sec(x_end, x_start, glob_h + array_x , 1 clock_sec1 - glob_orig_start_sec), opt_clock_sec : clock_sec1 - glob_optimal_clock_start_sec, glob_optimal_expect_sec : comp_expect_sec(x_end, x_start, glob_h + array_x , 1 opt_clock_sec), glob_total_exp_sec : total_clock_sec + glob_optimal_expect_sec, percent_done : comp_percent(x_end, x_start, glob_h + array_x ), 1 glob_percent_done : percent_done, omniout_str_noeol(INFO, "Total Elapsed Time "), omniout_timestr(total_clock_sec), omniout_str_noeol(INFO, "Elapsed Time(since restart) "), omniout_timestr(glob_clock_sec), if percent_done < 100.0 then (omniout_str_noeol(INFO, "Expected Time Remaining "), omniout_timestr(expect_sec), omniout_str_noeol(INFO, "Optimized Time Remaining "), omniout_timestr(glob_optimal_expect_sec), omniout_str_noeol(INFO, "Expected Total Time "), omniout_timestr(glob_total_exp_sec)), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(left_sec), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")), 0) (%i219) check_for_pole():=( block(mode_declare([cnt],fixnum,[dr1,dr2,ds1,ds2,hdrc], convfloat,[m,n],fixnum,[nr1,nr2], convfloat,[ord_no],fixnum, [term1,term2,term3,part1,part2, part3,part4,part5,part6,part7, part8,part9,part10,part11,part12, part13,part14,rad_c,rcs,rm0,rm1, rm2,rm3,rm4],convfloat, [found_sing],fixnum, [h_new,ratio,term,local_test, tmp_rad,tmp_ord,tmp_ratio, prev_tmp_rad],convfloat,[last_no], fixnum), glob_min_pole_est:glob_larger_float, tmp_rad:glob_larger_float, prev_tmp_rad:glob_larger_float, tmp_ratio:glob_larger_float, rad_c:glob_larger_float, array_rad_test_poles[1,1]:glob_larger_float, array_ord_test_poles[1,1]:glob_larger_float, found_sing:1,last_no:-10-1+MAX_TERMS,cnt:0, while last_no < MAX_TERMS-3 and found_sing = 1 do (tmp_rad :comp_rad_from_ratio( array_y_higher[1,last_no-1], array_y_higher[1,last_no],last_no), tmp_ratio:tmp_rad/prev_tmp_rad, if cnt > 0 and tmp_ratio < glob_upper_ratio_limit and tmp_ratio > glob_lower_ratio_limit then rad_c:tmp_rad elseif cnt = 0 then rad_c:tmp_rad elseif cnt > 0 then found_sing:0, prev_tmp_rad:tmp_rad,cnt:1+cnt, last_no:1+last_no), if found_sing = 1 then (if rad_c < array_rad_test_poles[1,1] then ( array_rad_test_poles[1,1]:rad_c, last_no:last_no-1, tmp_ord :comp_ord_from_ratio( array_y_higher[1,last_no-1], array_y_higher[1,last_no], last_no), array_rad_test_poles[1,1]:rad_c, array_ord_test_poles[1,1] :tmp_ord)), glob_min_pole_est:glob_larger_float, tmp_rad:glob_larger_float, prev_tmp_rad:glob_larger_float, tmp_ratio:glob_larger_float, rad_c:glob_larger_float, array_rad_test_poles[1,2]:glob_larger_float, array_ord_test_poles[1,2]:glob_larger_float, found_sing:1,last_no:-10-1+MAX_TERMS,cnt:0, while last_no < MAX_TERMS-4 and found_sing = 1 do (tmp_rad :comp_rad_from_three_terms( array_y_higher[1,last_no-2], array_y_higher[1,last_no-1], array_y_higher[1,last_no],last_no), tmp_ratio:tmp_rad/prev_tmp_rad, if cnt > 0 and tmp_ratio < glob_upper_ratio_limit and tmp_ratio > glob_lower_ratio_limit then rad_c:tmp_rad elseif cnt = 0 then rad_c:tmp_rad elseif cnt > 0 then found_sing:0, prev_tmp_rad:tmp_rad,cnt:1+cnt, last_no:1+last_no), if found_sing = 1 then (if rad_c < array_rad_test_poles[1,2] then ( array_rad_test_poles[1,2]:rad_c, last_no:last_no-1, tmp_ord :comp_ord_from_three_terms( array_y_higher[1,last_no-2], array_y_higher[1,last_no-1], array_y_higher[1,last_no], last_no), array_rad_test_poles[1,2]:rad_c, if rad_c < glob_min_pole_est then glob_min_pole_est:rad_c, array_ord_test_poles[1,2] :tmp_ord)), glob_min_pole_est:glob_larger_float, tmp_rad:glob_larger_float, prev_tmp_rad:glob_larger_float, tmp_ratio:glob_larger_float, rad_c:glob_larger_float, array_rad_test_poles[1,3]:glob_larger_float, array_ord_test_poles[1,3]:glob_larger_float, found_sing:1,last_no:-10-1+MAX_TERMS,cnt:0, while last_no < MAX_TERMS-7 and found_sing = 1 do (tmp_rad :comp_rad_from_six_terms( array_y_higher[1,last_no-5], array_y_higher[1,last_no-4], array_y_higher[1,last_no-3], array_y_higher[1,last_no-2], array_y_higher[1,last_no-1], array_y_higher[1,last_no],last_no), tmp_ratio:tmp_rad/prev_tmp_rad, if cnt > 0 and tmp_ratio < glob_upper_ratio_limit and tmp_ratio > glob_lower_ratio_limit then rad_c:tmp_rad elseif cnt = 0 then rad_c:tmp_rad elseif cnt > 0 then found_sing:0, prev_tmp_rad:tmp_rad,cnt:1+cnt, last_no:1+last_no), if found_sing = 1 then (if rad_c < array_rad_test_poles[1,3] then ( array_rad_test_poles[1,3]:rad_c, last_no:last_no-1, tmp_ord :comp_ord_from_six_terms( array_y_higher[1,last_no-5], array_y_higher[1,last_no-4], array_y_higher[1,last_no-3], array_y_higher[1,last_no-2], array_y_higher[1,last_no-1], array_y_higher[1,last_no], last_no), array_rad_test_poles[1,3]:rad_c, if rad_c < glob_min_pole_est then glob_min_pole_est:rad_c, array_ord_test_poles[1,3] :tmp_ord)), if abs(glob_min_pole_est)*glob_ratio_of_radius < abs(glob_h) then (h_new :glob_check_sign*glob_min_pole_est *glob_ratio_of_radius, term:1,ratio:1.0, while term <= MAX_TERMS do ( array_y[term] :array_y[term]*ratio, array_y_higher[1,term] :array_y_higher[1,term]*ratio, array_x[term] :array_x[term]*ratio, ratio:ratio*h_new/abs(glob_h), term:1+term),glob_h:h_new), if reached_interval() then display_poles()),0) (%o219) check_for_pole() := (block(mode_declare([cnt], fixnum, [dr1, dr2, ds1, ds2, hdrc], convfloat, [m, n], fixnum, [nr1, nr2], convfloat, [ord_no], fixnum, [term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4], convfloat, [found_sing], fixnum, [h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio, prev_tmp_rad], convfloat, [last_no], fixnum), glob_min_pole_est : glob_larger_float, tmp_rad : glob_larger_float, prev_tmp_rad : glob_larger_float, tmp_ratio : glob_larger_float, rad_c : glob_larger_float, array_rad_test_poles : glob_larger_float, 1, 1 array_ord_test_poles : glob_larger_float, found_sing : 1, 1, 1 last_no : - 10 - 1 + MAX_TERMS, cnt : 0, while (last_no < MAX_TERMS - 3) and (found_sing = 1) do (tmp_rad : comp_rad_from_ratio(array_y_higher , array_y_higher , 1, last_no - 1 1, last_no tmp_rad last_no), tmp_ratio : ------------, if (cnt > 0) prev_tmp_rad and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit) then rad_c : tmp_rad elseif cnt = 0 then rad_c : tmp_rad elseif cnt > 0 then found_sing : 0, prev_tmp_rad : tmp_rad, cnt : 1 + cnt, last_no : 1 + last_no), if found_sing = 1 then (if rad_c < array_rad_test_poles 1, 1 then (array_rad_test_poles : rad_c, last_no : last_no - 1, 1, 1 tmp_ord : comp_ord_from_ratio(array_y_higher , 1, last_no - 1 array_y_higher , last_no), array_rad_test_poles : rad_c, 1, last_no 1, 1 array_ord_test_poles : tmp_ord)), glob_min_pole_est : glob_larger_float, 1, 1 tmp_rad : glob_larger_float, prev_tmp_rad : glob_larger_float, tmp_ratio : glob_larger_float, rad_c : glob_larger_float, array_rad_test_poles : glob_larger_float, 1, 2 array_ord_test_poles : glob_larger_float, found_sing : 1, 1, 2 last_no : - 10 - 1 + MAX_TERMS, cnt : 0, while (last_no < MAX_TERMS - 4) and (found_sing = 1) do (tmp_rad : comp_rad_from_three_terms(array_y_higher , 1, last_no - 2 array_y_higher , array_y_higher , last_no), 1, last_no - 1 1, last_no tmp_rad tmp_ratio : ------------, if (cnt > 0) and (tmp_ratio < glob_upper_ratio_limit) prev_tmp_rad and (tmp_ratio > glob_lower_ratio_limit) then rad_c : tmp_rad elseif cnt = 0 then rad_c : tmp_rad elseif cnt > 0 then found_sing : 0, prev_tmp_rad : tmp_rad, cnt : 1 + cnt, last_no : 1 + last_no), if found_sing = 1 then (if rad_c < array_rad_test_poles 1, 2 then (array_rad_test_poles : rad_c, last_no : last_no - 1, 1, 2 tmp_ord : comp_ord_from_three_terms(array_y_higher , 1, last_no - 2 array_y_higher , array_y_higher , last_no), 1, last_no - 1 1, last_no array_rad_test_poles : rad_c, if rad_c < glob_min_pole_est 1, 2 then glob_min_pole_est : rad_c, array_ord_test_poles : tmp_ord)), 1, 2 glob_min_pole_est : glob_larger_float, tmp_rad : glob_larger_float, prev_tmp_rad : glob_larger_float, tmp_ratio : glob_larger_float, rad_c : glob_larger_float, array_rad_test_poles : glob_larger_float, 1, 3 array_ord_test_poles : glob_larger_float, found_sing : 1, 1, 3 last_no : - 10 - 1 + MAX_TERMS, cnt : 0, while (last_no < MAX_TERMS - 7) and (found_sing = 1) do (tmp_rad : comp_rad_from_six_terms(array_y_higher , 1, last_no - 5 array_y_higher , array_y_higher , 1, last_no - 4 1, last_no - 3 array_y_higher , array_y_higher , 1, last_no - 2 1, last_no - 1 tmp_rad array_y_higher , last_no), tmp_ratio : ------------, 1, last_no prev_tmp_rad if (cnt > 0) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit) then rad_c : tmp_rad elseif cnt = 0 then rad_c : tmp_rad elseif cnt > 0 then found_sing : 0, prev_tmp_rad : tmp_rad, cnt : 1 + cnt, last_no : 1 + last_no), if found_sing = 1 then (if rad_c < array_rad_test_poles 1, 3 then (array_rad_test_poles : rad_c, last_no : last_no - 1, 1, 3 tmp_ord : comp_ord_from_six_terms(array_y_higher , 1, last_no - 5 array_y_higher , array_y_higher , 1, last_no - 4 1, last_no - 3 array_y_higher , array_y_higher , 1, last_no - 2 1, last_no - 1 array_y_higher , last_no), array_rad_test_poles : rad_c, 1, last_no 1, 3 if rad_c < glob_min_pole_est then glob_min_pole_est : rad_c, array_ord_test_poles : tmp_ord)), if mabs(glob_min_pole_est) 1, 3 glob_ratio_of_radius < mabs(glob_h) then (h_new : glob_check_sign glob_min_pole_est glob_ratio_of_radius, term : 1, ratio : 1.0, while term <= MAX_TERMS do (array_y : array_y ratio, term term array_y_higher : array_y_higher ratio, 1, term 1, term ratio h_new array_x : array_x ratio, ratio : ------------, term : 1 + term), term term mabs(glob_h) glob_h : h_new), if reached_interval() then display_poles()), 0) (%i220) atomall():=( block(mode_declare([[kkk,order_d],fixnum, [adj2,adj3,temporary,term,temp,temp2], convfloat]), array_tmp1[1]:array_const_1D0[1]+array_const_0D0[1], array_tmp2[1]:sin(array_x[1]), array_tmp2_g[1]:cos(array_x[1]), array_tmp3[1]:array_tmp1[1]-array_tmp2[1], if not array_y_set_initial[1,2] then (if 1 <= MAX_TERMS then ( temporary :array_tmp3[1]*expt(glob_h,1) *factorial_3(0,1), if 2 <= MAX_TERMS then (array_y[2]:temporary, array_y_higher[1,2]:temporary), temporary:temporary*1.0/glob_h, array_y_higher[2,1]:temporary,0)),kkk:2, array_tmp2[2]:array_tmp2_g[1]*array_x[2]/1, array_tmp2_g[2]:(-array_tmp2[1]*array_x[2])/1, array_tmp3[2]:array_tmp1[2]-array_tmp2[2], if not array_y_set_initial[1,3] then (if 2 <= MAX_TERMS then ( temporary :array_tmp3[2]*expt(glob_h,1) *factorial_3(1,2), if 3 <= MAX_TERMS then (array_y[3]:temporary, array_y_higher[1,3]:temporary), temporary:temporary*2.0/glob_h, array_y_higher[2,2]:temporary,0)),kkk:3, array_tmp2[3]:array_tmp2_g[2]*array_x[2]/2, array_tmp2_g[3]:(-array_tmp2[2]*array_x[2])/2, array_tmp3[3]:array_tmp1[3]-array_tmp2[3], if not array_y_set_initial[1,4] then (if 3 <= MAX_TERMS then ( temporary :array_tmp3[3]*expt(glob_h,1) *factorial_3(2,3), if 4 <= MAX_TERMS then (array_y[4]:temporary, array_y_higher[1,4]:temporary), temporary:temporary*3.0/glob_h, array_y_higher[2,3]:temporary,0)),kkk:4, array_tmp2[4]:array_tmp2_g[3]*array_x[2]/3, array_tmp2_g[4]:(-array_tmp2[3]*array_x[2])/3, array_tmp3[4]:array_tmp1[4]-array_tmp2[4], if not array_y_set_initial[1,5] then (if 4 <= MAX_TERMS then ( temporary :array_tmp3[4]*expt(glob_h,1) *factorial_3(3,4), if 5 <= MAX_TERMS then (array_y[5]:temporary, array_y_higher[1,5]:temporary), temporary:temporary*4.0/glob_h, array_y_higher[2,4]:temporary,0)),kkk:5, array_tmp2[5]:array_tmp2_g[4]*array_x[2]/4, array_tmp2_g[5]:(-array_tmp2[4]*array_x[2])/4, array_tmp3[5]:array_tmp1[5]-array_tmp2[5], if not array_y_set_initial[1,6] then (if 5 <= MAX_TERMS then ( temporary :array_tmp3[5]*expt(glob_h,1) *factorial_3(4,5), if 6 <= MAX_TERMS then (array_y[6]:temporary, array_y_higher[1,6]:temporary), temporary:temporary*5.0/glob_h, array_y_higher[2,5]:temporary,0)),kkk:6, while kkk <= MAX_TERMS do (array_tmp2[kkk] :array_tmp2_g[kkk-1]*array_x[2]/(kkk-1), array_tmp2_g[kkk] :(-array_tmp2[kkk-1]*array_x[2])/(kkk-1), array_tmp3[kkk]:-array_tmp2[kkk],order_d:1, if order_d+kkk <= MAX_TERMS then (if not array_y_set_initial[1,order_d+kkk] then ( temporary :array_tmp3[kkk]*expt(glob_h,order_d) *factorial_3(kkk-1, -1+order_d +kkk), array_y[order_d+kkk]:temporary, array_y_higher[1,order_d+kkk]:temporary, term:-1+order_d+kkk,adj2:-1+order_d+kkk, adj3:2, while term >= 1 and term <= MAX_TERMS and adj3 < 1+order_d do ( if adj3 <= 1+order_d then ( if adj2 > 0 then temporary :temporary*adj2/glob_h else temporary:temporary, array_y_higher[adj3,term] :temporary),term:term-1, adj2:adj2-1,adj3:1+adj3))), kkk:1+kkk)),0) (%o220) atomall() := (block(mode_declare([[kkk, order_d], fixnum, [adj2, adj3, temporary, term, temp, temp2], convfloat]), array_tmp1 : array_const_1D0 + array_const_0D0 , 1 1 1 array_tmp2 : sin(array_x ), array_tmp2_g : cos(array_x ), 1 1 1 1 array_tmp3 : array_tmp1 - array_tmp2 , 1 1 1 if not array_y_set_initial then (if 1 <= MAX_TERMS 1, 2 then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(0, 1), 1 if 2 <= MAX_TERMS then (array_y : temporary, array_y_higher : temporary), 2 1, 2 temporary 1.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 2, glob_h 2, 1 array_tmp2_g array_x - array_tmp2 array_x 1 2 1 2 array_tmp2 : ----------------------, array_tmp2_g : ----------------------, 2 1 2 1 array_tmp3 : array_tmp1 - array_tmp2 , 2 2 2 if not array_y_set_initial then (if 2 <= MAX_TERMS 1, 3 then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(1, 2), 2 if 3 <= MAX_TERMS then (array_y : temporary, array_y_higher : temporary), 3 1, 3 temporary 2.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 3, glob_h 2, 2 array_tmp2_g array_x - array_tmp2 array_x 2 2 2 2 array_tmp2 : ----------------------, array_tmp2_g : ----------------------, 3 2 3 2 array_tmp3 : array_tmp1 - array_tmp2 , 3 3 3 if not array_y_set_initial then (if 3 <= MAX_TERMS 1, 4 then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(2, 3), 3 if 4 <= MAX_TERMS then (array_y : temporary, array_y_higher : temporary), 4 1, 4 temporary 3.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 4, glob_h 2, 3 array_tmp2_g array_x - array_tmp2 array_x 3 2 3 2 array_tmp2 : ----------------------, array_tmp2_g : ----------------------, 4 3 4 3 array_tmp3 : array_tmp1 - array_tmp2 , 4 4 4 if not array_y_set_initial then (if 4 <= MAX_TERMS 1, 5 then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(3, 4), 4 if 5 <= MAX_TERMS then (array_y : temporary, array_y_higher : temporary), 5 1, 5 temporary 4.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 5, glob_h 2, 4 array_tmp2_g array_x - array_tmp2 array_x 4 2 4 2 array_tmp2 : ----------------------, array_tmp2_g : ----------------------, 5 4 5 4 array_tmp3 : array_tmp1 - array_tmp2 , 5 5 5 if not array_y_set_initial then (if 5 <= MAX_TERMS 1, 6 then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(4, 5), 5 if 6 <= MAX_TERMS then (array_y : temporary, array_y_higher : temporary), 6 1, 6 temporary 5.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 6, glob_h 2, 5 array_tmp2_g array_x kkk - 1 2 while kkk <= MAX_TERMS do (array_tmp2 : ----------------------------, kkk kkk - 1 - array_tmp2 array_x kkk - 1 2 array_tmp2_g : ----------------------------, kkk kkk - 1 array_tmp3 : - array_tmp2 , order_d : 1, kkk kkk if order_d + kkk <= MAX_TERMS then (if not array_y_set_initial 1, order_d + kkk then (temporary : array_tmp3 expt(glob_h, order_d) kkk factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary, order_d + kkk array_y_higher : temporary, term : - 1 + order_d + kkk, 1, order_d + kkk adj2 : - 1 + order_d + kkk, adj3 : 2, while (term >= 1) and (term <= MAX_TERMS) and (adj3 < 1 + order_d) do (if adj3 <= 1 + order_d temporary adj2 then (if adj2 > 0 then temporary : -------------- else temporary : temporary, glob_h array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1, adj3, term adj3 : 1 + adj3))), kkk : 1 + kkk)), 0) (%i221) exact_soln_y(x):=block(x+cos(x)+2.0) (%o221) exact_soln_y(x) := block(x + cos(x) + 2.0) (%i222) main_prog():=block( mode_declare([[d1,d2,d3,d4,est_err_2],convfloat, [niii,done_once,term,ord,order_diff,term_no, html_log_file,iiif,jjjf,rows,r_order, sub_iter,calc_term,iii],fixnum,[temp_sum], convfloat,[current_iter],fixnum, [x_start,x_end],convfloat,[it,opt_iter], fixnum,[tmp],convfloat,[subiter],fixnum, [est_needed_step_err,estimated_step_error, min_value,est_answer,best_h,found_h], convfloat,[repeat_it],fixnum]),Digits:32, max_terms:30,glob_html_log:true,term:1, while term <= MAX_TERMS do (array_y_init[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_norms[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_fact_1[term]:0.0,term:1+term),term:1, while term <= 2 do (array_1st_rel_error[term]:0.0,term:1+term),term:1, while term <= 2 do (array_last_rel_error[term]:0.0,term:1+term),term:1, while term <= 2 do (array_type_pole[term]:0,term:1+term), term:1, while term <= 2 do (array_type_real_pole[term]:0,term:1+term),term:1, while term <= 2 do (array_type_complex_pole[term]:0,term:1+term),term:1, while term <= MAX_TERMS do (array_y[term]:0.0,term:1+term), term:1, while term <= MAX_TERMS do (array_x[term]:0.0,term:1+term), term:1, while term <= MAX_TERMS do (array_tmp0[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp1[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp2_g[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp2[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp3[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_m1[term]:0.0,term:1+term), ord:1, while ord <= 2 do (term:1, while term <= MAX_TERMS do (array_y_higher[ord,term]:0.0,term:1+term), ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= MAX_TERMS do (array_y_higher_work[ord,term]:0.0, term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= MAX_TERMS do (array_y_higher_work2[ord,term]:0.0, term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= MAX_TERMS do (array_y_set_initial[ord,term]:0.0, term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 3 do (array_given_rad_poles[ord,term]:0.0, term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 3 do (array_given_ord_poles[ord,term]:0.0, term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 3 do (array_rad_test_poles[ord,term]:0.0, term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 3 do (array_ord_test_poles[ord,term]:0.0, term:1+term),ord:1+ord),ord:1, while ord <= MAX_TERMS do (term:1, while term <= MAX_TERMS do (array_fact_2[ord,term]:0.0,term:1+term), ord:1+ord),zero_ats_ar(array_y),zero_ats_ar(array_x), zero_ats_ar(array_tmp0),zero_ats_ar(array_tmp1), zero_ats_ar(array_tmp2_g),zero_ats_ar(array_tmp2), zero_ats_ar(array_tmp3),zero_ats_ar(array_m1), zero_ats_ar(array_const_1),array_const_1[1]:1, zero_ats_ar(array_const_0D0),array_const_0D0[1]:0.0, zero_ats_ar(array_const_1D0),array_const_1D0[1]:1.0, zero_ats_ar(array_m1),array_m1[1]:-1.0,iiif:0, while iiif <= MAX_TERMS do (jjjf:0, while jjjf <= MAX_TERMS do (array_fact_1[iiif]:0, array_fact_2[iiif,jjjf]:0,jjjf:1+jjjf), iiif:1+iiif),array_y_set_initial[1,1]:true, array_y_set_initial[1,2]:false, array_y_set_initial[1,3]:false, array_y_set_initial[1,4]:false, array_y_set_initial[1,5]:false, array_y_set_initial[1,6]:false, array_y_set_initial[1,7]:false, array_y_set_initial[1,8]:false, array_y_set_initial[1,9]:false, array_y_set_initial[1,10]:false, array_y_set_initial[1,11]:false, array_y_set_initial[1,12]:false, array_y_set_initial[1,13]:false, array_y_set_initial[1,14]:false, array_y_set_initial[1,15]:false, array_y_set_initial[1,16]:false, array_y_set_initial[1,17]:false, array_y_set_initial[1,18]:false, array_y_set_initial[1,19]:false, array_y_set_initial[1,20]:false, array_y_set_initial[1,21]:false, array_y_set_initial[1,22]:false, array_y_set_initial[1,23]:false, array_y_set_initial[1,24]:false, array_y_set_initial[1,25]:false, array_y_set_initial[1,26]:false, array_y_set_initial[1,27]:false, array_y_set_initial[1,28]:false, array_y_set_initial[1,29]:false, array_y_set_initial[1,30]:false,ALWAYS:1,INFO:2,DEBUGL:3, DEBUGMASSIVE:4,MAX_TERMS:30,glob_iolevel:INFO, glob_orig_start_sec:elapsed_time_seconds(), glob_curr_iter_when_opt:0,glob_display_flag:true, glob_no_eqs:1,glob_iter:-1,opt_iter:-1,glob_max_iter:50000, glob_max_hours:0.0,glob_max_minutes:15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "##############temp/sub_c_sinpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = 1.0 - sin ( x ) ; "), omniout_str(ALWAYS,"!"), omniout_str(ALWAYS,"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS,"Digits:32,"), omniout_str(ALWAYS,"max_terms:30,"),omniout_str(ALWAYS,"!"), omniout_str(ALWAYS,"/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS,"/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS,"x_start:0.1,"), omniout_str(ALWAYS,"x_end:5.0,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS,"glob_look_poles:true,"), omniout_str(ALWAYS,"glob_max_iter:1000000,"), omniout_str(ALWAYS,"/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS,"/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS,"glob_desired_digits_correct:10,"), omniout_str(ALWAYS,"glob_display_interval:0.01,"), omniout_str(ALWAYS,"glob_look_poles:true,"), omniout_str(ALWAYS,"glob_max_iter:1000000000,"), omniout_str(ALWAYS,"glob_max_minutes:10.0,"), omniout_str(ALWAYS,"glob_subiter_method:3,"), omniout_str(ALWAYS,"/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS,"!"), omniout_str(ALWAYS,"/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS,"exact_soln_y (x) := (block("), omniout_str(ALWAYS," (2.0 + cos(x) + x) "), omniout_str(ALWAYS,"));"), omniout_str(ALWAYS,"/* END USER DEF BLOCK */"), omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt:0,glob_warned:false,glob_warned2:false, glob_small_float:0.0,glob_smallish_float:0.0, glob_large_float:1.0E+100,glob_larger_float:1.1E+100, glob_almost_1:0.99,x_start:0.1,x_end:5.0, array_y_init[1+0]:exact_soln_y(x_start), glob_look_poles:true,glob_max_iter:1000000, glob_desired_digits_correct:10,glob_display_interval:0.01, glob_look_poles:true,glob_max_iter:1000000000, glob_max_minutes:10.0,glob_subiter_method:3, glob_last_good_h:glob_h, glob_max_sec:3600.0*glob_max_hours+60.0*glob_max_minutes, omniout_str(ALWAYS,"START of Optimize"), glob_check_sign:my_check_sign(x_start,x_end),found_h:false, glob_h:glob_min_h*glob_check_sign, if abs(glob_max_h) < abs(glob_h) then glob_h:abs(glob_max_h)*glob_check_sign, if abs(glob_display_interval) < abs(glob_h) then glob_h:abs(glob_display_interval), if glob_h > 0.0 then (glob_neg_h:false, glob_display_interval:abs(glob_display_interval)) else (glob_neg_h:true, glob_display_interval :-abs(glob_display_interval)),chk_data(), best_h:glob_h,min_value:glob_larger_float, est_answer:est_size_answer(),opt_iter:1, est_needed_step_err:estimated_needed_step_error( x_start,x_end,glob_h,est_answer), omniout_float(ALWAYS,"est_needed_step_err",32, est_needed_step_err,16,""), estimated_step_error:0.0, while opt_iter <= 100 and not found_h do (omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,""), array_x[1]:x_start,array_x[2]:glob_h, glob_next_display:x_start,order_diff:1,term_no:1, while term_no <= order_diff do (array_y[term_no] :array_y_init[term_no]*expt(glob_h,term_no-1) /factorial_1(term_no-1),term_no:1+term_no), rows:order_diff,r_order:1, while r_order <= rows do (term_no:1, while term_no <= 1-r_order+rows do (it:-1+r_order+term_no, if term_no < MAX_TERMS then array_y_higher[ r_order,term_no] :array_y_init[it] *expt(glob_h,term_no-1) /factorial_1(term_no-1), term_no:1+term_no),r_order:1+r_order), atomall(),estimated_step_error:test_suggested_h(), omniout_float(ALWAYS,"estimated_step_error",32, estimated_step_error,32,""), if estimated_step_error > est_needed_step_err and opt_iter = 1 or glob_check_sign*glob_h >= glob_check_sign*glob_max_h then (found_h:true, glob_h:glob_check_sign*glob_max_h, best_h:glob_h) elseif estimated_step_error > est_needed_step_err and not found_h then (glob_h:glob_h/2.0,best_h:glob_h, found_h:true) else (glob_h:glob_h*2.0,best_h:glob_h), omniout_float(ALWAYS,"best_h",32,best_h,32,""), opt_iter:1+opt_iter), if not found_h and opt_iter = 1 then (omniout_str(ALWAYS,"Beginning glob_h too large."), found_h:false), if opt_iter > 100 then (glob_h:glob_check_sign*glob_max_h,found_h:false), if glob_check_sign*glob_display_interval < glob_check_sign*glob_h then glob_h:glob_check_sign*glob_display_interval, if glob_html_log then html_log_file:openw("entry.html"), if found_h then (omniout_str(ALWAYS,"START of Soultion"), array_x[1]:x_start,array_x[2]:glob_h, glob_next_display:x_start,order_diff:1,term_no:1, while term_no <= order_diff do (array_y[term_no] :array_y_init[term_no] *expt(glob_h,term_no-1) /factorial_1(term_no-1), term_no:1+term_no),rows:order_diff, r_order:1, while r_order <= rows do (term_no:1, while term_no <= 1-r_order+rows do (it:-1+r_order+term_no, if term_no < MAX_TERMS then array_y_higher[ r_order,term_no] :array_y_init[it] *expt(glob_h,term_no-1) /factorial_1(term_no-1), term_no:1+term_no), r_order:1+r_order),current_iter:1, glob_clock_start_sec:elapsed_time_seconds(), glob_clock_sec:elapsed_time_seconds(), glob_current_iter:0,glob_iter:0, omniout_str(DEBUGL," "), glob_reached_optimal_h:true, glob_optimal_clock_start_sec :elapsed_time_seconds(), while glob_current_iter < glob_max_iter and glob_check_sign*array_x[1] < glob_check_sign*x_end and glob_clock_sec-glob_orig_start_sec < glob_max_sec do (if reached_interval() then (omniout_str(INFO," "), omniout_str(INFO, "TOP MAIN SOLVE Loop")), glob_iter:1+glob_iter, glob_clock_sec:elapsed_time_seconds(), glob_current_iter:1+glob_current_iter, atomall(),display_alot(current_iter), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display :glob_display_interval +glob_next_display, array_x[1]:glob_h+array_x[1], array_x[2]:glob_h,order_diff:2,ord:2, calc_term:1,iii:MAX_TERMS, while iii >= calc_term do ( array_y_higher_work[2,iii] :array_y_higher[2,iii] /expt(glob_h,calc_term-1) /factorial_3(iii-calc_term,iii-1), iii:iii-1),temp_sum:0.0,ord:2, calc_term:1,iii:MAX_TERMS, while iii >= calc_term do ( temp_sum :array_y_higher_work[ord,iii] +temp_sum,iii:iii-1), array_y_higher_work2[ord,calc_term] :temp_sum*expt(glob_h,calc_term-1) /factorial_1(calc_term-1),ord:1, calc_term:2,iii:MAX_TERMS, while iii >= calc_term do ( array_y_higher_work[1,iii] :array_y_higher[1,iii] /expt(glob_h,calc_term-1) /factorial_3(iii-calc_term,iii-1), iii:iii-1),temp_sum:0.0,ord:1, calc_term:2,iii:MAX_TERMS, while iii >= calc_term do ( temp_sum :array_y_higher_work[ord,iii] +temp_sum,iii:iii-1), array_y_higher_work2[ord,calc_term] :temp_sum*expt(glob_h,calc_term-1) /factorial_1(calc_term-1),ord:1, calc_term:1,iii:MAX_TERMS, while iii >= calc_term do ( array_y_higher_work[1,iii] :array_y_higher[1,iii] /expt(glob_h,calc_term-1) /factorial_3(iii-calc_term,iii-1), iii:iii-1),temp_sum:0.0,ord:1, calc_term:1,iii:MAX_TERMS, while iii >= calc_term do ( temp_sum :array_y_higher_work[ord,iii] +temp_sum,iii:iii-1), array_y_higher_work2[ord,calc_term] :temp_sum*expt(glob_h,calc_term-1) /factorial_1(calc_term-1), term_no:MAX_TERMS, while term_no >= 1 do ( array_y[term_no] :array_y_higher_work2[1,term_no], ord:1, while ord <= order_diff do ( array_y_higher[ord,term_no] :array_y_higher_work2[ ord,term_no],ord:1+ord), term_no:term_no-1)), omniout_str(ALWAYS,"Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds()-glob_orig_start_sec >= glob_max_sec then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec:elapsed_time_seconds(), omniout_str(INFO, "diff ( y , x , 1 ) = 1.0 - sin ( x ) ; "), omniout_int(INFO, "Iterations ",32, glob_iter,4," "), prog_report(x_start,x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2014-01-09T00:51:30-06:00"), logitem_str(html_log_file,"Maxima"), logitem_str(html_log_file, "sub_c_sin"), logitem_str(html_log_file, "diff ( y , x , 1 ) = 1.0 - sin ( x ) ; "), logitem_float(html_log_file,x_start), logitem_float(html_log_file,x_end), logitem_float(html_log_file,array_x[1]), logitem_float(html_log_file,glob_h), logitem_str(html_log_file,"16"), logitem_good_digits(html_log_file, array_last_rel_error[ 1]), logitem_integer(html_log_file, MAX_TERMS), if glob_least_given_sing < glob_large_float then ( logitem_float(html_log_file, glob_least_given_sing), 0) else ( logitem_str(html_log_file, "NOT GIVEN"),0), if glob_least_ratio_sing < glob_large_float then ( logitem_float(html_log_file, glob_least_ratio_sing), 0) else ( logitem_str(html_log_file,"NONE"),0), if glob_least_3_sing < glob_large_float then ( logitem_float(html_log_file, glob_least_3_sing),0) else ( logitem_str(html_log_file,"NONE"), 0), if glob_least_6_sing < glob_large_float then ( logitem_float(html_log_file, glob_least_6_sing),0) else ( logitem_str(html_log_file,"NONE"), 0), logitem_integer(html_log_file, glob_iter), logitem_time(html_log_file, glob_clock_sec), if glob_percent_done < 100.0 then ( logitem_time(html_log_file, glob_total_exp_sec),0) else ( logitem_str(html_log_file,"Done"), 0), log_revs(html_log_file, " 225 "), logitem_str(html_log_file, "sub_c_sin diffeq.max"), logitem_str(html_log_file, "sub_c_sin maxima results"), logitem_str(html_log_file, "All Tests - Maxima only - to save time"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%o222) main_prog() := block(mode_declare([[d1, d2, d3, d4, est_err_2], convfloat, [niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii], fixnum, [temp_sum], convfloat, [current_iter], fixnum, [x_start, x_end], convfloat, [it, opt_iter], fixnum, [tmp], convfloat, [subiter], fixnum, [est_needed_step_err, estimated_step_error, min_value, est_answer, best_h, found_h], convfloat, [repeat_it], fixnum]), Digits : 32, max_terms : 30, glob_html_log : true, term : 1, while term <= MAX_TERMS do (array_y_init : 0.0, term : 1 + term), term : 1, term while term <= MAX_TERMS do (array_norms : 0.0, term : 1 + term), term term : 1, while term <= MAX_TERMS do (array_fact_1 : 0.0, term term : 1 + term), term : 1, while term <= 2 do (array_1st_rel_error : 0.0, term : 1 + term), term : 1, term while term <= 2 do (array_last_rel_error : 0.0, term : 1 + term), term term : 1, while term <= 2 do (array_type_pole : 0, term : 1 + term), term term : 1, while term <= 2 do (array_type_real_pole : 0, term : 1 + term), term term : 1, while term <= 2 do (array_type_complex_pole : 0, term term : 1 + term), term : 1, while term <= MAX_TERMS do (array_y : 0.0, term term : 1 + term), term : 1, while term <= MAX_TERMS do (array_x : 0.0, term term : 1 + term), term : 1, while term <= MAX_TERMS do (array_tmp0 : 0.0, term term : 1 + term), term : 1, while term <= MAX_TERMS do (array_tmp1 : 0.0, term term : 1 + term), term : 1, while term <= MAX_TERMS do (array_tmp2_g : 0.0, term : 1 + term), term : 1, term while term <= MAX_TERMS do (array_tmp2 : 0.0, term : 1 + term), term : 1, term while term <= MAX_TERMS do (array_tmp3 : 0.0, term : 1 + term), term : 1, term while term <= MAX_TERMS do (array_m1 : 0.0, term : 1 + term), ord : 1, term while ord <= 2 do (term : 1, while term <= MAX_TERMS do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 2 do (term : 1, while term <= MAX_TERMS do (array_y_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= MAX_TERMS do (array_y_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= MAX_TERMS do (array_y_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_given_rad_poles : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_given_ord_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_rad_test_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_ord_test_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= MAX_TERMS do (term : 1, while term <= MAX_TERMS do (array_fact_2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), zero_ats_ar(array_y), zero_ats_ar(array_x), zero_ats_ar(array_tmp0), zero_ats_ar(array_tmp1), zero_ats_ar(array_tmp2_g), zero_ats_ar(array_tmp2), zero_ats_ar(array_tmp3), zero_ats_ar(array_m1), zero_ats_ar(array_const_1), array_const_1 : 1, zero_ats_ar(array_const_0D0), 1 array_const_0D0 : 0.0, zero_ats_ar(array_const_1D0), array_const_1D0 : 1.0, 1 1 zero_ats_ar(array_m1), array_m1 : - 1.0, iiif : 0, 1 while iiif <= MAX_TERMS do (jjjf : 0, while jjjf <= MAX_TERMS do (array_fact_1 : 0, array_fact_2 : 0, iiif iiif, jjjf jjjf : 1 + jjjf), iiif : 1 + iiif), array_y_set_initial : true, 1, 1 array_y_set_initial : false, array_y_set_initial : false, 1, 2 1, 3 array_y_set_initial : false, array_y_set_initial : false, 1, 4 1, 5 array_y_set_initial : false, array_y_set_initial : false, 1, 6 1, 7 array_y_set_initial : false, array_y_set_initial : false, 1, 8 1, 9 array_y_set_initial : false, array_y_set_initial : false, 1, 10 1, 11 array_y_set_initial : false, array_y_set_initial : false, 1, 12 1, 13 array_y_set_initial : false, array_y_set_initial : false, 1, 14 1, 15 array_y_set_initial : false, array_y_set_initial : false, 1, 16 1, 17 array_y_set_initial : false, array_y_set_initial : false, 1, 18 1, 19 array_y_set_initial : false, array_y_set_initial : false, 1, 20 1, 21 array_y_set_initial : false, array_y_set_initial : false, 1, 22 1, 23 array_y_set_initial : false, array_y_set_initial : false, 1, 24 1, 25 array_y_set_initial : false, array_y_set_initial : false, 1, 26 1, 27 array_y_set_initial : false, array_y_set_initial : false, 1, 28 1, 29 array_y_set_initial : false, ALWAYS : 1, INFO : 2, DEBUGL : 3, 1, 30 DEBUGMASSIVE : 4, MAX_TERMS : 30, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1, glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "##############temp/sub_c_sinpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = 1.0 - sin ( x ) ; "), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:0.1,"), omniout_str(ALWAYS, "x_end:5.0,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:1000000,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_desired_digits_correct:10,"), omniout_str(ALWAYS, "glob_display_interval:0.01,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:1000000000,"), omniout_str(ALWAYS, "glob_max_minutes:10.0,"), omniout_str(ALWAYS, "glob_subiter_method:3,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (2.0 + cos(x) + x) "), omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"), omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false, glob_small_float : 0.0, glob_smallish_float : 0.0, glob_large_float : 1.0E+100, glob_larger_float : 1.1E+100, glob_almost_1 : 0.99, x_start : 0.1, x_end : 5.0, array_y_init : exact_soln_y(x_start), glob_look_poles : true, 1 + 0 glob_max_iter : 1000000, glob_desired_digits_correct : 10, glob_display_interval : 0.01, glob_look_poles : true, glob_max_iter : 1000000000, glob_max_minutes : 10.0, glob_subiter_method : 3, glob_last_good_h : glob_h, glob_max_sec : 3600.0 glob_max_hours + 60.0 glob_max_minutes, omniout_str(ALWAYS, "START of Optimize"), glob_check_sign : my_check_sign(x_start, x_end), found_h : false, glob_h : glob_min_h glob_check_sign, if mabs(glob_max_h) < mabs(glob_h) then glob_h : mabs(glob_max_h) glob_check_sign, if mabs(glob_display_interval) < mabs(glob_h) then glob_h : mabs(glob_display_interval), if glob_h > 0.0 then (glob_neg_h : false, glob_display_interval : mabs(glob_display_interval)) else (glob_neg_h : true, glob_display_interval : - mabs(glob_display_interval)), chk_data(), best_h : glob_h, min_value : glob_larger_float, est_answer : est_size_answer(), opt_iter : 1, est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h, est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""), estimated_step_error : 0.0, while (opt_iter <= 100) and (not found_h) do (omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h, 1 2 glob_next_display : x_start, order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : term_no array_y_init expt(glob_h, term_no - 1) term_no ---------------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, if term_no < MAX_TERMS then array_y_higher : r_order, term_no array_y_init expt(glob_h, term_no - 1) it ----------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) r_order : 1 + r_order), atomall(), estimated_step_error : test_suggested_h(), omniout_float(ALWAYS, "estimated_step_error", 32, estimated_step_error, 32, ""), if ((estimated_step_error > est_needed_step_err) and (opt_iter = 1)) or (glob_check_sign glob_h >= glob_check_sign glob_max_h) then (found_h : true, glob_h : glob_check_sign glob_max_h, best_h : glob_h) elseif (estimated_step_error > est_needed_step_err) and (not found_h) glob_h then (glob_h : ------, best_h : glob_h, found_h : true) 2.0 else (glob_h : glob_h 2.0, best_h : glob_h), omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter), if (not found_h) and (opt_iter = 1) then (omniout_str(ALWAYS, "Beginning glob_h too large."), found_h : false), if opt_iter > 100 then (glob_h : glob_check_sign glob_max_h, found_h : false), if glob_check_sign glob_display_interval < glob_check_sign glob_h then glob_h : glob_check_sign glob_display_interval, if glob_html_log then html_log_file : openw("entry.html"), if found_h then (omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, 1 array_x : glob_h, glob_next_display : x_start, order_diff : 1, term_no : 1, 2 while term_no <= order_diff do (array_y : term_no array_y_init expt(glob_h, term_no - 1) term_no ---------------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, if term_no < MAX_TERMS then array_y_higher : r_order, term_no array_y_init expt(glob_h, term_no - 1) it ----------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) r_order : 1 + r_order), current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "), glob_reached_optimal_h : true, glob_optimal_clock_start_sec : elapsed_time_seconds(), while (glob_current_iter < glob_max_iter) and (glob_check_sign array_x < glob_check_sign x_end) 1 and (glob_clock_sec - glob_orig_start_sec < glob_max_sec) do (if reached_interval () then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")), glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 1 + glob_current_iter, atomall(), display_alot(current_iter), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display : glob_display_interval + glob_next_display, array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1, iii : MAX_TERMS, 2 while iii >= calc_term do (array_y_higher_work : 2, iii array_y_higher 2, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : MAX_TERMS, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 2, iii : MAX_TERMS, factorial_1(calc_term - 1) while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : MAX_TERMS, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 1, iii : MAX_TERMS, factorial_1(calc_term - 1) while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : MAX_TERMS, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, term_no : MAX_TERMS, factorial_1(calc_term - 1) while term_no >= 1 do (array_y : array_y_higher_work2 , term_no 1, term_no ord : 1, while ord <= order_diff do (array_y_higher : ord, term_no array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)), ord, term_no omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - glob_orig_start_sec >= glob_max_sec then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y , x , 1 ) = 1.0 - sin ( x ) ; "), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2014-01-09T00:51:30-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "sub_c_sin"), logitem_str(html_log_file, "diff ( y , x , 1 ) = 1.0 - sin ( x ) ; "), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, MAX_TERMS), 1 if glob_least_given_sing < glob_large_float then (logitem_float(html_log_file, glob_least_given_sing), 0) else (logitem_str(html_log_file, "NOT GIVEN"), 0), if glob_least_ratio_sing < glob_large_float then (logitem_float(html_log_file, glob_least_ratio_sing), 0) else (logitem_str(html_log_file, "NONE"), 0), if glob_least_3_sing < glob_large_float then (logitem_float(html_log_file, glob_least_3_sing), 0) else (logitem_str(html_log_file, "NONE"), 0), if glob_least_6_sing < glob_large_float then (logitem_float(html_log_file, glob_least_6_sing), 0) else (logitem_str(html_log_file, "NONE"), 0), logitem_integer(html_log_file, glob_iter), logitem_time(html_log_file, glob_clock_sec), if glob_percent_done < 100.0 then (logitem_time(html_log_file, glob_total_exp_sec), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 225 "), logitem_str(html_log_file, "sub_c_sin diffeq.max"), logitem_str(html_log_file, "sub_c_sin maxima results"), logitem_str(html_log_file, "All Tests - Maxima only - to save time"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%i223) main():=(alias(convfloat,convfloat),compile(all),main_prog()) (%o223) main() := (alias(convfloat, convfloat), compile(all), main_prog()) (%i224) main() warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable secs in translation. warning: encountered undefined variable glob_sec_in_year in translation. warning: encountered undefined variable sec_temp in translation. warning: encountered undefined variable glob_sec_in_day in translation. warning: encountered undefined variable glob_sec_in_hour in translation. warning: encountered undefined variable glob_sec_in_minute in translation. warning: encountered undefined variable years_int in translation. warning: encountered undefined variable days_int in translation. warning: encountered undefined variable hours_int in translation. warning: encountered undefined variable minutes_int in translation. warning: encountered undefined variable sec_int in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob_sec_in_year in translation. warning: encountered undefined variable glob_sec_in_day in translation. warning: encountered undefined variable glob_sec_in_hour in translation. warning: encountered undefined variable glob_sec_in_minute in translation. warning: encountered undefined variable iii in translation. warning: encountered undefined variable fixnum in translation. warning: encountered undefined variable MAX_TERMS in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable iii_ats in translation. warning: encountered undefined variable ma_ats in translation. warning: encountered undefined variable ret_ats in translation. warning: encountered undefined variable lll_ats in translation. warning: encountered undefined variable MAX_TERMS in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable iii_att in translation. warning: encountered undefined variable MAX_TERMS in translation. warning: encountered undefined variable ma_att in translation. warning: encountered undefined variable lll_att in translation. warning: encountered undefined variable ret_att in translation. warning: encountered undefined variable al_att in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable good_digits in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable ALWAYS in translation. warning: encountered undefined variable glob_max_iter in translation. warning: encountered undefined variable errflag in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable sub1 in translation. warning: encountered undefined variable sub2 in translation. warning: encountered undefined variable rrr in translation. warning: encountered undefined variable ms2 in translation. warning: encountered undefined variable sec_left in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob_small_float in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable ret in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable temp in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable rm0 in translation. warning: encountered undefined variable rm1 in translation. warning: encountered undefined variable rm2 in translation. warning: encountered undefined variable rm3 in translation. warning: encountered undefined variable rm4 in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable nr1 in translation. warning: encountered undefined variable dr2 in translation. warning: encountered undefined variable nr2 in translation. warning: encountered undefined variable dr1 in translation. warning: encountered undefined variable ds1 in translation. warning: encountered undefined variable ds2 in translation. warning: encountered undefined variable rcs in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable ord_no in translation. warning: variable glob_six_term_ord_save (declared type convfloat) assigned type any. warning: encountered undefined variable rad_c in translation. warning: encountered undefined variable glob_six_term_ord_save in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable array_fact_1 in translation. warning: encountered undefined variable MAX_TERMS in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable array_fact_2 in translation. warning: encountered undefined variable MAX_TERMS in translation. warning: encountered undefined variable glob_log_10 in translation. warning: encountered undefined variable ALWAYS in translation. warning: encountered undefined variable glob_desired_digits_correct in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable array_x in translation. warning: encountered undefined variable array_given_rad_poles in translation. warning: encountered undefined variable rad_given in translation. warning: variable glob_least_given_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_given_sing in translation. warning: encountered undefined variable ALWAYS in translation. warning: encountered undefined variable array_given_ord_poles in translation. warning: encountered undefined variable glob_type_given_pole in translation. warning: encountered undefined variable array_rad_test_poles in translation. warning: variable glob_least_ratio_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_ratio_sing in translation. warning: encountered undefined variable array_ord_test_poles in translation. warning: encountered undefined variable glob_large_float in translation. warning: variable glob_least_3_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_3_sing in translation. warning: variable glob_least_6_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_6_sing in translation. warning: encountered undefined variable glob_estimated_size_answer in translation. warning: encountered undefined variable array_y in translation. warning: encountered undefined variable ALWAYS in translation. warning: encountered undefined variable MAX_TERMS in translation. warning: encountered undefined variable ALWAYS in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob_check_sign in translation. warning: encountered undefined variable glob_next_display in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable ALWAYS in translation. warning: encountered undefined variable ind_var in translation. warning: encountered undefined variable analytic_val_y in translation. warning: encountered undefined variable term_no in translation. warning: encountered undefined variable numeric_val in translation. warning: encountered undefined variable abserr in translation. warning: encountered undefined variable relerr in translation. warning: variable glob_good_digits (declared type fixnum) assigned type any. warning: encountered undefined variable array_1st_rel_error in translation. warning: encountered undefined variable glob_iter in translation. warning: encountered undefined variable array_last_rel_error in translation. warning: encountered undefined variable INFO in translation. warning: encountered undefined variable glob_good_digits in translation. warning: encountered undefined variable glob_h in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob_small_float in translation. warning: encountered undefined variable array_y_higher in translation. warning: encountered undefined variable tmp in translation. warning: variable glob_normmax (declared type convfloat) assigned type any. warning: encountered undefined variable glob_normmax in translation. warning: encountered undefined variable glob_min_pole_est in translation. warning: encountered undefined variable INFO in translation. warning: encountered undefined variable hnew in translation. warning: encountered undefined variable sz2 in translation. warning: encountered undefined variable glob_look_poles in translation. warning: encountered undefined variable glob_large_float in translation. warning: encountered undefined variable glob_current_iter in translation. warning: variable glob_optimal_clock_start_sec (declared type convfloat) assigned type any. warning: variable glob_optimal_start (declared type convfloat) assigned type any. warning: encountered undefined variable glob_reached_optimal_h in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable clock_sec1 in translation. warning: encountered undefined variable glob_orig_start_sec in translation. warning: encountered undefined variable glob_clock_start_sec in translation. warning: variable glob_clock_sec (declared type convfloat) assigned type any. warning: encountered undefined variable glob_max_sec in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob_optimal_clock_start_sec in translation. warning: encountered undefined variable opt_clock_sec in translation. warning: variable glob_optimal_expect_sec (declared type convfloat) assigned type any. warning: encountered undefined variable glob_optimal_expect_sec in translation. warning: encountered undefined variable total_clock_sec in translation. warning: variable glob_total_exp_sec (declared type convfloat) assigned type any. warning: encountered undefined variable percent_done in translation. warning: variable glob_percent_done (declared type convfloat) assigned type any. warning: encountered undefined variable INFO in translation. warning: encountered undefined variable glob_clock_sec in translation. warning: encountered undefined variable expect_sec in translation. warning: encountered undefined variable glob_total_exp_sec in translation. warning: encountered undefined variable left_sec in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable MAX_TERMS in translation. warning: encountered undefined variable last_no in translation. warning: encountered undefined variable found_sing in translation. warning: variable tmp_rad (declared type convfloat) assigned type any. warning: encountered undefined variable tmp_rad in translation. warning: encountered undefined variable prev_tmp_rad in translation. warning: encountered undefined variable cnt in translation. warning: encountered undefined variable tmp_ratio in translation. warning: encountered undefined variable glob_upper_ratio_limit in translation. warning: encountered undefined variable glob_lower_ratio_limit in translation. warning: variable tmp_ord (declared type convfloat) assigned type any. warning: encountered undefined variable tmp_ord in translation. warning: encountered undefined variable glob_min_pole_est in translation. warning: encountered undefined variable glob_check_sign in translation. warning: encountered undefined variable glob_ratio_of_radius in translation. warning: encountered undefined variable term in translation. warning: encountered undefined variable ratio in translation. warning: encountered undefined variable h_new in translation. warning: encountered undefined variable glob_h in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable array_const_0D0 in translation. warning: encountered undefined variable array_const_1D0 in translation. warning: encountered undefined variable array_tmp1 in translation. warning: encountered undefined variable array_tmp2 in translation. warning: encountered undefined variable array_tmp2_g in translation. warning: encountered undefined variable array_tmp3 in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable temporary in translation. warning: encountered undefined variable MAX_TERMS in translation. warning: encountered undefined variable array_y_set_initial in translation. warning: encountered undefined variable kkk in translation. warning: encountered undefined variable order_d in translation. warning: encountered undefined variable adj3 in translation. warning: encountered undefined variable adj2 in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable MAX_TERMS in translation. warning: encountered undefined variable array_y_init in translation. warning: encountered undefined variable array_norms in translation. warning: encountered undefined variable array_type_pole in translation. warning: encountered undefined variable array_type_real_pole in translation. warning: encountered undefined variable array_type_complex_pole in translation. warning: encountered undefined variable array_tmp0 in translation. warning: encountered undefined variable array_m1 in translation. warning: encountered undefined variable ord in translation. warning: encountered undefined variable array_y_higher_work in translation. warning: encountered undefined variable array_y_higher_work2 in translation. warning: encountered undefined variable array_const_1 in translation. warning: encountered undefined variable iiif in translation. warning: encountered undefined variable jjjf in translation. warning: encountered undefined variable INFO in translation. warning: variable glob_orig_start_sec (declared type convfloat) assigned type any. warning: encountered undefined variable ALWAYS in translation. warning: encountered undefined variable x_start in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob_max_minutes in translation. warning: encountered undefined variable glob_max_hours in translation. warning: encountered undefined variable x_end in translation. warning: variable glob_check_sign (declared type convfloat) assigned type any. warning: encountered undefined variable glob_min_h in translation. warning: encountered undefined variable glob_check_sign in translation. warning: encountered undefined variable glob_max_h in translation. warning: encountered undefined variable glob_display_interval in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable est_answer in translation. warning: encountered undefined variable est_needed_step_err in translation. warning: encountered undefined variable opt_iter in translation. warning: encountered undefined variable found_h in translation. warning: variable glob_next_display (declared type convfloat) assigned type any. warning: encountered undefined variable order_diff in translation. warning: encountered undefined variable r_order in translation. warning: encountered undefined variable rows in translation. warning: encountered undefined variable it in translation. warning: encountered undefined variable estimated_step_error in translation. warning: encountered undefined variable best_h in translation. warning: encountered undefined variable glob_html_log in translation. warning: variable glob_clock_start_sec (declared type convfloat) assigned type any. warning: variable glob_clock_sec (declared type convfloat) assigned type any. warning: encountered undefined variable DEBUGL in translation. warning: variable glob_optimal_clock_start_sec (declared type convfloat) assigned type any. warning: encountered undefined variable glob_current_iter in translation. warning: encountered undefined variable glob_max_iter in translation. warning: encountered undefined variable glob_clock_sec in translation. warning: encountered undefined variable glob_orig_start_sec in translation. warning: encountered undefined variable glob_max_sec in translation. warning: encountered undefined variable glob_iter in translation. warning: encountered undefined variable current_iter in translation. warning: encountered undefined variable glob_look_poles in translation. warning: encountered undefined variable glob_next_display in translation. warning: encountered undefined variable calc_term in translation. warning: encountered undefined variable temp_sum in translation. warning: encountered undefined variable html_log_file in translation. warning: encountered undefined variable glob_least_given_sing in translation. warning: encountered undefined variable glob_large_float in translation. warning: encountered undefined variable glob_least_ratio_sing in translation. warning: encountered undefined variable glob_least_3_sing in translation. warning: encountered undefined variable glob_least_6_sing in translation. warning: encountered undefined variable glob_total_exp_sec in translation. warning: encountered undefined variable glob_percent_done in translation. WARNING: in $ADJUST_FOR_POLE : $GLOB_CURR_ITER_WHEN_OPT is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $ADJUST_FOR_POLE : $GLOB_OPTIMAL_START is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : |$Digits| is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $MAX_TERMS is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : |$debugmassive| is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_CURR_ITER_WHEN_OPT is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_DISPLAY_FLAG is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_NO_EQS is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_UNCHANGED_H_CNT is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_WARNED is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_WARNED2 is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_SMALLISH_FLOAT is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_ALMOST_1 is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_SUBITER_METHOD is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_LAST_GOOD_H is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_NEG_H is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_NEG_H is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $MIN_VALUE is neither declared nor bound, it will be treated as if it were declared SPECIAL. Warning: modedcclare has a function or macro call which has not been translated properly. The function was totaly undefined. Maybe you want to quote it."##############ECHO OF PROBLEM#################" "##############temp/sub_c_sinpostode.ode#################" "diff ( y , x , 1 ) = 1.0 - sin ( x ) ; " "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:0.1," "x_end:5.0," "array_y_init[0 + 1] : exact_soln_y(x_start)," "glob_look_poles:true," "glob_max_iter:1000000," "/* END SECOND INPUT BLOCK */" "/* BEGIN OVERRIDE BLOCK */" "glob_desired_digits_correct:10," "glob_display_interval:0.01," "glob_look_poles:true," "glob_max_iter:1000000000," "glob_max_minutes:10.0," "glob_subiter_method:3," "/* END OVERRIDE BLOCK */" "!" "/* BEGIN USER DEF BLOCK */" "exact_soln_y (x) := (block(" " (2.0 + cos(x) + x) " "));" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Optimize" min_size = 0.0 "" min_size = 1. "" glob_desired_digits_correct = 10. "" estimated_h = 1.000000E-6 "" estimated_answer = 1. "" desired_abs_gbl_error = 1.0000000000E-10 "" range = 4.9 "" estimated_steps = 4900000. "" step_error = 2.040816326530612300000000000000000E-17 "" est_needed_step_err = 2.040816326530612300000000000000000E-17 "" opt_iter = 1 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 2.4672086055323014000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-183 "" estimated_step_error = 2.4672086055323014000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-183 "" best_h = 2.000000E-6 "" opt_iter = 2 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.65571566460656540000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-175 "" estimated_step_error = 1.65571566460656540000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-175 "" best_h = 4.000000E-6 "" opt_iter = 3 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.111131969458435300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-167 "" estimated_step_error = 1.111131969458435300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-167 "" best_h = 8.000000E-6 "" opt_iter = 4 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 7.4566803670241850000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-160 "" estimated_step_error = 7.4566803670241850000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-160 "" best_h = 1.600000E-5 "" opt_iter = 5 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 5.004093412037816000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-152 "" estimated_step_error = 5.004093412037816000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-152 "" best_h = 3.200000E-5 "" opt_iter = 6 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 3.3581901424816235000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-144 "" estimated_step_error = 3.3581901424816235000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-144 "" best_h = 6.400000E-5 "" opt_iter = 7 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 2.25364312158091970000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-136 "" estimated_step_error = 2.25364312158091970000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-136 "" best_h = 1.280000E-4 "" opt_iter = 8 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.512394117654306500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-128 "" estimated_step_error = 1.512394117654306500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-128 "" best_h = 2.560000E-4 "" opt_iter = 9 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.0149502701580553000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-120 "" estimated_step_error = 1.0149502701580553000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-120 "" best_h = 5.120000E-4 "" opt_iter = 10 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 6.81121272440810700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-113 "" estimated_step_error = 6.81121272440810700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-113 "" best_h = 1.024000E-3 "" opt_iter = 11 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 4.570923134360027000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-105 "" estimated_step_error = 4.570923134360027000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-105 "" best_h = 2.048000E-3 "" opt_iter = 12 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 3.0674887502340364000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-97 "" estimated_step_error = 3.0674887502340364000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-97 "" best_h = 4.096000E-3 "" opt_iter = 13 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 2.05854901161817100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-89 "" estimated_step_error = 2.05854901161817100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-89 "" best_h = 8.192000E-3 "" opt_iter = 14 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.3814583197406785000000000000000000000000000000000000000000000000000000000000000000000000000000000E-81 "" estimated_step_error = 1.3814583197406785000000000000000000000000000000000000000000000000000000000000000000000000000000000E-81 "" best_h = 1.638400E-2 "" opt_iter = 15 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 9.27066811845142800000000000000000000000000000000000000000000000000000000000000000000000000E-74 "" estimated_step_error = 9.27066811845142800000000000000000000000000000000000000000000000000000000000000000000000000E-74 "" best_h = 3.276800E-2 "" opt_iter = 16 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 6.22124900214134000000000000000000000000000000000000000000000000000000000000000000E-66 "" estimated_step_error = 6.22124900214134000000000000000000000000000000000000000000000000000000000000000000E-66 "" best_h = 6.553600E-2 "" opt_iter = 17 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 4.1747508757515434000000000000000000000000000000000000000000000000000000000E-58 "" estimated_step_error = 4.1747508757515434000000000000000000000000000000000000000000000000000000000E-58 "" best_h = 0.131072 "" opt_iter = 18 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 2.80127475800900200000000000000000000000000000000000000000000000000E-50 "" estimated_step_error = 2.80127475800900200000000000000000000000000000000000000000000000000E-50 "" best_h = 0.1 "" "START of Soultion" " " "TOP MAIN SOLVE Loop" x[1] = 0.1 " " y[1] (analytic) = 3.095004165278026 " " y[1] (numeric) = 3.095004165278026 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 9.9334665397530600E-2 " " Order of pole (three term test) = 22.00996671107938 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11 " " y[1] (analytic) = 3.1039560979566967 " " y[1] (numeric) = 3.1039560979566967 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.10911481154043474 " " Order of pole (three term test) = 22.0120512753347 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.12 " " y[1] (analytic) = 3.1128086358538662 " " y[1] (numeric) = 3.1128086358538662 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.11885131321356734 " " Order of pole (three term test) = 22.014331012573983 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.13 " " y[1] (analytic) = 3.121561893714788 " " y[1] (numeric) = 3.121561893714788 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1285402759460775 " " Order of pole (three term test) = 22.016805010932735 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.14 " " y[1] (analytic) = 3.130215996212637 " " y[1] (numeric) = 3.1302159962126375 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.418717463546868300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.13817782428205685 " " Order of pole (three term test) = 22.019472280844614 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.15000000000000002 " " y[1] (analytic) = 3.1387710779360423 " " y[1] (numeric) = 3.1387710779360427 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.414850585860762400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.14776010333066988 " " Order of pole (three term test) = 22.0223317554372 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16000000000000003 " " y[1] (analytic) = 3.147227283375627 " " y[1] (numeric) = 3.1472272833756274 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.411049059582837300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.15728328030805885 " " Order of pole (three term test) = 22.025382290958774 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.17000000000000004 " " y[1] (analytic) = 3.1555847669095605 " " y[1] (numeric) = 3.1555847669095614 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.814623866276194700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.16674354607040723 " " Order of pole (three term test) = 22.028622667235826 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.18000000000000005 " " y[1] (analytic) = 3.1638436927881215 " " y[1] (numeric) = 3.163843692788122 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.403638273478394200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.17613711663754492 " " Order of pole (three term test) = 22.032051588161032 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.19000000000000006 " " y[1] (analytic) = 3.1720042351172704 " " y[1] (numeric) = 3.172004235117271 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.400027165580516600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.18546023470649134 " " Order of pole (three term test) = 22.035667682211745 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.20000000000000007 " " y[1] (analytic) = 3.1800665778412416 " " y[1] (numeric) = 3.180066577841242 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.396477711958874800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.19470917115432534 " " Order of pole (three term test) = 22.039469502998557 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.21000000000000008 " " y[1] (analytic) = 3.1880309147241483 " " y[1] (numeric) = 3.188030914724149 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.392989032192269200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.20388022652978527 " " Order of pole (three term test) = 22.04345552984385 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22000000000000008 " " y[1] (analytic) = 3.1958974493306056 " " y[1] (numeric) = 3.195897449330606 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.389560262464238400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.21296973253299992 " " Order of pole (three term test) = 22.04762416839002 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2300000000000001 " " y[1] (analytic) = 3.2036663950053748 " " y[1] (numeric) = 3.203666395005375 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.386190555116515500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.22197405348275998 " " Order of pole (three term test) = 22.051973751237238 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2400000000000001 " " y[1] (analytic) = 3.2113379748520297 " " y[1] (numeric) = 3.21133797485203 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.382879078215133000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23088958777074148 " " Order of pole (three term test) = 22.056502538610356 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2500000000000001 " " y[1] (analytic) = 3.2189124217106446 " " y[1] (numeric) = 3.218912421710645 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.379625015128736800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2397127693021017 " " Order of pole (three term test) = 22.061208719054815 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2600000000000001 " " y[1] (analytic) = 3.2263899781345136 " " y[1] (numeric) = 3.2263899781345136 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2484400689218684 " " Order of pole (three term test) = 22.066090410161177 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.27000000000000013 " " y[1] (analytic) = 3.2337708963658907 " " y[1] (numeric) = 3.2337708963658907 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2570679958265566 " " Order of pole (three term test) = 22.071145659318088 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.28000000000000014 " " y[1] (analytic) = 3.241055438310771 " " y[1] (numeric) = 3.241055438310771 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.26559309896044203 " " Order of pole (three term test) = 22.076372444493295 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.29000000000000015 " " y[1] (analytic) = 3.248243875512697 " " y[1] (numeric) = 3.2482438755126974 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.367167081258541300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.274011968395937 " " Order of pole (three term test) = 22.08176867504241 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.30000000000000016 " " y[1] (analytic) = 3.255336489125606 " " y[1] (numeric) = 3.2553364891256065 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.364188345301737000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.28232123669751796 " " Order of pole (three term test) = 22.087332192545162 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.31000000000000016 " " y[1] (analytic) = 3.262333569885713 " " y[1] (numeric) = 3.2623335698857137 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.361262422547489800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.29051758026865254 " " Order of pole (three term test) = 22.093060771668732 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3200000000000002 " " y[1] (analytic) = 3.2692354180824412 " " y[1] (numeric) = 3.2692354180824412 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2985977206811961 " " Order of pole (three term test) = 22.098952121057852 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3300000000000002 " " y[1] (analytic) = 3.276042343528387 " " y[1] (numeric) = 3.2760423435283874 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.355566147450238400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3065584259867172 " " Order of pole (three term test) = 22.105003884251314 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3400000000000002 " " y[1] (analytic) = 3.2827546655283464 " " y[1] (numeric) = 3.282754665528347 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.352794390983184400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.31439651200923424 " " Order of pole (three term test) = 22.111213640624534 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3500000000000002 " " y[1] (analytic) = 3.289372712847379 " " y[1] (numeric) = 3.2893727128473795 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.35007263882129600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3221088436188457 " " Order of pole (three term test) = 22.117578906357753 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3600000000000002 " " y[1] (analytic) = 3.295896823677935 " " y[1] (numeric) = 3.2958968236779356 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.347400217930661800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3296923359857368 " " Order of pole (three term test) = 22.12409713542955 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3700000000000002 " " y[1] (analytic) = 3.3023273456060345 " " y[1] (numeric) = 3.3023273456060354 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.689552932667034000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3371439558140727 " " Order of pole (three term test) = 22.130765720635207 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3800000000000002 " " y[1] (analytic) = 3.3086646355765104 " " y[1] (numeric) = 3.3086646355765112 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.684401465624414000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3444607225552759 " " Order of pole (three term test) = 22.137581994629546 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.39000000000000024 " " y[1] (analytic) = 3.314909059857313 " " y[1] (numeric) = 3.314909059857314 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.67934475324145400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.35163970960020535 " " Order of pole (three term test) = 22.14454323099386 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.40000000000000024 " " y[1] (analytic) = 3.3210609940028855 " " y[1] (numeric) = 3.321060994002886 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.337190767203587000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3586780454497616 " " Order of pole (three term test) = 22.151646645326416 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.41000000000000025 " " y[1] (analytic) = 3.327120822816605 " " y[1] (numeric) = 3.327120822816606 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.669510567843549300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3655729148634481 " " Order of pole (three term test) = 22.158889396356194 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.42000000000000026 " " y[1] (analytic) = 3.3330889403123085 " " y[1] (numeric) = 3.333088940312309 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.332365315785577800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.37232155998543004 " " Order of pole (three term test) = 22.166268587079344 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.43000000000000027 " " y[1] (analytic) = 3.3389657496748852 " " y[1] (numeric) = 3.3389657496748857 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.330020261194064500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3789212814476387 " " Order of pole (three term test) = 22.173781265917974 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4400000000000003 " " y[1] (analytic) = 3.344751663219964 " " y[1] (numeric) = 3.344751663219964 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3853694394494849 " " Order of pole (three term test) = 22.18142442790071 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4500000000000003 " " y[1] (analytic) = 3.350447102352677 " " y[1] (numeric) = 3.3504471023526774 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.325462531666965000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3916634548137418 " " Order of pole (three term test) = 22.189195015864662 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4600000000000003 " " y[1] (analytic) = 3.3560524975255253 " " y[1] (numeric) = 3.3560524975255257 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.323248698217614800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.39780081001818307 " " Order of pole (three term test) = 22.19708992167827 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4700000000000003 " " y[1] (analytic) = 3.361568288195329 " " y[1] (numeric) = 3.3615682881953295 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.321077460807656700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.40377905020255717 " " Order of pole (three term test) = 22.205105987484455 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4800000000000003 " " y[1] (analytic) = 3.3669949227792846 " " y[1] (numeric) = 3.3669949227792846 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.40959578415049913 " " Order of pole (three term test) = 22.213240006963773 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4900000000000003 " " y[1] (analytic) = 3.3723328586101218 " " y[1] (numeric) = 3.3723328586101218 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.41524868524598557 " " Order of pole (three term test) = 22.221488726616897 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5000000000000003 " " y[1] (analytic) = 3.377582561890373 " " y[1] (numeric) = 3.377582561890373 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.42073549240394825 " " Order of pole (three term test) = 22.229848847065927 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5100000000000003 " " y[1] (analytic) = 3.3827445076457514 " " y[1] (numeric) = 3.382744507645752 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.312807422630715100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.42605401097468165 " " Order of pole (three term test) = 22.238317024374176 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5200000000000004 " " y[1] (analytic) = 3.38781917967765 " " y[1] (numeric) = 3.3878191796776504 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.31084094603985800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4312021136216694 " " Order of pole (three term test) = 22.246889871383612 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5300000000000004 " " y[1] (analytic) = 3.392807070514761 " " y[1] (numeric) = 3.3928070705147615 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.30891383040735300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.43617774117249336 " " Order of pole (three term test) = 22.25556395906974 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5400000000000004 " " y[1] (analytic) = 3.397708681363824 " " y[1] (numeric) = 3.3977086813638246 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.3070255619201800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4409789034424741 " " Order of pole (three term test) = 22.264335817913135 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5500000000000004 " " y[1] (analytic) = 3.402524522059506 " " y[1] (numeric) = 3.4025245220595064 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.305175633477171600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.44560368003071776 " " Order of pole (three term test) = 22.273201939287212 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5600000000000004 " " y[1] (analytic) = 3.4072551110134164 " " y[1] (numeric) = 3.407255111013417 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.303363544498367700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.45005022108825277 " " Order of pole (three term test) = 22.282158776861642 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5700000000000004 " " y[1] (analytic) = 3.411900975162269 " " y[1] (numeric) = 3.4119009751622693 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.301588800738690500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4543167480579418 " " Order of pole (three term test) = 22.29120274802082 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5800000000000004 " " y[1] (analytic) = 3.416462649915187 " " y[1] (numeric) = 3.4164626499151876 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.299850914105813400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4584015543858837 " " Order of pole (three term test) = 22.300330235296865 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5900000000000004 " " y[1] (analytic) = 3.4209406791001635 " " y[1] (numeric) = 3.420940679100164 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.298149402482111600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4623030062040104 " " Order of pole (three term test) = 22.309537587816557 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6000000000000004 " " y[1] (analytic) = 3.4253356149096787 " " y[1] (numeric) = 3.4253356149096787 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4660195429836133 " " Order of pole (three term test) = 22.318821122761666 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6100000000000004 " " y[1] (analytic) = 3.4296480178454796 " " y[1] (numeric) = 3.42964801784548 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.294853604624539600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4695496781595341 " " Order of pole (three term test) = 22.32817712684198 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6200000000000004 " " y[1] (analytic) = 3.433878456662534 " " y[1] (numeric) = 3.4338784566625344 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.293258382481257700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4728919997247698 " " Order of pole (three term test) = 22.337601857780612 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6300000000000004 " " y[1] (analytic) = 3.438027508312152 " " y[1] (numeric) = 3.4380275083121523 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.291697663198982400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.47604517079525815 " " Order of pole (three term test) = 22.347091545810855 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6400000000000005 " " y[1] (analytic) = 3.442095757884293 " " y[1] (numeric) = 3.4420957578842932 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.290170991997692300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4790079301446125 " " Order of pole (three term test) = 22.35664239518402 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6500000000000005 " " y[1] (analytic) = 3.446083798549056 " " y[1] (numeric) = 3.4460837985490564 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.288677919083228700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.48177909270859653 " " Order of pole (three term test) = 22.366250585687705 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6600000000000005 " " y[1] (analytic) = 3.4499922314973652 " " y[1] (numeric) = 3.4499922314973657 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.287217999494796000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.48435755005913284 " " Order of pole (three term test) = 22.37591227417382 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6700000000000005 " " y[1] (analytic) = 3.453821665880849 " " y[1] (numeric) = 3.45382166588085 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.57158158591146500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.48674227084765975 " " Order of pole (three term test) = 22.385623596095773 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6800000000000005 " " y[1] (analytic) = 3.457572718750928 " " y[1] (numeric) = 3.457572718750929 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.56879172745493500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.48893230121765835 " " Order of pole (three term test) = 22.395380667054294 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6900000000000005 " " y[1] (analytic) = 3.4612460149971067 " " y[1] (numeric) = 3.4612460149971076 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.566065560933170600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49092676518617984 " " Order of pole (three term test) = 22.405179584351078 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7000000000000005 " " y[1] (analytic) = 3.464842187284489 " " y[1] (numeric) = 3.4648421872844892 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.281701116084914500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49272486499423024 " " Order of pole (three term test) = 22.41501642854988 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7100000000000005 " " y[1] (analytic) = 3.4683618759905084 " " y[1] (numeric) = 3.468361875990509 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.28040044761257200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49432588142586004 " " Order of pole (three term test) = 22.42488726504416 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7200000000000005 " " y[1] (analytic) = 3.471805729140895 " " y[1] (numeric) = 3.4718057291408955 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.279130356063884200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49572917409584344 " " Order of pole (three term test) = 22.434788145630925 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7300000000000005 " " y[1] (analytic) = 3.4751744023448703 " " y[1] (numeric) = 3.4751744023448707 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.277890426306127000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4969341817058226 " " Order of pole (three term test) = 22.444715110089966 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7400000000000005 " " y[1] (analytic) = 3.4784685587295883 " " y[1] (numeric) = 3.4784685587295883 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4979404222688202 " " Order of pole (three term test) = 22.45466418776785 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7500000000000006 " " y[1] (analytic) = 3.481688868873821 " " y[1] (numeric) = 3.4816888688738215 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.275499410128817000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49874749330202733 " " Order of pole (three term test) = 22.464631399166155 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7600000000000006 " " y[1] (analytic) = 3.4848360107409055 " " y[1] (numeric) = 3.4848360107409055 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4993550719877917 " " Order of pole (three term test) = 22.474612757533215 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7700000000000006 " " y[1] (analytic) = 3.4879106696109434 " " y[1] (numeric) = 3.487910669610944 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.27322415026070100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49976291530273964 " " Order of pole (three term test) = 22.484604270458767 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7800000000000006 " " y[1] (analytic) = 3.4909135380122778 " " y[1] (numeric) = 3.4909135380122778 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4999708601149831 " " Order of pole (three term test) = 22.494601941470865 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7900000000000006 " " y[1] (analytic) = 3.493845315652236 " " y[1] (numeric) = 3.4938453156522367 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.271061451577627800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4999788232493701 " " Order of pole (three term test) = 22.504601771634402 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8000000000000006 " " y[1] (analytic) = 3.4967067093471655 " " y[1] (numeric) = 3.496706709347166 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.270021327962544400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4997868015207525 " " Order of pole (three term test) = 22.51459976115064 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8100000000000006 " " y[1] (analytic) = 3.4994984329517473 " " y[1] (numeric) = 3.499498432951748 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.269008168909175600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49939487173526215 " " Order of pole (three term test) = 22.52459191095709 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8200000000000006 " " y[1] (analytic) = 3.5022212072876138 " " y[1] (numeric) = 3.502221207287614 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.26802158848783600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4988031906595868 " " Order of pole (three term test) = 22.53457422432703 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8300000000000006 " " y[1] (analytic) = 3.504875760071267 " " y[1] (numeric) = 3.504875760071268 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.534122406901137000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4980119949582683 " " Order of pole (three term test) = 22.544542708468235 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8400000000000006 " " y[1] (analytic) = 3.5074628258413085 " " y[1] (numeric) = 3.507462825841309 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.266126633127016300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4970216010990379 " " Order of pole (three term test) = 22.554493376119932 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8500000000000006 " " y[1] (analytic) = 3.5099831458849824 " " y[1] (numeric) = 3.509983145884983 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.265217499322473800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49583240522623423 " " Order of pole (three term test) = 22.564422247147764 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8600000000000007 " " y[1] (analytic) = 3.5124374681640522 " " y[1] (numeric) = 3.5124374681640527 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.264333426218083300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4944448830023508 " " Order of pole (three term test) = 22.574325350135688 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8700000000000007 " " y[1] (analytic) = 3.514826547240001 " " y[1] (numeric) = 3.514826547240002 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.526948080546287000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49285958941777663 " " Order of pole (three term test) = 22.584198723974538 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8800000000000007 " " y[1] (analytic) = 3.5171511441985803 " " y[1] (numeric) = 3.517151144198581 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.525277940258965000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49107715856880907 " " Order of pole (three term test) = 22.594038419446434 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8900000000000007 " " y[1] (analytic) = 3.519412026573697 " " y[1] (numeric) = 3.519412026573698 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.523655693035765600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4890983034040223 " " Order of pole (three term test) = 22.603840500804395 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9000000000000007 " " y[1] (analytic) = 3.5216099682706647 " " y[1] (numeric) = 3.5216099682706656 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.522080604333016300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.48692381543909746 " " Order of pole (three term test) = 22.613601047346545 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9100000000000007 " " y[1] (analytic) = 3.523745749488812 " " y[1] (numeric) = 3.5237457494888127 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.52055194342262870000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.48455456444022804 " " Order of pole (three term test) = 22.623316154984416 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9200000000000007 " " y[1] (analytic) = 3.525820156643463 " " y[1] (numeric) = 3.525820156643464 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.5190689832168300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.48199149807622393 " " Order of pole (three term test) = 22.632981937804487 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9300000000000007 " " y[1] (analytic) = 3.5278339822872984 " " y[1] (numeric) = 3.5278339822872993 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.517631000096744500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4792356415394569 " " Order of pole (three term test) = 22.64259452962251 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9400000000000007 " " y[1] (analytic) = 3.5297880250310985 " " y[1] (numeric) = 3.5297880250310993 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.516237273744788000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.47628809713579756 " " Order of pole (three term test) = 22.652150085529918 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9500000000000007 " " y[1] (analytic) = 3.5316830894638835 " " y[1] (numeric) = 3.5316830894638844 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.51488708698082100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4731500438437071 " " Order of pole (three term test) = 22.661644783431754 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9600000000000007 " " y[1] (analytic) = 3.5335199860724567 " " y[1] (numeric) = 3.5335199860724575 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.51357972560201800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4698227368426621 " " Order of pole (three term test) = 22.67107482557545 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9700000000000008 " " y[1] (analytic) = 3.535299531160354 " " y[1] (numeric) = 3.535299531160355 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.512314478226425600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4663075070111001 " " Order of pole (three term test) = 22.68043644006989 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9800000000000008 " " y[1] (analytic) = 3.5370225467662175 " " y[1] (numeric) = 3.537022546766218 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.255545318070077400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4626057603940838 " " Order of pole (three term test) = 22.689725882394082 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9900000000000008 " " y[1] (analytic) = 3.5386898605815875 " " y[1] (numeric) = 3.5386898605815884 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.509907493148191000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4587189776409047 " " Order of pole (three term test) = 22.698939436894964 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0000000000000007 " " y[1] (analytic) = 3.54030230586814 " " y[1] (numeric) = 3.5403023058681407 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.254382172714385300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.45464871341284047 " " Order of pole (three term test) = 22.70807341827357 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0100000000000007 " " y[1] (analytic) = 3.5418607213743556 " " y[1] (numeric) = 3.5418607213743565 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.507660491391326000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4503965957613134 " " Order of pole (three term test) = 22.71712417305915 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0200000000000007 " " y[1] (analytic) = 3.5433659512516495 " " y[1] (numeric) = 3.5433659512516504 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.506595231537932000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4459643254766893 " " Order of pole (three term test) = 22.72608808107045 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0300000000000007 " " y[1] (analytic) = 3.5448188449699556 " " y[1] (numeric) = 3.544818844969956 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.25278393416413500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.44135367540798665 " " Order of pole (three term test) = 22.7349615568638 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0400000000000007 " " y[1] (analytic) = 3.546220257232778 " " y[1] (numeric) = 3.546220257232779 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.504577706048065600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.43656648975375795 " " Order of pole (three term test) = 22.743741051167184 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0500000000000007 " " y[1] (analytic) = 3.547571047891727 " " y[1] (numeric) = 3.5475710478917275 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.251812025340489600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4316046833244364 " " Order of pole (three term test) = 22.75242305229993 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0600000000000007 " " y[1] (analytic) = 3.5488720818605275 " " y[1] (numeric) = 3.548872081860528 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.251353104891977000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4264702407764377 " " Order of pole (three term test) = 22.76100408757736 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0700000000000007 " " y[1] (analytic) = 3.550124229028534 " " y[1] (numeric) = 3.5501242290285346 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.250911746182990500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.42116521581832234 " " Order of pole (three term test) = 22.76948072469976 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0800000000000007 " " y[1] (analytic) = 3.55132836417374 " " y[1] (numeric) = 3.5513283641737403 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.250487604385142300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4156917303893413 " " Order of pole (three term test) = 22.77784957312531 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0900000000000007 " " y[1] (analytic) = 3.552485366875301 " " y[1] (numeric) = 3.552485366875301 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4100519738106868 " " Order of pole (three term test) = 22.786107285426215 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1000000000000008 " " y[1] (analytic) = 3.553596121425578 " " y[1] (numeric) = 3.553596121425578 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.40424820190979466 " " Order of pole (three term test) = 22.79425055862767 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1100000000000008 " " y[1] (analytic) = 3.554661516741707 " " y[1] (numeric) = 3.554661516741707 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.39828273611804277 " " Order of pole (three term test) = 22.802276135528963 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1200000000000008 " " y[1] (analytic) = 3.5556824462767125 " " y[1] (numeric) = 3.5556824462767125 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.39215796254220964 " " Order of pole (three term test) = 22.810180806006343 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1300000000000008 " " y[1] (analytic) = 3.5566598079301572 " " y[1] (numeric) = 3.5566598079301577 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.248613119702628700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3858763310100625 " " Order of pole (three term test) = 22.817961408297002 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1400000000000008 " " y[1] (analytic) = 3.5575945039583585 " " y[1] (numeric) = 3.5575945039583585 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3794403540904604 " " Order of pole (three term test) = 22.82561483026377 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1500000000000008 " " y[1] (analytic) = 3.5584874408841576 " " y[1] (numeric) = 3.5584874408841576 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3728526060883595 " " Order of pole (three term test) = 22.833138010639914 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1600000000000008 " " y[1] (analytic) = 3.559339529406273 " " y[1] (numeric) = 3.5593395294062735 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.247673075808366000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3661157220151252 " " Order of pole (three term test) = 22.84052794025358 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1700000000000008 " " y[1] (analytic) = 3.5601516843082304 " " y[1] (numeric) = 3.5601516843082304 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.35923239653456274 " " Order of pole (three term test) = 22.847781663231448 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1800000000000008 " " y[1] (analytic) = 3.5609248243668814 " " y[1] (numeric) = 3.560924824366882 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.247117621835838600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.35220538288508735 " " Order of pole (three term test) = 22.85489627818106 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1900000000000008 " " y[1] (analytic) = 3.561659872260533 " " y[1] (numeric) = 3.561659872260533 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.34503749177846765 " " Order of pole (three term test) = 22.86186893935128 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2000000000000008 " " y[1] (analytic) = 3.5623577544766736 " " y[1] (numeric) = 3.5623577544766736 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3377315902755749 " " Order of pole (three term test) = 22.868696857770626 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2100000000000009 " " y[1] (analytic) = 3.5630194012193304 " " y[1] (numeric) = 3.5630194012193304 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.33029060063959975 " " Order of pole (three term test) = 22.875377302362747 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2200000000000009 " " y[1] (analytic) = 3.5636457463160474 " " y[1] (numeric) = 3.563645746316047 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.246165420087403800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3227174991671846 " " Order of pole (three term test) = 22.881907601038883 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2300000000000009 " " y[1] (analytic) = 3.5642377271245027 " " y[1] (numeric) = 3.5642377271245027 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3150153149979452 " " Order of pole (three term test) = 22.88828514176664 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2400000000000009 " " y[1] (analytic) = 3.564796284438776 " " y[1] (numeric) = 3.5647962844387764 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.24576322015544800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.30718712890285527 " " Order of pole (three term test) = 22.89450737361477 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2500000000000009 " " y[1] (analytic) = 3.5653223623952686 " " y[1] (numeric) = 3.565322362395269 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.245579402676264400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2992360720519778 " " Order of pole (three term test) = 22.90057180777347 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.260000000000001 " " y[1] (analytic) = 3.565816908378289 " " y[1] (numeric) = 3.56581690837829 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.490813304556523700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.29116532476204 " " Order of pole (three term test) = 22.906476018549945 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.270000000000001 " " y[1] (analytic) = 3.5662808729253186 " " y[1] (numeric) = 3.566280872925319 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.245244627874161000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.28297811522435073 " " Order of pole (three term test) = 22.91221764433861 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.280000000000001 " " y[1] (analytic) = 3.5667152096319557 " " y[1] (numeric) = 3.5667152096319557 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2746777182135627 " " Order of pole (three term test) = 22.917794388565703 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.290000000000001 " " y[1] (analytic) = 3.5671208750565575 " " y[1] (numeric) = 3.567120875056558 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.244951391906565400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2662674537778101 " " Order of pole (three term test) = 22.923204020607894 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.300000000000001 " " y[1] (analytic) = 3.5674988286245872 " " y[1] (numeric) = 3.5674988286245877 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.244819497309482400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2577506859107314 " " Order of pole (three term test) = 22.928444376684478 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.310000000000001 " " y[1] (analytic) = 3.56785003253267 " " y[1] (numeric) = 3.56785003253267 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24913082120591865 " " Order of pole (three term test) = 22.933513360722902 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.320000000000001 " " y[1] (analytic) = 3.5681754516523734 " " y[1] (numeric) = 3.568175451652373 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.244583445705874600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24041130749432332 " " Order of pole (three term test) = 22.93840894519714 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.330000000000001 " " y[1] (analytic) = 3.568476053433723 " " y[1] (numeric) = 3.568476053433723 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23159563246517184 " " Order of pole (three term test) = 22.94312917193868 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.340000000000001 " " y[1] (analytic) = 3.568752807808459 " " y[1] (numeric) = 3.5687528078084596 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.244382095835811200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.22268732227093482 " " Order of pole (three term test) = 22.947672152919743 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.350000000000001 " " y[1] (analytic) = 3.5690066870930415 " " y[1] (numeric) = 3.569006687093042 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.24429357741487900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.21368994011691422 " " Order of pole (three term test) = 22.952036071008536 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.360000000000001 " " y[1] (analytic) = 3.5692386658914197 " " y[1] (numeric) = 3.5692386658914197 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.20460708483600784 " " Order of pole (three term test) = 22.956219180695985 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.370000000000001 " " y[1] (analytic) = 3.569449720997573 " " y[1] (numeric) = 3.5694497209975733 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.244139137855542200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.19544238944922526 " " Order of pole (three term test) = 22.96021980879399 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.380000000000001 " " y[1] (analytic) = 3.5696408312978347 " " y[1] (numeric) = 3.5696408312978347 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1861995197125269 " " Order of pole (three term test) = 22.964036355104668 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.390000000000001 " " y[1] (analytic) = 3.5698129776729997 " " y[1] (numeric) = 3.5698129776729997 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1768821726505705 " " Order of pole (three term test) = 22.967667293060373 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.400000000000001 " " y[1] (analytic) = 3.569967142900241 " " y[1] (numeric) = 3.569967142900241 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.16749407507795155 " " Order of pole (three term test) = 22.97111117033433 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.410000000000001 " " y[1] (analytic) = 3.5701043115548314 " " y[1] (numeric) = 3.5701043115548314 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1580389821085259 " " Order of pole (three term test) = 22.97436660942156 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.420000000000001 " " y[1] (analytic) = 3.570225469911686 " " y[1] (numeric) = 3.570225469911686 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.14852067565341515 " " Order of pole (three term test) = 22.97743230818981 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.430000000000001 " " y[1] (analytic) = 3.5703316058467367 " " y[1] (numeric) = 3.570331605846737 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.243831830978464000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.13894296290829242 " " Order of pole (three term test) = 22.980307040400476 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.440000000000001 " " y[1] (analytic) = 3.5704237087381454 " " y[1] (numeric) = 3.570423708738146 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.24379974500844900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.12930967483055433 " " Order of pole (three term test) = 22.982989656198992 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.450000000000001 " " y[1] (analytic) = 3.5705027693673665 " " y[1] (numeric) = 3.570502769367367 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.243772203903787500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.11962466460699014 " " Order of pole (three term test) = 22.985479082574802 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.460000000000001 " " y[1] (analytic) = 3.5705697798200697 " " y[1] (numeric) = 3.57056977982007 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.243748861484066700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.10989180611255746 " " Order of pole (three term test) = 22.987774323790543 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.470000000000001 " " y[1] (analytic) = 3.570625733386932 " " y[1] (numeric) = 3.5706257333869322 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.243729371290952700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.10011499236088425 " " Order of pole (three term test) = 22.989874461780346 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.480000000000001 " " y[1] (analytic) = 3.5706716244643095 " " y[1] (numeric) = 3.57067162446431 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.24371338660044700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 9.02981339471153400E-2 " " Order of pole (three term test) = 22.991778656517 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.490000000000001 " " y[1] (analytic) = 3.5707084484548006 " " y[1] (numeric) = 3.570708448454801 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.243700560437072800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 8.04451574837267700E-2 " " Order of pole (three term test) = 22.99348614634802 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.500000000000001 " " y[1] (analytic) = 3.5707372016677033 " " y[1] (numeric) = 3.5707372016677033 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 7.0560004029932500E-2 " " Order of pole (three term test) = 22.99499624830023 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.5100000000000011 " " y[1] (analytic) = 3.570758881219386 " " y[1] (numeric) = 3.5707588812193864 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.24368299463112900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.06466275153138200E-2 " " Order of pole (three term test) = 22.996308358352973 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.5200000000000011 " " y[1] (analytic) = 3.5707744849335796 " " y[1] (numeric) = 3.5707744849335796 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 5.070899315829984000E-2 " " Order of pole (three term test) = 22.99742195167973 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.5300000000000011 " " y[1] (analytic) = 3.570785011241591 " " y[1] (numeric) = 3.5707850112415915 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.243673893701175700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 4.07510758801334470E-2 " " Order of pole (three term test) = 22.998336582858023 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.5400000000000011 " " y[1] (analytic) = 3.570791459082466 " " y[1] (numeric) = 3.5707914590824665 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.24367164797737500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.07768587149554600E-2 " " Order of pole (three term test) = 22.999051886047567 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.5500000000000012 " " y[1] (analytic) = 3.5707948278030925 " " y[1] (numeric) = 3.570794827803093 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.243670474686123400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.079033121664413700E-2 " " Order of pole (three term test) = 22.999567575136634 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.5600000000000012 " " y[1] (analytic) = 3.5707961170582676 " " y[1] (numeric) = 3.570796117058268 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.243670025652198500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.079548786304687400E-2 " " Order of pole (three term test) = 22.99988344385646 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.5700000000000012 " " y[1] (analytic) = 3.570796326710733 " " y[1] (numeric) = 3.570796326710734 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.48733990526499100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 7.9632645824230410000E-4 " " Order of pole (three term test) = 22.999999365863776 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.5800000000000012 " " y[1] (analytic) = 3.570796456731192 " " y[1] (numeric) = 3.5707964567311925 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.243669907347769700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 9.203153466528015000E-3 " " Order of pole (three term test) = 22.999915294791297 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.5900000000000012 " " y[1] (analytic) = 3.570797507098307 " " y[1] (numeric) = 3.570797507098308 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.48733908303267100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.91989522526188100E-2 " " Order of pole (three term test) = 22.99963126426636 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6000000000000012 " " y[1] (analytic) = 3.570800477698711 " " y[1] (numeric) = 3.570800477698712 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.487337013779424300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.918707171379117400E-2 " " Order of pole (three term test) = 22.99914738789738 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6100000000000012 " " y[1] (analytic) = 3.5708063682270126 " " y[1] (numeric) = 3.570806368227013 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.243666455290218100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.916351673543377000E-2 " " Order of pole (three term test) = 22.998463859228444 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6200000000000012 " " y[1] (analytic) = 3.5708161780858294 " " y[1] (numeric) = 3.5708161780858303 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.487326077301021700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 4.91242968725554730E-2 " " Order of pole (three term test) = 22.997580951661917 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6300000000000012 " " y[1] (analytic) = 3.5708309062858516 " " y[1] (numeric) = 3.5708309062858525 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.48731581811010820000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 5.906542794591003000E-2 " " Order of pole (three term test) = 22.99649901834904 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6400000000000012 " " y[1] (analytic) = 3.570851551345938 " " y[1] (numeric) = 3.570851551345939 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.487301437567041600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.89829336356147400E-2 " " Order of pole (three term test) = 22.995218492048735 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6500000000000012 " " y[1] (analytic) = 3.570879111193266 " " y[1] (numeric) = 3.570879111193267 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 3.73092336106833230000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 7.88728470716254600E-2 " " Order of pole (three term test) = 22.99373988495443 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6600000000000013 " " y[1] (analytic) = 3.5709145830635407 " " y[1] (numeric) = 3.570914583063542 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 3.730886299742336000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 8.8731212420431400E-2 " " Order of pole (three term test) = 22.99206378848926 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6700000000000013 " " y[1] (analytic) = 3.5709589634012717 " " y[1] (numeric) = 3.570958963401273 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 3.73083993180707900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 9.85540864673362200E-2 " " Order of pole (three term test) = 22.990190873069448 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6800000000000013 " " y[1] (analytic) = 3.5710132477601286 " " y[1] (numeric) = 3.57101324776013 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 3.730783217860743600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.10833754019369103 " " Order of pole (three term test) = 22.988121887836215 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6900000000000013 " " y[1] (analytic) = 3.5710784307033876 " " y[1] (numeric) = 3.571078430703389 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 3.730715119823828600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.11807766034844973 " " Order of pole (three term test) = 22.98585766035603 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7000000000000013 " " y[1] (analytic) = 3.5711555057044753 " " y[1] (numeric) = 3.5711555057044766 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 3.730634601103358600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.12777055101341683 " " Order of pole (three term test) = 22.983399096289727 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7100000000000013 " " y[1] (analytic) = 3.5712454650476224 " " y[1] (numeric) = 3.5712454650476237 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 3.730540626762607300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1374123351615633 " " Order of pole (three term test) = 22.98074717903015 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7200000000000013 " " y[1] (analytic) = 3.5713492997286362 " " y[1] (numeric) = 3.5713492997286376 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 3.730432163696277000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.14699915620778514 " " Order of pole (three term test) = 22.97790296930883 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7300000000000013 " " y[1] (analytic) = 3.5714679993558023 " " y[1] (numeric) = 3.5714679993558036 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 3.730308180811065500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.15652717955148637 " " Order of pole (three term test) = 22.974867604771752 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7400000000000013 " " y[1] (analytic) = 3.5716025520509227 " " y[1] (numeric) = 3.5716025520509245 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 4.97355686561544300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.16599259411036824 " " Order of pole (three term test) = 22.97164229952424 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7500000000000013 " " y[1] (analytic) = 3.571753944350508 " " y[1] (numeric) = 3.5717539443505095 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 3.73000954239150100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.17539161384481136 " " Order of pole (three term test) = 22.968228343645396 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7600000000000013 " " y[1] (analytic) = 3.5719231611071196 " " y[1] (numeric) = 3.5719231611071214 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 4.97311044857322100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1847204792722396 " " Order of pole (three term test) = 22.964627102672058 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7700000000000014 " " y[1] (analytic) = 3.572111185390891 " " y[1] (numeric) = 3.5721111853908925 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 3.7296365101927800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.19397545897086632 " " Order of pole (three term test) = 22.960840017052597 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7800000000000014 " " y[1] (analytic) = 3.572318998391216 " " y[1] (numeric) = 3.572318998391218 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 4.97255939405251300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2031528510722095 " " Order of pole (three term test) = 22.956868601570772 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7900000000000014 " " y[1] (analytic) = 3.5725475793186354 " " y[1] (numeric) = 3.5725475793186368 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 3.72918092753373800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.21224898474179243 " " Order of pole (three term test) = 22.952714444739815 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8000000000000014 " " y[1] (analytic) = 3.572797905306913 " " y[1] (numeric) = 3.5727979053069143 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 3.728919644660792500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.22126022164742734 " " Order of pole (three term test) = 22.94837920816707 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8100000000000014 " " y[1] (analytic) = 3.5730709513153256 " " y[1] (numeric) = 3.573070951315327 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 3.72863468904738870000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23018295741450043 " " Order of pole (three term test) = 22.943864625889375 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8200000000000014 " " y[1] (analytic) = 3.573367690031166 " " y[1] (numeric) = 3.5733676900311675 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 3.72832505668782100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23901362306767268 " " Order of pole (three term test) = 22.939172503679433 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8300000000000014 " " y[1] (analytic) = 3.5736890917724775 " " y[1] (numeric) = 3.573689091772479 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 3.72798974767390900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24774868645842363 " " Order of pole (three term test) = 22.93430471832358 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8400000000000014 " " y[1] (analytic) = 3.5740361243910197 " " y[1] (numeric) = 3.574036124391021 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 3.72762776642945400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2563846536778632 " " Order of pole (three term test) = 22.929263216871053 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8500000000000014 " " y[1] (analytic) = 3.5744097531754875 " " y[1] (numeric) = 3.5744097531754884 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.484825414632645400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2649180704542478 " " Order of pole (three term test) = 22.924050015855205 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8600000000000014 " " y[1] (analytic) = 3.574810940754979 " " y[1] (numeric) = 3.5748109407549804 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 3.7268198280405300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2733455235346447 " " Order of pole (three term test) = 22.91866720048694 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8700000000000014 " " y[1] (analytic) = 3.5752406470027394 " " y[1] (numeric) = 3.5752406470027402 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.48424793571509400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2816636420501862 " " Order of pole (three term test) = 22.913116923820635 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8800000000000014 " " y[1] (analytic) = 3.5756998289401665 " " y[1] (numeric) = 3.575699828940168 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 3.72589337272494270000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.28986909886437257 " " Order of pole (three term test) = 22.90740140589296 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8900000000000015 " " y[1] (analytic) = 3.5761894406411177 " " y[1] (numeric) = 3.5761894406411185 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.483588843495097600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2979586119038832 " " Order of pole (three term test) = 22.901522932834858 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9000000000000015 " " y[1] (analytic) = 3.5767104331364967 " " y[1] (numeric) = 3.5767104331364976 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.483227077796347800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3059289454713606 " " Order of pole (three term test) = 22.895483855957213 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9100000000000015 " " y[1] (analytic) = 3.577263754319155 " " y[1] (numeric) = 3.577263754319156 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.482842979156196800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.31377691153964776 " " Order of pole (three term test) = 22.889286590810215 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9200000000000015 " " y[1] (analytic) = 3.577850348849102 " " y[1] (numeric) = 3.5778503488491027 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.482435912910187800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3214993710269557 " " Order of pole (three term test) = 22.882933616217315 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9300000000000015 " " y[1] (analytic) = 3.57847115805904 " " y[1] (numeric) = 3.578471158059041 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.482005248805393700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.32909323505245364 " " Order of pole (three term test) = 22.87642747328365 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9400000000000015 " " y[1] (analytic) = 3.5791271198602326 " " y[1] (numeric) = 3.5791271198602335 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.481550361180826800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3365554661717818 " " Order of pole (three term test) = 22.869770764379624 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9500000000000015 " " y[1] (analytic) = 3.5798191686487133 " " y[1] (numeric) = 3.5798191686487137 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.240535314574826700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.34388307959198794 " " Order of pole (three term test) = 22.86296615210007 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9600000000000015 " " y[1] (analytic) = 3.580548235211846 " " y[1] (numeric) = 3.5805482352118463 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.24028271839155300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.35107314436540377 " " Order of pole (three term test) = 22.85601635819915 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9700000000000015 " " y[1] (analytic) = 3.5813152466352483 " " y[1] (numeric) = 3.5813152466352487 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.240017086647978300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3581227845619863 " " Order of pole (three term test) = 22.848924162501778 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9800000000000015 " " y[1] (analytic) = 3.582121126210084 " " y[1] (numeric) = 3.582121126210085 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.479476233233424700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3650291804196506 " " Order of pole (three term test) = 22.841692401791665 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9900000000000015 " " y[1] (analytic) = 3.5829667933407343 " " y[1] (numeric) = 3.582966793340735 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.478891016659391400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.37178956947213837 " " Order of pole (three term test) = 22.834323968676674 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.0000000000000013 " " y[1] (analytic) = 3.583853163452858 " " y[1] (numeric) = 3.5838531634528583 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.239138964672887200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3784012476539652 " " Order of pole (three term test) = 22.826821810431806 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.010000000000001 " " y[1] (analytic) = 3.5847811479018477 " " y[1] (numeric) = 3.584781147901848 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.238818191481467500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.38486157038201296 " " Order of pole (three term test) = 22.819188927820328 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.020000000000001 " " y[1] (analytic) = 3.5857516538816996 " " y[1] (numeric) = 3.5857516538817 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.238482897635481100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3911679536133269 " " Order of pole (three term test) = 22.811428373893516 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.0300000000000007 " " y[1] (analytic) = 3.586765584334291 " " y[1] (numeric) = 3.5867655843342914 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.238132795155851400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.397317874878699 " " Order of pole (three term test) = 22.803543252769472 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.0400000000000005 " " y[1] (analytic) = 3.587823837859088 " " y[1] (numeric) = 3.5878238378590885 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.237767599300688400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4033088742916204 " " Order of pole (three term test) = 22.795536718391514 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.0500000000000003 " " y[1] (analytic) = 3.588927308623287 " " y[1] (numeric) = 3.5889273086232873 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.237387028661818400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.40913855553220535 " " Order of pole (three term test) = 22.787411973266632 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.06 " " y[1] (analytic) = 3.590076886272398 " " y[1] (numeric) = 3.590076886272398 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4148045868056855 " " Order of pole (three term test) = 22.779172267184556 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.07 " " y[1] (analytic) = 3.59127345584128 " " y[1] (numeric) = 3.59127345584128 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4203047017750974 " " Order of pole (three term test) = 22.770820895917847 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.0799999999999996 " " y[1] (analytic) = 3.5925178976656404 " " y[1] (numeric) = 3.5925178976656404 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4256367004677872 " " Order of pole (three term test) = 22.762361199903673 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.0899999999999994 " " y[1] (analytic) = 3.593811087294001 " " y[1] (numeric) = 3.5938110872940006 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.235705492200605100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.43079845015536994 " " Order of pole (three term test) = 22.753796562907635 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.099999999999999 " " y[1] (analytic) = 3.5951538954001423 " " y[1] (numeric) = 3.5951538954001423 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.43578788620679354 " " Order of pole (three term test) = 22.745130410670352 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.109999999999999 " " y[1] (analytic) = 3.59654718769604 " " y[1] (numeric) = 3.59654718769604 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4406030129141622 " " Order of pole (three term test) = 22.736366209537156 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.1199999999999988 " " y[1] (analytic) = 3.5979918248452925 " " y[1] (numeric) = 3.5979918248452925 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4452419042909938 " " Order of pole (three term test) = 22.727507465071657 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.1299999999999986 " " y[1] (analytic) = 3.599488662377055 " " y[1] (numeric) = 3.599488662377055 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4497027048425882 " " Order of pole (three term test) = 22.718557720653514 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.1399999999999983 " " y[1] (analytic) = 3.6010385506004883 " " y[1] (numeric) = 3.6010385506004883 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.45398363030820194 " " Order of pole (three term test) = 22.70952055606118 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.149999999999998 " " y[1] (analytic) = 3.6026423345197287 " " y[1] (numeric) = 3.6026423345197287 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.45808296837472673 " " Order of pole (three term test) = 22.70039958603999 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.159999999999998 " " y[1] (analytic) = 3.604300853749387 " " y[1] (numeric) = 3.604300853749387 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.46199907936159323 " " Order of pole (three term test) = 22.691198458856338 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.1699999999999977 " " y[1] (analytic) = 3.6060149424305896 " " y[1] (numeric) = 3.6060149424305896 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4657303968766204 " " Order of pole (three term test) = 22.68192085483843 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.1799999999999975 " " y[1] (analytic) = 3.6077854291475626 " " y[1] (numeric) = 3.607785429147563 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.23091912912068810000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.46927542844255316 " " Order of pole (three term test) = 22.67257048490416 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.1899999999999973 " " y[1] (analytic) = 3.6096131368447777 " " y[1] (numeric) = 3.6096131368447777 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.47263275609403077 " " Order of pole (three term test) = 22.663151089076845 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.199999999999997 " " y[1] (analytic) = 3.6114988827446535 " " y[1] (numeric) = 3.611498882744654 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.229653460428500300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4758010369447572 " " Order of pole (three term test) = 22.65366643498921 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.209999999999997 " " y[1] (analytic) = 3.6134434782658396 " " y[1] (numeric) = 3.6134434782658396 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4787790037246347 " " Order of pole (three term test) = 22.644120316376444 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.2199999999999966 " " y[1] (analytic) = 3.61544772894207 " " y[1] (numeric) = 3.61544772894207 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.48156546528665733 " " Order of pole (three term test) = 22.6345165515587 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.2299999999999964 " " y[1] (analytic) = 3.617512434341614 " " y[1] (numeric) = 3.6175124343416143 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.227609352864288700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4841593070833526 " " Order of pole (three term test) = 22.624858981913864 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.239999999999996 " " y[1] (analytic) = 3.6196383879873197 " " y[1] (numeric) = 3.6196383879873197 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.486559491612586 " " Order of pole (three term test) = 22.615151470341036 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.249999999999996 " " y[1] (analytic) = 3.62182637727726 " " y[1] (numeric) = 3.62182637727726 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4887650588325477 " " Order of pole (three term test) = 22.6053978997154 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.259999999999996 " " y[1] (analytic) = 3.6240771834059964 " " y[1] (numeric) = 3.624077183405997 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.225385628880830600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4907751265457568 " " Order of pole (three term test) = 22.59560217133515 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.2699999999999956 " " y[1] (analytic) = 3.6263915812864584 " " y[1] (numeric) = 3.626391581286459 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.224603576022318100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4925888907519289 " " Order of pole (three term test) = 22.58576820336106 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.2799999999999954 " " y[1] (analytic) = 3.628770339472453 " " y[1] (numeric) = 3.6287703394724535 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.223800814891536800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49420562596956447 " " Order of pole (three term test) = 22.57589992924918 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.289999999999995 " " y[1] (analytic) = 3.631214220081811 " " y[1] (numeric) = 3.6312142200818114 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.222977172192439100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4956246855261329 " " Order of pole (three term test) = 22.56600129617759 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.299999999999995 " " y[1] (analytic) = 3.6337239787201745 " " y[1] (numeric) = 3.633723978720175 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.222132480206915100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49684550181673165 " " Order of pole (three term test) = 22.556076263467535 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.3099999999999947 " " y[1] (analytic) = 3.6363003644054377 " " y[1] (numeric) = 3.636300364405438 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.221266576867817400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4978675865311221 " " Order of pole (three term test) = 22.54612880099976 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.3199999999999945 " " y[1] (analytic) = 3.638944119492846 " " y[1] (numeric) = 3.6389441194928462 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.220379305829941300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49869053084904635 " " Order of pole (three term test) = 22.536162887626634 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.3299999999999943 " " y[1] (analytic) = 3.64165597960076 " " y[1] (numeric) = 3.6416559796007606 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.219470516538876300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49931400560374906 " " Order of pole (three term test) = 22.526182509580618 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.339999999999994 " " y[1] (analytic) = 3.644436673537096 " " y[1] (numeric) = 3.6444366735370965 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.218540064297655400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4997377614136418 " " Order of pole (three term test) = 22.51619165887987 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.349999999999994 " " y[1] (analytic) = 3.6472869232264444 " " y[1] (numeric) = 3.647286923226445 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.217587810331123300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49996162878205047 " " Order of pole (three term test) = 22.506194331731457 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.3599999999999937 " " y[1] (analytic) = 3.6502074436378775 " " y[1] (numeric) = 3.650207443637878 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.216613621847950400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49998551816501247 " " Order of pole (three term test) = 22.496194526932936 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.3699999999999934 " " y[1] (analytic) = 3.653198942713455 " " y[1] (numeric) = 3.6531989427134555 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.215617372100218200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4998094200070929 " " Order of pole (three term test) = 22.486196244272904 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.3799999999999932 " " y[1] (analytic) = 3.6562621212974293 " " y[1] (numeric) = 3.65626212129743 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.214598940440509100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49943340474520753 " " Order of pole (three term test) = 22.47620348293111 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.389999999999993 " " y[1] (analytic) = 3.6593976730661604 " " y[1] (numeric) = 3.6593976730661613 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.427116424752853700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4988576227804472 " " Order of pole (three term test) = 22.466220239878872 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.399999999999993 " " y[1] (analytic) = 3.662606284458752 " " y[1] (numeric) = 3.662606284458753 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.42499015924496880000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4980823044179209 " " Order of pole (three term test) = 22.45625050828028 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.4099999999999926 " " y[1] (analytic) = 3.665888634608405 " " y[1] (numeric) = 3.6658886346084056 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.211409440149293600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4971077597746365 " " Order of pole (three term test) = 22.446298275895067 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.4199999999999924 " " y[1] (analytic) = 3.6692453952745065 " " y[1] (numeric) = 3.669245395274507 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.210301198229994800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49593437865545725 " " Order of pole (three term test) = 22.436367523483476 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.429999999999992 " " y[1] (analytic) = 3.6726772307754536 " " y[1] (numeric) = 3.672677230775454 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.209170264483865500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.494562630397186 " " Order of pole (three term test) = 22.426462223214077 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.439999999999992 " " y[1] (analytic) = 3.676184797922223 " " y[1] (numeric) = 3.6761847979222235 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.208016555917051500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4929930636808364 " " Order of pole (three term test) = 22.416586337074897 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.4499999999999917 " " y[1] (analytic) = 3.6797687459526895 " " y[1] (numeric) = 3.6797687459526904 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.413679991920732500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49122630631216796 " " Order of pole (three term test) = 22.40674381528872 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.4599999999999915 " " y[1] (analytic) = 3.683429716466704 " " y[1] (numeric) = 3.6834297164667045 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.20564051450410490000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4892630649705709 " " Order of pole (three term test) = 22.396938594733026 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.4699999999999913 " " y[1] (analytic) = 3.6871683433619316 " " y[1] (numeric) = 3.6871683433619324 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.40883609585965080000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4871041249264064 " " Order of pole (three term test) = 22.38717459736531 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.479999999999991 " " y[1] (analytic) = 3.6909852527704654 " " y[1] (numeric) = 3.6909852527704663 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.406345078278098200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4847503497269066 " " Order of pole (three term test) = 22.37745572865433 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.489999999999991 " " y[1] (analytic) = 3.6948810629962123 " " y[1] (numeric) = 3.694881062996213 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.40380787515767390000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.48220268085076773 " " Order of pole (three term test) = 22.36778587601798 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.4999999999999907 " " y[1] (analytic) = 3.6988563844530624 " " y[1] (numeric) = 3.6988563844530638 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 3.60183659779260600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4794621373315719 " " Order of pole (three term test) = 22.358168907268393 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.5099999999999905 " " y[1] (analytic) = 3.70291181960385 " " y[1] (numeric) = 3.7029118196038513 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 3.59789186039196200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.47652981535018674 " " Order of pole (three term test) = 22.348608669064845 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.5199999999999902 " " y[1] (analytic) = 3.707047962900106 " " y[1] (numeric) = 3.7070479629001074 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 3.593877508150515300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4734068877963075 " " Order of pole (three term test) = 22.339108985375145 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.52999999999999 " " y[1] (analytic) = 3.7112654007226142 " " y[1] (numeric) = 3.7112654007226156 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 3.58979346853174200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4700946037993176 " " Order of pole (three term test) = 22.329673655946113 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.53999999999999 " " y[1] (analytic) = 3.715564711322773 " " y[1] (numeric) = 3.715564711322775 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 4.78085291849984200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4665942882286527 " " Order of pole (three term test) = 22.320306454783715 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.5499999999999896 " " y[1] (analytic) = 3.719946464764773 " " y[1] (numeric) = 3.719946464764775 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 4.7752215152176300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4629073411638701 " " Order of pole (three term test) = 22.31101112864352 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.5599999999999894 " " y[1] (analytic) = 3.7244112228685875 " " y[1] (numeric) = 3.7244112228685893 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 4.769497064376469500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.45903523733463775 " " Order of pole (three term test) = 22.30179139553205 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.569999999999989 " " y[1] (analytic) = 3.7289595391537933 " " y[1] (numeric) = 3.728959539153795 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 4.763679575357785400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4549795255308598 " " Order of pole (three term test) = 22.29265094321962 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.579999999999989 " " y[1] (analytic) = 3.7335919587842192 " " y[1] (numeric) = 3.733591958784221 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 4.757769084061052600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.45074182798318213 " " Order of pole (three term test) = 22.283593427765286 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.5899999999999888 " " y[1] (analytic) = 3.738309018513429 " " y[1] (numeric) = 3.738309018513431 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 4.75176565287434200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4463238397141223 " " Order of pole (three term test) = 22.27462247205446 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.5999999999999885 " " y[1] (analytic) = 3.743111246631047 " " y[1] (numeric) = 3.743111246631049 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 5.93208671328912600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4417273278600822 " " Order of pole (three term test) = 22.265741664349825 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.6099999999999883 " " y[1] (analytic) = 3.747999162909931 " " y[1] (numeric) = 3.7479991629099327 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 4.739480352554546500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.43695413096451674 " " Order of pole (three term test) = 22.256954556856037 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.619999999999988 " " y[1] (analytic) = 3.7529732785541916 " " y[1] (numeric) = 3.752973278554194 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 5.91649842523186200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.43200615824254324 " " Order of pole (three term test) = 22.24826466429895 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.629999999999988 " " y[1] (analytic) = 3.7580340961480774 " " y[1] (numeric) = 3.7580340961480796 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 5.90853087662571600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4268853888172781 " " Order of pole (three term test) = 22.23967546251972 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.6399999999999877 " " y[1] (analytic) = 3.763182109605712 " " y[1] (numeric) = 3.7631821096057148 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 7.0805376447209790000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.421593870928215 " " Order of pole (three term test) = 22.231190387084528 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.6499999999999875 " " y[1] (analytic) = 3.7684178041217073 " " y[1] (numeric) = 3.76841780412171 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 7.07070021850029400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4161337211119574 " " Order of pole (three term test) = 22.222812831910428 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.6599999999999873 " " y[1] (analytic) = 3.7737416561226413 " " y[1] (numeric) = 3.773741656122644 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 7.06072514205456200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4105071233556311 " " Order of pole (three term test) = 22.214546147907782 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.669999999999987 " " y[1] (analytic) = 3.7791541332194165 " " y[1] (numeric) = 3.779154133219419 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 7.05061282279717300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4047163282233173 " " Order of pole (three term test) = 22.206393641639973 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.679999999999987 " " y[1] (analytic) = 3.7846556941605005 " " y[1] (numeric) = 3.7846556941605036 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 8.21375765765657900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3987636519558602 " " Order of pole (three term test) = 22.198358574000807 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.6899999999999866 " " y[1] (analytic) = 3.7902467887860514 " " y[1] (numeric) = 3.790246788786054 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 7.0299782773611410000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.39265147554439855 " " Order of pole (three term test) = 22.190444158910207 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.6999999999999864 " " y[1] (analytic) = 3.795927857982931 " " y[1] (numeric) = 3.7959278579829343 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 8.18936656662987800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.38638224377800245 " " Order of pole (three term test) = 22.182653562028694 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.709999999999986 " " y[1] (analytic) = 3.801699333640622 " " y[1] (numeric) = 3.801699333640625 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 8.17693403958257100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.37995846426578944 " " Order of pole (three term test) = 22.174989899491134 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.719999999999986 " " y[1] (analytic) = 3.8075616386080338 " " y[1] (numeric) = 3.8075616386080373 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 9.33067935861256500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.37338270643391563 " " Order of pole (three term test) = 22.167456236660367 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.7299999999999858 " " y[1] (analytic) = 3.8135151866512222 " " y[1] (numeric) = 3.813515186651226 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 9.31611257570540900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3666576004978378 " " Order of pole (three term test) = 22.160055586901084 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.7399999999999856 " " y[1] (analytic) = 3.8195603824120106 " " y[1] (numeric) = 3.8195603824120146 " " absolute error = 3.9968028886505635000000000000000E-15 " " relative error = 1.04640390214923790000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.35978583641026407 " " Order of pole (three term test) = 22.1527909103745 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.7499999999999853 " " y[1] (analytic) = 3.8256976213675276 " " y[1] (numeric) = 3.8256976213675316 " " absolute error = 3.9968028886505635000000000000000E-15 " " relative error = 1.04472524601196080000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3527701627852064 " " Order of pole (three term test) = 22.14566511285438 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.759999999999985 " " y[1] (analytic) = 3.831927289790658 " " y[1] (numeric) = 3.8319272897906624 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 1.1589186752923060000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.34561338579857404 " " Order of pole (three term test) = 22.138681044564713 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.769999999999985 " " y[1] (analytic) = 3.838249764711418 " " y[1] (numeric) = 3.838249764711423 " " absolute error = 4.884981308350689000000000000000E-15 " " relative error = 1.2727106383911860000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.33831836806573956 " " Order of pole (three term test) = 22.1318414990397 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.7799999999999847 " " y[1] (analytic) = 3.8446654138792513 " " y[1] (numeric) = 3.844665413879256 " " absolute error = 4.884981308350689000000000000000E-15 " " relative error = 1.27058684761381160000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3308880274965303 " " Order of pole (three term test) = 22.125149212006363 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.7899999999999845 " " y[1] (analytic) = 3.8511745957262535 " " y[1] (numeric) = 3.8511745957262584 " " absolute error = 4.884981308350689000000000000000E-15 " " relative error = 1.26843932595828740000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3233253361281034 " " Order of pole (three term test) = 22.118606860290267 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.7999999999999843 " " y[1] (analytic) = 3.8577776593313313 " " y[1] (numeric) = 3.857777659331336 " " absolute error = 4.884981308350689000000000000000E-15 " " relative error = 1.26626823516765400000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3156333189361729 " " Order of pole (three term test) = 22.112217060744886 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.809999999999984 " " y[1] (analytic) = 3.8644749443852935 " " y[1] (numeric) = 3.8644749443852984 " " absolute error = 4.884981308350689000000000000000E-15 " " relative error = 1.26407374317385360000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.30781505262505593 " " Order of pole (three term test) = 22.10598236920484 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.819999999999984 " " y[1] (analytic) = 3.8712667811568817 " " y[1] (numeric) = 3.871266781156887 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 1.37657020801036670000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.29987366439703433 " " Order of pole (three term test) = 22.099905279463606 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.8299999999999836 " " y[1] (analytic) = 3.8781534904597463 " " y[1] (numeric) = 3.8781534904597517 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 1.37412573569103400000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.29181233070151685 " " Order of pole (three term test) = 22.093988222276067 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.8399999999999834 " " y[1] (analytic) = 3.885135383620362 " " y[1] (numeric) = 3.8851353836203675 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 1.37165632391292840000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.28363427596449786 " " Order of pole (three term test) = 22.0882335643862 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.849999999999983 " " y[1] (analytic) = 3.892212762446898 " " y[1] (numeric) = 3.8922127624469036 " " absolute error = 5.773159728050814000000000000000E-15 " " relative error = 1.48325903037773070000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.27534277129883283 " " Order of pole (three term test) = 22.08264360758043 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.859999999999983 " " y[1] (analytic) = 3.8993859191990357 " " y[1] (numeric) = 3.8993859191990414 " " absolute error = 5.773159728050814000000000000000E-15 " " relative error = 1.48053048548645980000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2669411331958364 " " Order of pole (three term test) = 22.077220587766952 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.869999999999983 " " y[1] (analytic) = 3.906655136558744 " " y[1] (numeric) = 3.9066551365587503 " " absolute error = 6.217248937900877000000000000000E-15 " " relative error = 1.59145067086148450000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.25843272219872915 " " Order of pole (three term test) = 22.071966674081384 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.8799999999999826 " " y[1] (analytic) = 3.9140206876020125 " " y[1] (numeric) = 3.9140206876020187 " " absolute error = 6.217248937900877000000000000000E-15 " " relative error = 1.58845581925372380000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24982094155846624 " " Order of pole (three term test) = 22.066883968019145 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.8899999999999824 " " y[1] (analytic) = 3.92148283577154 " " y[1] (numeric) = 3.9214828357715468 " " absolute error = 6.661338147750939000000000000000E-15 " " relative error = 1.6986783894568140000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24110923587248131 " " Order of pole (three term test) = 22.061974502594893 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.899999999999982 " " y[1] (analytic) = 3.9290418348503957 " " y[1] (numeric) = 3.929041834850403 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 1.8084376945483840000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23230108970689434 " " Order of pole (three term test) = 22.05724024152935 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.909999999999982 " " y[1] (analytic) = 3.9366979289366375 " " y[1] (numeric) = 3.9366979289366446 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 1.80492064310361940000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2234000262027314 " " Order of pole (three term test) = 22.052683078463804 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.9199999999999817 " " y[1] (analytic) = 3.944451352418903 " " y[1] (numeric) = 3.9444513524189104 " " absolute error = 7.549516567451064000000000000000E-15 " " relative error = 1.9139585947286140000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.21440960566671463 " " Order of pole (three term test) = 22.04830483620273 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.9299999999999815 " " y[1] (analytic) = 3.952302329952972 " " y[1] (numeric) = 3.9523023299529796 " " absolute error = 7.549516567451064000000000000000E-15 " " relative error = 1.91015664723728130000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2053334241471875 " " Order of pole (three term test) = 22.04410726598465 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.9399999999999813 " " y[1] (analytic) = 3.9602510764393006 " " y[1] (numeric) = 3.960251076439308 " " absolute error = 7.549516567451064000000000000000E-15 " " relative error = 1.90632271079108130000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.19617511199574417 " " Order of pole (three term test) = 22.040092046781687 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.949999999999981 " " y[1] (analytic) = 3.9682977970015307 " " y[1] (numeric) = 3.9682977970015383 " " absolute error = 7.549516567451064000000000000000E-15 " " relative error = 1.9024571626543560000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.18693833241513558 " " Order of pole (three term test) = 22.036260784627988 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.959999999999981 " " y[1] (analytic) = 3.976442686965978 " " y[1] (numeric) = 3.976442686965986 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 2.0102404099781562000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.17762677999403914 " " Order of pole (three term test) = 22.032615011977327 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.9699999999999807 " " y[1] (analytic) = 3.9846859318421 " " y[1] (numeric) = 3.984685931842108 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 2.00608176253572970000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1682441792292705 " " Order of pole (three term test) = 22.02915618709017 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.9799999999999804 " " y[1] (analytic) = 3.9930277073039457 " " y[1] (numeric) = 3.993027707303954 " " absolute error = 8.43769498715119000000000000000E-15 " " relative error = 2.11310704699523370000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.158794283036036 " " Order of pole (three term test) = 22.025885693450338 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.9899999999999802 " " y[1] (analytic) = 4.001468179172587 " " y[1] (numeric) = 4.001468179172596 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 2.21963134512238060000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.14928087124681594 " " Order of pole (three term test) = 22.022804839211677 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.99999999999998 " " y[1] (analytic) = 4.010007503399537 " " y[1] (numeric) = 4.010007503399546 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 2.21490463283961460000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.13970774909948208 " " Order of pole (three term test) = 22.01991485667482 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.00999999999998 " " y[1] (analytic) = 4.018645826051157 " " y[1] (numeric) = 4.0186458260511655 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 2.21014356115297740000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.13007874571525377 " " Order of pole (three term test) = 22.017216901794253 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.0199999999999796 " " y[1] (analytic) = 4.027383283294045 " " y[1] (numeric) = 4.027383283294054 " " absolute error = 9.769962616701378000000000000000E-15 " " relative error = 2.4258834904609347000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.12039771256709944 " " Order of pole (three term test) = 22.01471205371593 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.0299999999999794 " " y[1] (analytic) = 4.036220001381427 " " y[1] (numeric) = 4.0362200013814356 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 2.200520336840260000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.11066852193919968 " " Order of pole (three term test) = 22.01240131434571 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.039999999999979 " " y[1] (analytic) = 4.045156096640522 " " y[1] (numeric) = 4.0451560966405316 " " absolute error = 9.769962616701378000000000000000E-15 " " relative error = 2.41522511944972260000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.10089506537808485 " " Order of pole (three term test) = 22.010285607948514 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.049999999999979 " " y[1] (analytic) = 4.0541916754609195 " " y[1] (numeric) = 4.054191675460930 " " absolute error = 9.769962616701378000000000000000E-15 " " relative error = 2.40984230613384480000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 9.1081252136068500E-2 " " Order of pole (three term test) = 22.008365780778714 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.0599999999999787 " " y[1] (analytic) = 4.063326834283934 " " y[1] (numeric) = 4.063326834283944 " " absolute error = 9.769962616701378000000000000000E-15 " " relative error = 2.40442450611362240000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 8.12310076075980700E-2 " " Order of pole (three term test) = 22.00664260074155 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.0699999999999785 " " y[1] (analytic) = 4.072561659592962 " " y[1] (numeric) = 4.072561659592972 " " absolute error = 9.769962616701378000000000000000E-15 " " relative error = 2.3989723013003691000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 7.13482717591504700E-2 " " Order of pole (three term test) = 22.0051167570861 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.0799999999999783 " " y[1] (analytic) = 4.081896227904834 " " y[1] (numeric) = 4.081896227904845 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 2.61107594150479900000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.14369975532966600E-2 " " Order of pole (three term test) = 22.003788860129443 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.089999999999978 " " y[1] (analytic) = 4.091330605762166 " " y[1] (numeric) = 4.0913306057621766 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 2.60505494750063570000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 5.15011493675705800E-2 " " Order of pole (three term test) = 22.002659441012685 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.099999999999978 " " y[1] (analytic) = 4.100864849726700 " " y[1] (numeric) = 4.100864849726710 " " absolute error = 1.154631945610162800000000000000E-14 " " relative error = 2.81558156125801900000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 4.15447014087703400E-2 " " Order of pole (three term test) = 22.001728951488392 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.1099999999999777 " " y[1] (analytic) = 4.110499006373650 " " y[1] (numeric) = 4.110499006373662 " " absolute error = 1.154631945610162800000000000000E-14 " " relative error = 2.808982422376980000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.157163612332855600E-2 " " Order of pole (three term test) = 22.000997763739985 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.1199999999999775 " " y[1] (analytic) = 4.12023311228705 " " y[1] (numeric) = 4.120233112287061 " " absolute error = 1.154631945610162800000000000000E-14 " " relative error = 2.80234616378113640000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.15859426043869800E-2 " " Order of pole (three term test) = 22.000466170232805 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.1299999999999772 " " y[1] (analytic) = 4.130067194056084 " " y[1] (numeric) = 4.130067194056095 " " absolute error = 1.154631945610162800000000000000E-14 " " relative error = 2.7956735117333870000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.159161499621236500E-2 " " Order of pole (three term test) = 22.00013438359717 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.139999999999977 " " y[1] (analytic) = 4.140001268272437 " " y[1] (numeric) = 4.140001268272450 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 3.00350098225706350000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.5926508965920890000E-3 " " Order of pole (three term test) = 22.000002536543313 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.149999999999977 " " y[1] (analytic) = 4.150035341528635 " " y[1] (numeric) = 4.150035341528647 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 2.9962390323214927000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 8.406950242151767000E-3 " " Order of pole (three term test) = 22.000070681808293 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.1599999999999766 " " y[1] (analytic) = 4.160169410417378 " " y[1] (numeric) = 4.1601694104173905 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 2.9889402687940620000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.84031887128899500E-2 " " Order of pole (three term test) = 22.000338792134915 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.1699999999999764 " " y[1] (analytic) = 4.17040346153189 " " y[1] (numeric) = 4.170403461531903 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 2.98160549464781540000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.839206615351552700E-2 " " Order of pole (three term test) = 22.000806760282615 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.179999999999976 " " y[1] (analytic) = 4.180737471467254 " " y[1] (numeric) = 4.180737471467268 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 3.18668091130491550000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.836958714623557300E-2 " " Order of pole (three term test) = 22.001474399070393 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.189999999999976 " " y[1] (analytic) = 4.191171406822756 " " y[1] (numeric) = 4.19117140682277 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 3.39066416898825300000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 4.833176081568479000E-2 " " Order of pole (three term test) = 22.002341441451613 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.1999999999999758 " " y[1] (analytic) = 4.201705224205221 " " y[1] (numeric) = 4.201705224205235 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 3.38216365901538860000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 5.82746024252225800E-2 " " Order of pole (three term test) = 22.003407540620906 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.2099999999999755 " " y[1] (analytic) = 4.212338870233356 " " y[1] (numeric) = 4.212338870233370 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 3.3736257107953770000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.81941349707746200E-2 " " Order of pole (three term test) = 22.0046722701528 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.2199999999999753 " " y[1] (analytic) = 4.223072281543086 " " y[1] (numeric) = 4.223072281543101 " " absolute error = 1.50990331349021300000000000000E-14 " " relative error = 3.57536696705201400000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 7.80863907715813300E-2 " " Order of pole (three term test) = 22.006135124172342 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.229999999999975 " " y[1] (analytic) = 4.233905384793892 " " y[1] (numeric) = 4.233905384793907 " " absolute error = 1.50990331349021300000000000000E-14 " " relative error = 3.5662188364271050000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 8.79474130572175500E-2 " " Order of pole (three term test) = 22.00779551755744 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.239999999999975 " " y[1] (analytic) = 4.244838096676142 " " y[1] (numeric) = 4.244838096676157 " " absolute error = 1.50990331349021300000000000000E-14 " " relative error = 3.5570339294507375000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 9.77732575502473900E-2 " " Order of pole (three term test) = 22.009652786172882 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.2499999999999747 " " y[1] (analytic) = 4.255870323919426 " " y[1] (numeric) = 4.255870323919441 " " absolute error = 1.50990331349021300000000000000E-14 " " relative error = 3.54781325221317800000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.10755999404388317 " " Order of pole (three term test) = 22.01170618713598 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.2599999999999745 " " y[1] (analytic) = 4.267001963301879 " " y[1] (numeric) = 4.267001963301895 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 3.74670827248250850000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.11730370797401542 " " Order of pole (three term test) = 22.013954899113724 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.2699999999999743 " " y[1] (analytic) = 4.278232901660506 " " y[1] (numeric) = 4.278232901660522 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 3.73687265796052200000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.12700050198498672 " " Order of pole (three term test) = 22.01639802265131 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.279999999999974 " " y[1] (analytic) = 4.289563015902497 " " y[1] (numeric) = 4.289563015902514 " " absolute error = 1.68753899743023800000000000000E-14 " " relative error = 3.93405806412938400000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.13664649748848143 " " Order of pole (three term test) = 22.01903458053189 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.289999999999974 " " y[1] (analytic) = 4.300992173017537 " " y[1] (numeric) = 4.300992173017554 " " absolute error = 1.68753899743023800000000000000E-14 " " relative error = 3.92360397216504560000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.14623783621490985 " " Order of pole (three term test) = 22.021863518167475 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.2999999999999736 " " y[1] (analytic) = 4.3125202300911045 " " y[1] (numeric) = 4.312520230091121 " " absolute error = 1.68753899743023800000000000000E-14 " " relative error = 3.9131155505201826000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.15577068175666406 " " Order of pole (three term test) = 22.024883704020727 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.3099999999999734 " " y[1] (analytic) = 4.3241470343187665 " " y[1] (numeric) = 4.324147034318783 " " absolute error = 1.68753899743023800000000000000E-14 " " relative error = 3.9025939313279984000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.16524122110263043 " " Order of pole (three term test) = 22.02809393005757 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.319999999999973 " " y[1] (analytic) = 4.3358724230214545 " " y[1] (numeric) = 4.335872423021471 " " absolute error = 1.68753899743023800000000000000E-14 " " relative error = 3.8920402465492190000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.17464566616334262 " " Order of pole (three term test) = 22.031492912230387 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.329999999999973 " " y[1] (analytic) = 4.347696223661736 " " y[1] (numeric) = 4.347696223661754 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 4.0857427658645370000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.18398025528616735 " " Order of pole (three term test) = 22.035079290991643 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.3399999999999728 " " y[1] (analytic) = 4.359618253861068 " " y[1] (numeric) = 4.359618253861087 " " absolute error = 1.86517468137026300000000000000E-14 " " relative error = 4.27829817374120460000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.19324125475991474 " " Order of pole (three term test) = 22.038851631837638 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.3499999999999726 " " y[1] (analytic) = 4.3716383214180325 " " y[1] (numeric) = 4.371638321418051 " " absolute error = 1.86517468137026300000000000000E-14 " " relative error = 4.2665347502152340000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.20242496030827395 " " Order of pole (three term test) = 22.042808425882328 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.3599999999999723 " " y[1] (analytic) = 4.3837562243275565 " " y[1] (numeric) = 4.383756224327575 " " absolute error = 1.86517468137026300000000000000E-14 " " relative error = 4.2547408795669750000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2115276985714734 " " Order of pole (three term test) = 22.046948090460866 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.369999999999972 " " y[1] (analytic) = 4.395971750801113 " " y[1] (numeric) = 4.395971750801133 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 4.44496151046508360000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.22054582857557606 " " Order of pole (three term test) = 22.051268969762603 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.379999999999972 " " y[1] (analytic) = 4.408284679287903 " " y[1] (numeric) = 4.408284679287923 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 4.4325461386852080000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2294757431888202 " " Order of pole (three term test) = 22.05576933549344 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.3899999999999717 " " y[1] (analytic) = 4.420694778497004 " " y[1] (numeric) = 4.420694778497023 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 4.4201027694669640000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23831387056442466 " " Order of pole (three term test) = 22.06044738756708 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.3999999999999715 " " y[1] (analytic) = 4.433201807420503 " " y[1] (numeric) = 4.433201807420523 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 4.4076326957856740000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24705667556927938 " " Order of pole (three term test) = 22.065301254825073 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.4099999999999713 " " y[1] (analytic) = 4.445805515357598 " " y[1] (numeric) = 4.445805515357618 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 4.39513720649812600000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.25570066119795143 " " Order of pole (three term test) = 22.070328995785232 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.419999999999971 " " y[1] (analytic) = 4.458505641939665 " " y[1] (numeric) = 4.458505641939684 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 4.3826175859456680000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.26424236997144096 " " Order of pole (three term test) = 22.0755285994182 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.429999999999971 " " y[1] (analytic) = 4.471301917156294 " " y[1] (numeric) = 4.471301917156314 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 4.37007511356557240000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.27267838532012667 " " Order of pole (three term test) = 22.080897985951857 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.4399999999999706 " " y[1] (analytic) = 4.484194061382295 " " y[1] (numeric) = 4.484194061382316 " " absolute error = 2.04281036531028800000000000000E-14 " " relative error = 4.5555797482158310000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2810053329503472 " " Order of pole (three term test) = 22.08643500770318 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.4499999999999704 " " y[1] (analytic) = 4.497181785405656 " " y[1] (numeric) = 4.497181785405677 " " absolute error = 2.04281036531028800000000000000E-14 " " relative error = 4.5424233726545293000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.28921988219407585 " " Order of pole (three term test) = 22.0921374499373 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.45999999999997 " " y[1] (analytic) = 4.510264790456465 " " y[1] (numeric) = 4.510264790456485 " " absolute error = 2.04281036531028800000000000000E-14 " " relative error = 4.52924708463412300000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.29731874734114033 " " Order of pole (three term test) = 22.098003031753354 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.46999999999997 " " y[1] (analytic) = 4.523442768236784 " " y[1] (numeric) = 4.523442768236805 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 4.7124022928916130000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3052986889534658 " " Order of pole (three term test) = 22.104029406996816 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.47999999999997 " " y[1] (analytic) = 4.5367154009514845 " " y[1] (numeric) = 4.536715400951506 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 4.698615669903460000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.31315651516080456 " " Order of pole (three term test) = 22.110214165197938 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.4899999999999696 " " y[1] (analytic) = 4.550082361340020 " " y[1] (numeric) = 4.550082361340043 " " absolute error = 2.22044604925031300000000000000E-14 " " relative error = 4.8800128721106960000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.32088908293744345 " " Order of pole (three term test) = 22.11655483253591 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.4999999999999694 " " y[1] (analytic) = 4.563543312709163 " " y[1] (numeric) = 4.563543312709184 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 4.6709937020732530000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3284932993593715 " " Order of pole (three term test) = 22.12304887282833 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.509999999999969 " " y[1] (analytic) = 4.577097908966655 " " y[1] (numeric) = 4.577097908966676 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 4.6571610432549080000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3359661228414083 " " Order of pole (three term test) = 22.12969368854567 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.519999999999969 " " y[1] (analytic) = 4.5907457946558345 " " y[1] (numeric) = 4.590745794655857 " " absolute error = 2.22044604925031300000000000000E-14 " " relative error = 4.836787198792780000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3433045643537967 " " Order of pole (three term test) = 22.136486621850242 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.5299999999999687 " " y[1] (analytic) = 4.604486604991172 " " y[1] (numeric) = 4.604486604991195 " " absolute error = 2.309263891220325600000000000000E-14 " " relative error = 5.0152472779856260000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3505056886177768 " " Order of pole (three term test) = 22.143424955659288 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.5399999999999685 " " y[1] (analytic) = 4.618319965894753 " " y[1] (numeric) = 4.618319965894776 " " absolute error = 2.309263891220325600000000000000E-14 " " relative error = 5.0002249914984590000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.357566615279657 " " Order of pole (three term test) = 22.15050591473181 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.5499999999999683 " " y[1] (analytic) = 4.63224549403368 " " y[1] (numeric) = 4.632245494033703 " " absolute error = 2.309263891220325600000000000000E-14 " " relative error = 4.9851932376957380000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3644845200629164 " " Order of pole (three term test) = 22.157726666778572 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.559999999999968 " " y[1] (analytic) = 4.6462627968584105 " " y[1] (numeric) = 4.646262796858434 " " absolute error = 2.309263891220325600000000000000E-14 " " relative error = 4.9701534161643710000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3712566358978797 " " Order of pole (three term test) = 22.165084323595046 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.569999999999968 " " y[1] (analytic) = 4.6603714726420105 " " y[1] (numeric) = 4.6603714726420336 " " absolute error = 2.309263891220325600000000000000E-14 " " relative error = 4.9551069153532110000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.37788025402850584 " " Order of pole (three term test) = 22.17257594221659 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.5799999999999677 " " y[1] (analytic) = 4.674571110520324 " " y[1] (numeric) = 4.674571110520348 " " absolute error = 2.39808173319033800000000000000E-14 " " relative error = 5.1300572319743980000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.38435272509585733 " " Order of pole (three term test) = 22.180198526095666 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.5899999999999674 " " y[1] (analytic) = 4.688861290533065 " " y[1] (numeric) = 4.688861290533088 " " absolute error = 2.309263891220325600000000000000E-14 " " relative error = 4.924999372198940000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.39067146019780474 " " Order of pole (three term test) = 22.18794902630032 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.5999999999999672 " " y[1] (analytic) = 4.703241583665806 " " y[1] (numeric) = 4.70324158366583 " " absolute error = 2.39808173319033800000000000000E-14 " " relative error = 5.0987849348814920000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3968339319245565 " " Order of pole (three term test) = 22.19582434273385 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.609999999999967 " " y[1] (analytic) = 4.717711551892884 " " y[1] (numeric) = 4.717711551892908 " " absolute error = 2.39808173319033800000000000000E-14 " " relative error = 5.0831461542581110000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4028376753695873 " " Order of pole (three term test) = 22.20382132537465 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.619999999999967 " " y[1] (analytic) = 4.732270748221201 " " y[1] (numeric) = 4.732270748221226 " " absolute error = 2.486899575160350700000000000000E-14 " " relative error = 5.2551929242322910000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4086802891155673 " " Order of pole (three term test) = 22.211936775536316 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.6299999999999666 " " y[1] (analytic) = 4.746918716734925 " " y[1] (numeric) = 4.74691871673495 " " absolute error = 2.486899575160350700000000000000E-14 " " relative error = 5.2389765310136090000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.41435943619489923 " " Order of pole (three term test) = 22.22016744714697 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.6399999999999664 " " y[1] (analytic) = 4.761654992641076 " " y[1] (numeric) = 4.761654992641101 " " absolute error = 2.486899575160350700000000000000E-14 " " relative error = 5.2227630498298220000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.41987284502447153 " " Order of pole (three term test) = 22.228510048047713 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.649999999999966 " " y[1] (analytic) = 4.776479102316012 " " y[1] (numeric) = 4.776479102316037 " " absolute error = 2.486899575160350700000000000000E-14 " " relative error = 5.2065538692601130000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4252183103142644 " " Order of pole (three term test) = 22.236961241309423 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.659999999999966 " " y[1] (analytic) = 4.791390563352785 " " y[1] (numeric) = 4.7913905633528096 " " absolute error = 2.486899575160350700000000000000E-14 " " relative error = 5.1903503633820610000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4303936939494332 " " Order of pole (three term test) = 22.24551764656746 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.6699999999999657 " " y[1] (analytic) = 4.806388884609382 " " y[1] (numeric) = 4.806388884609408 " " absolute error = 2.575717417130363000000000000000E-14 " " relative error = 5.3589451019623290000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.43539692584552875 " " Order of pole (three term test) = 22.25417584137383 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.6799999999999655 " " y[1] (analytic) = 4.821473566257846 " " y[1] (numeric) = 4.821473566257872 " " absolute error = 2.575717417130363000000000000000E-14 " " relative error = 5.3421788624042770000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.44022600477650065 " " Order of pole (three term test) = 22.262932362566037 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.6899999999999653 " " y[1] (analytic) = 4.836644099834247 " " y[1] (numeric) = 4.836644099834274 " " absolute error = 2.664535259100375700000000000000E-14 " " relative error = 5.5090579420381370000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.444878999175164 " " Order of pole (three term test) = 22.27178370765236 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.699999999999965 " " y[1] (analytic) = 4.851899968289539 " " y[1] (numeric) = 4.8518999682895645 " " absolute error = 2.575717417130363000000000000000E-14 " " relative error = 5.3086779075504960000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.44935404790579814 " " Order of pole (three term test) = 22.28072633621277 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.709999999999965 " " y[1] (analytic) = 4.867240646041252 " " y[1] (numeric) = 4.867240646041279 " " absolute error = 2.664535259100375700000000000000E-14 " " relative error = 5.4744267910146650000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4536493610085773 " " Order of pole (three term test) = 22.289756671315097 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.7199999999999647 " " y[1] (analytic) = 4.8826655990260655 " " y[1] (numeric) = 4.882665599026092 " " absolute error = 2.664535259100375700000000000000E-14 " " relative error = 5.4571323902088740000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.45776322041553064 " " Order of pole (three term test) = 22.298871100945682 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.7299999999999645 " " y[1] (analytic) = 4.898174284753199 " " y[1] (numeric) = 4.898174284753226 " " absolute error = 2.753353101070388000000000000000E-14 " " relative error = 5.621182385528610000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4616939806377458 " " Order of pole (three term test) = 22.3080659794542 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.7399999999999642 " " y[1] (analytic) = 4.913766152358672 " " y[1] (numeric) = 4.9137661523587 " " absolute error = 2.753353101070388000000000000000E-14 " " relative error = 5.6033458160167890000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.46544006942354377 " " Order of pole (three term test) = 22.317337629011863 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.749999999999964 " " y[1] (analytic) = 4.929440642660383 " " y[1] (numeric) = 4.929440642660410 " " absolute error = 2.753353101070388000000000000000E-14 " " relative error = 5.5855284618751870000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.468999988387357 " " Order of pole (three term test) = 22.326682341082453 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.759999999999964 " " y[1] (analytic) = 4.94519718821403 " " y[1] (numeric) = 4.945197188214059 " " absolute error = 2.84217094304040100000000000000E-14 " " relative error = 5.7473359198177030000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4723723136090652 " " Order of pole (three term test) = 22.33609637790574 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.7699999999999636 " " y[1] (analytic) = 4.961035213369857 " " y[1] (numeric) = 4.961035213369885 " " absolute error = 2.84217094304040100000000000000E-14 " " relative error = 5.7289876422985800000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4755556962035432 " " Order of pole (three term test) = 22.345575973992503 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.7799999999999634 " " y[1] (analytic) = 4.976954134330211 " " y[1] (numeric) = 4.9769541343302395 " " absolute error = 2.84217094304040100000000000000E-14 " " relative error = 5.7106633220418350000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4785488628601978 " " Order of pole (three term test) = 22.35511733763072 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.789999999999963 " " y[1] (analytic) = 4.992953359207930 " " y[1] (numeric) = 4.9929533592079585 " " absolute error = 2.93098878501041300000000000000E-14 " " relative error = 5.8702506796005380000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4813506163522751 " " Order of pole (three term test) = 22.364716652402137 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.799999999999963 " " y[1] (analytic) = 5.009032288085524 " " y[1] (numeric) = 5.009032288085553 " " absolute error = 2.93098878501041300000000000000E-14 " " relative error = 5.8514072508217970000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.48395983601573395 " " Order of pole (three term test) = 22.374370078708836 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.8099999999999627 " " y[1] (analytic) = 5.025190313075171 " " y[1] (numeric) = 5.025190313075202 " " absolute error = 3.01980662698042600000000000000E-14 " " relative error = 6.0093378336798780000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4863754781974983 " " Order of pole (three term test) = 22.38407375530901 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.8199999999999625 " " y[1] (analytic) = 5.041426818379507 " " y[1] (numeric) = 5.041426818379537 " " absolute error = 3.01980662698042600000000000000E-14 " " relative error = 5.9899840576305310000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4885965766729035 " " Order of pole (three term test) = 22.393823800861398 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.8299999999999623 " " y[1] (analytic) = 5.057741180353195 " " y[1] (numeric) = 5.057741180353226 " " absolute error = 3.10862446895043830000000000000E-14 " " relative error = 6.146270356865820000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4906222430321738 " " Order of pole (three term test) = 22.40361631547778 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.839999999999962 " " y[1] (analytic) = 5.074132767565300 " " y[1] (numeric) = 5.074132767565332 " " absolute error = 3.10862446895043830000000000000E-14 " " relative error = 6.1264153134133230000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49245166703577403 " " Order of pole (three term test) = 22.413447382282875 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.849999999999962 " " y[1] (analytic) = 5.090600940862429 " " y[1] (numeric) = 5.090600940862461 " " absolute error = 3.19744231092045100000000000000E-14 " " relative error = 6.2810704434803980000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49408411693849436 " " Order of pole (three term test) = 22.42331306898103 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.8599999999999617 " " y[1] (analytic) = 5.1071450534326415 " " y[1] (numeric) = 5.107145053432673 " " absolute error = 3.19744231092045100000000000000E-14 " " relative error = 6.2607235108220960000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49551893978213973 " " Order of pole (three term test) = 22.433209429429116 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.8699999999999615 " " y[1] (analytic) = 5.123764450870133 " " y[1] (numeric) = 5.123764450870166 " " absolute error = 3.286260152890463400000000000000E-14 " " relative error = 6.4137611796974410000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4967555616567036 " " Order of pole (three term test) = 22.443132505214905 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.8799999999999613 " " y[1] (analytic) = 5.140458471240677 " " y[1] (numeric) = 5.14045847124071 " " absolute error = 3.286260152890463400000000000000E-14 " " relative error = 6.3929320142864730000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4977934879299238 " " Order of pole (three term test) = 22.453078327240377 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.889999999999961 " " y[1] (analytic) = 5.157226445147813 " " y[1] (numeric) = 5.157226445147848 " " absolute error = 3.463895836830488400000000000000E-14 " " relative error = 6.7165866646974580000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4986323034451301 " " Order of pole (three term test) = 22.463042917309348 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.899999999999961 " " y[1] (analytic) = 5.174067695799794 " " y[1] (numeric) = 5.174067695799828 " " absolute error = 3.463895836830488400000000000000E-14 " " relative error = 6.6947246160741390000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4992716726873003 " " Order of pole (three term test) = 22.47302228971863 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.9099999999999606 " " y[1] (analytic) = 5.190981539077252 " " y[1] (numeric) = 5.190981539077287 " " absolute error = 3.463895836830488400000000000000E-14 " " relative error = 6.6729111069931290000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49971133991726263 " " Order of pole (three term test) = 22.48301245285234 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.9199999999999604 " " y[1] (analytic) = 5.207967283601622 " " y[1] (numeric) = 5.207967283601658 " " absolute error = 3.55271367880050100000000000000E-14 " " relative error = 6.8216897022125410000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49995112927398716 " " Order of pole (three term test) = 22.493009410778406 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.92999999999996 " " y[1] (analytic) = 5.225024230804275 " " y[1] (numeric) = 5.225024230804310 " " absolute error = 3.463895836830488400000000000000E-14 " " relative error = 6.6294349725863370000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4999909448449281 " " Order of pole (three term test) = 22.503009164846954 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.93999999999996 " " y[1] (analytic) = 5.242151674996368 " " y[1] (numeric) = 5.242151674996403 " " absolute error = 3.55271367880050100000000000000E-14 " " relative error = 6.7772050468245220000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49983077070438814 " " Order of pole (three term test) = 22.51300771528968 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.9499999999999598 " " y[1] (analytic) = 5.259348903439423 " " y[1] (numeric) = 5.259348903439460 " " absolute error = 3.641531520770513500000000000000E-14 " " relative error = 6.9239207887293510000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4994706709198879 " " Order of pole (three term test) = 22.52300106281973 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.9599999999999596 " " y[1] (analytic) = 5.276615196416594 " " y[1] (numeric) = 5.27661519641663 " " absolute error = 3.641531520770513500000000000000E-14 " " relative error = 6.9012641347118080000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4989107895265397 " " Order of pole (three term test) = 22.532985210231317 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.9699999999999593 " " y[1] (analytic) = 5.293949827304638 " " y[1] (numeric) = 5.293949827304674 " " absolute error = 3.641531520770513500000000000000E-14 " " relative error = 6.8786664769442350000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4981513504694364 " " Order of pole (three term test) = 22.54295616399863 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.979999999999959 " " y[1] (analytic) = 5.311352062646577 " " y[1] (numeric) = 5.311352062646614 " " absolute error = 3.73034936274052600000000000000E-14 " " relative error = 7.0233517167411070000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49719265751407454 " " Order of pole (three term test) = 22.55290993587307 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.989999999999959 " " y[1] (analytic) = 5.328821162225048 " " y[1] (numeric) = 5.328821162225085 " " absolute error = 3.73034936274052600000000000000E-14 " " relative error = 7.0003275568417080000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4960350941248543 " " Order of pole (three term test) = 22.56284254447862 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.9999999999999587 " " y[1] (analytic) = 5.346356379136315 " " y[1] (numeric) = 5.3463563791363535 " " absolute error = 3.819167204710538500000000000000E-14 " " relative error = 7.143495371192430000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49467912331169683 " " Order of pole (three term test) = 22.572750016904266 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.009999999999959 " " y[1] (analytic) = 5.363956959864969 " " y[1] (numeric) = 5.363956959865007 " " absolute error = 3.819167204710538500000000000000E-14 " " relative error = 7.1200556478862610000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4931252874448486 " " Order of pole (three term test) = 22.582628390293145 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.019999999999959 " " y[1] (analytic) = 5.381622144359268 " " y[1] (numeric) = 5.381622144359306 " " absolute error = 3.819167204710538500000000000000E-14 " " relative error = 7.0966840522491680000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49137420803793863 " " Order of pole (three term test) = 22.592473713427594 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.0299999999999585 " " y[1] (analytic) = 5.3993511661071505 " " y[1] (numeric) = 5.39935116610719 " " absolute error = 3.90798504668055100000000000000E-14 " " relative error = 7.2378790088923740000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.48942658549938217 " " Order of pole (three term test) = 22.60228204830964 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.039999999999958 " " y[1] (analytic) = 5.417143252212885 " " y[1] (numeric) = 5.417143252212924 " " absolute error = 3.90798504668055100000000000000E-14 " " relative error = 7.2141068912736480000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.487283198852227 " " Order of pole (three term test) = 22.612049471736114 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.049999999999958 " " y[1] (analytic) = 5.4349976234743504 " " y[1] (numeric) = 5.43499762347439 " " absolute error = 3.996802888650563500000000000000E-14 " " relative error = 7.3538263777484170000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4849449054225534 " " Order of pole (three term test) = 22.621772076867856 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.059999999999958 " " y[1] (analytic) = 5.45291349446097 " " y[1] (numeric) = 5.45291349446101 " " absolute error = 3.996802888650563500000000000000E-14 " " relative error = 7.3296649446401220000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.48241264049655663 " " Order of pole (three term test) = 22.63144597479246 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.069999999999958 " " y[1] (analytic) = 5.470890073592239 " " y[1] (numeric) = 5.470890073592279 " " absolute error = 3.996802888650563500000000000000E-14 " " relative error = 7.3055806914179580000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4796874169464442 " " Order of pole (three term test) = 22.64106729607974 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.079999999999957 " " y[1] (analytic) = 5.488926563216891 " " y[1] (numeric) = 5.488926563216932 " " absolute error = 4.08562073062057600000000000000E-14 " " relative error = 7.4433874885477050000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4767703248253001 " " Order of pole (three term test) = 22.650632192329454 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.089999999999957 " " y[1] (analytic) = 5.507022159692664 " " y[1] (numeric) = 5.5070221596927045 " " absolute error = 4.08562073062057600000000000000E-14 " " relative error = 7.418929163794370000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4736625309310787 " " Order of pole (three term test) = 22.660136837710642 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.099999999999957 " " y[1] (analytic) = 5.525176053466653 " " y[1] (numeric) = 5.525176053466694 " " absolute error = 4.08562073062057600000000000000E-14 " " relative error = 7.3945530261558650000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.47036527833990116 " " Order of pole (three term test) = 22.669577430491877 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.109999999999957 " " y[1] (analytic) = 5.543387429156278 " " y[1] (numeric) = 5.543387429156320 " " absolute error = 4.174438572590588600000000000000E-14 " " relative error = 7.5304831674483050000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.46687988590884094 " " Order of pole (three term test) = 22.67895019456191 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.119999999999957 " " y[1] (analytic) = 5.56165546563081 " " y[1] (numeric) = 5.561655465630853 " " absolute error = 4.26325641456060100000000000000E-14 " " relative error = 7.6654450116626520000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.46320774774839946 " " Order of pole (three term test) = 22.688251380940102 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.129999999999956 " " y[1] (analytic) = 5.579979336093495 " " y[1] (numeric) = 5.579979336093538 " " absolute error = 4.26325641456060100000000000000E-14 " " relative error = 7.6402727640659650000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.45935033266487957 " " Order of pole (three term test) = 22.697477269275897 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.139999999999956 " " y[1] (analytic) = 5.598358208164221 " " y[1] (numeric) = 5.598358208164264 " " absolute error = 4.26325641456060100000000000000E-14 " " relative error = 7.6151904827086470000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.45530918357288336 " " Order of pole (three term test) = 22.70662416933698 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.149999999999956 " " y[1] (analytic) = 5.616791243962764 " " y[1] (numeric) = 5.616791243962807 " " absolute error = 4.352074256530613600000000000000E-14 " " relative error = 7.7483283025846160000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4510859168781657 " " Order of pole (three term test) = 22.715688422485268 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.159999999999956 " " y[1] (analytic) = 5.6352776001925715 " " y[1] (numeric) = 5.635277600192615 " " absolute error = 4.352074256530613600000000000000E-14 " " relative error = 7.7229101479967780000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4466822218310959 " " Order of pole (three term test) = 22.724666403140382 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.1699999999999555 " " y[1] (analytic) = 5.653816428225093 " " y[1] (numeric) = 5.653816428225136 " " absolute error = 4.352074256530613600000000000000E-14 " " relative error = 7.6975867748448710000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4420998598509774 " " Order of pole (three term test) = 22.733554520229745 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.179999999999955 " " y[1] (analytic) = 5.67240687418464 " " y[1] (numeric) = 5.672406874184683 " " absolute error = 4.352074256530613600000000000000E-14 " " relative error = 7.6723591115035940000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.43734066382150427 " " Order of pole (three term test) = 22.742349218625037 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.189999999999955 " " y[1] (analytic) = 5.691048079033775 " " y[1] (numeric) = 5.69104807903382 " " absolute error = 4.44089209850062600000000000000E-14 " " relative error = 7.8032939395841470000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4324065373576337 " " Order of pole (three term test) = 22.75104698056416 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.199999999999955 " " y[1] (analytic) = 5.709739178659216 " " y[1] (numeric) = 5.709739178659260 " " absolute error = 4.44089209850062600000000000000E-14 " " relative error = 7.7777494900274140000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4272994540441637 " " Order of pole (three term test) = 22.7596443270583 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.209999999999955 " " y[1] (analytic) = 5.728479303958241 " " y[1] (numeric) = 5.728479303958286 " " absolute error = 4.52970994047063870000000000000E-14 " " relative error = 7.9073514978760920000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4220214566463265 " " Order of pole (three term test) = 22.76813781928351 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.2199999999999545 " " y[1] (analytic) = 5.747267580925604 " " y[1] (numeric) = 5.74726758092565 " " absolute error = 4.52970994047063870000000000000E-14 " " relative error = 7.881501733978991000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4165746562927081 " " Order of pole (three term test) = 22.776524059956113 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.229999999999954 " " y[1] (analytic) = 5.766103130740933 " " y[1] (numeric) = 5.766103130740978 " " absolute error = 4.52970994047063870000000000000E-14 " " relative error = 7.855756024066429000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.41096123163082754 " " Order of pole (three term test) = 22.784799694691678 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.239999999999954 " " y[1] (analytic) = 5.784985069856608 " " y[1] (numeric) = 5.784985069856654 " " absolute error = 4.52970994047063870000000000000E-14 " " relative error = 7.8301151788156920000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.40518342795570444 " " Order of pole (three term test) = 22.79296141334665 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.249999999999954 " " y[1] (analytic) = 5.8039125100861195 " " y[1] (numeric) = 5.803912510086166 " " absolute error = 4.61852778244065100000000000000E-14 " " relative error = 7.9576109640083470000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3992435563117728 " " Order of pole (three term test) = 22.801005951342372 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.259999999999954 " " y[1] (analytic) = 5.822884558692884 " " y[1] (numeric) = 5.82288455869293 " " absolute error = 4.61852778244065100000000000000E-14 " " relative error = 7.9316835769064510000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.39314399256849303 " " Order of pole (three term test) = 22.80893009097092 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.269999999999953 " " y[1] (analytic) = 5.841900318479517 " " y[1] (numeric) = 5.841900318479564 " " absolute error = 4.70734562441066400000000000000E-14 " " relative error = 8.0579013125575780000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.38688717647003606 " " Order of pole (three term test) = 22.8167306626821 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.279999999999953 " " y[1] (analytic) = 5.860958887877555 " " y[1] (numeric) = 5.860958887877602 " " absolute error = 4.70734562441066400000000000000E-14 " " relative error = 8.0316987620354170000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.38047561065941765 " " Order of pole (three term test) = 22.824404546351225 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.289999999999953 " " y[1] (analytic) = 5.880059361037604 " " y[1] (numeric) = 5.8800593610376515 " " absolute error = 4.70734562441066400000000000000E-14 " " relative error = 8.0056090174912760000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.37391185967747603 " " Order of pole (three term test) = 22.831948672527144 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.299999999999953 " " y[1] (analytic) = 5.899200827919934 " " y[1] (numeric) = 5.899200827919982 " " absolute error = 4.79616346638067600000000000000E-14 " " relative error = 8.1301918790105170000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.36719854893708864 " " Order of pole (three term test) = 22.839360023659975 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.3099999999999525 " " y[1] (analytic) = 5.918382374385474 " " y[1] (numeric) = 5.918382374385522 " " absolute error = 4.79616346638067600000000000000E-14 " " relative error = 8.1038418320828390000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.36033836367304156 " " Order of pole (three term test) = 22.84663563530808 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.319999999999952 " " y[1] (analytic) = 5.937603082287228 " " y[1] (numeric) = 5.937603082287277 " " absolute error = 4.88498130835068900000000000000E-14 " " relative error = 8.2271941061930020000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3533340478679729 " " Order of pole (three term test) = 22.853772597323815 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.329999999999952 " " y[1] (analytic) = 5.95686202956209 " " y[1] (numeric) = 5.9568620295621395 " " absolute error = 4.97379915032070130000000000000E-14 " " relative error = 8.3496967457652250000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.34618840315481464 " " Order of pole (three term test) = 22.860768055017513 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.339999999999952 " " y[1] (analytic) = 5.976158290323049 " " y[1] (numeric) = 5.976158290323099 " " absolute error = 4.97379915032070130000000000000E-14 " " relative error = 8.3227366289386500000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3389042876961786 " " Order of pole (three term test) = 22.867619210299384 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.349999999999952 " " y[1] (analytic) = 5.995490934951775 " " y[1] (numeric) = 5.9954909349518255 " " absolute error = 5.06261699229071400000000000000E-14 " " relative error = 8.4440407753388340000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3314846150411275 " " Order of pole (three term test) = 22.874323322798666 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.3599999999999515 " " y[1] (analytic) = 6.014859030191582 " " y[1] (numeric) = 6.014859030191634 " " absolute error = 5.151434834260726000000000000000E-14 " " relative error = 8.5645146601160580000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.32393235295979605 " " Order of pole (three term test) = 22.88087771095974 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.369999999999951 " " y[1] (analytic) = 6.034261639240754 " " y[1] (numeric) = 6.034261639240806 " " absolute error = 5.151434834260726000000000000000E-14 " " relative error = 8.5369762569806180000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.31625052225632116 " " Order of pole (three term test) = 22.887279753114726 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.379999999999951 " " y[1] (analytic) = 6.053697821846221 " " y[1] (numeric) = 6.053697821846273 " " absolute error = 5.24025267623073900000000000000E-14 " " relative error = 8.6562838622701490000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3084421955605607 " " Order of pole (three term test) = 22.89352688853213 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.389999999999950 " " y[1] (analytic) = 6.073166634397586 " " y[1] (numeric) = 6.073166634397638 " " absolute error = 5.24025267623073900000000000000E-14 " " relative error = 8.6285343243352890000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.30051049609908437 " " Order of pole (three term test) = 22.899616618441087 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.399999999999950 " " y[1] (analytic) = 6.092667130021484 " " y[1] (numeric) = 6.092667130021536 " " absolute error = 5.24025267623073900000000000000E-14 " " relative error = 8.6009174051369210000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2924585964459211 " " Order of pole (three term test) = 22.9055465070308 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.40999999999995 " " y[1] (analytic) = 6.11219835867627 " " y[1] (numeric) = 6.112198358676323 " " absolute error = 5.24025267623073900000000000000E-14 " " relative error = 8.5734335974096720000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2842897172535757 " " Order of pole (three term test) = 22.911314182424924 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.41999999999995 " " y[1] (analytic) = 6.131759367247021 " " y[1] (numeric) = 6.131759367247074 " " absolute error = 5.329070518200751000000000000000E-14 " " relative error = 8.6909322415131670000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.27600712596480786 " " Order of pole (three term test) = 22.91691733763019 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.42999999999995 " " y[1] (analytic) = 6.151349199640848 " " y[1] (numeric) = 6.151349199640902 " " absolute error = 5.41788836017076400000000000000E-14 " " relative error = 8.8076423307054210000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2676141355056999 " " Order of pole (three term test) = 22.922353731459232 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.43999999999995 " " y[1] (analytic) = 6.170966896882502 " " y[1] (numeric) = 6.170966896882557 " " absolute error = 5.41788836017076400000000000000E-14 " " relative error = 8.7796425595927520000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2591141029605311 " " Order of pole (three term test) = 22.927621189426997 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.4499999999999496 " " y[1] (analytic) = 6.190611497210274 " " y[1] (numeric) = 6.190611497210330 " " absolute error = 5.506706202140776000000000000000E-14 " " relative error = 8.8952540546637570000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.250510428228986 " " Order of pole (three term test) = 22.932717604620525 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.459999999999950 " " y[1] (analytic) = 6.21028203617217 " " y[1] (numeric) = 6.210282036172225 " " absolute error = 5.506706202140776000000000000000E-14 " " relative error = 8.8670790957103520000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24180655266624426 " " Order of pole (three term test) = 22.93764093854171 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.469999999999950 " " y[1] (analytic) = 6.22997754672235 " " y[1] (numeric) = 6.229977546722405 " " absolute error = 5.506706202140776000000000000000E-14 " " relative error = 8.8390466271229280000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23300595770648033 " " Order of pole (three term test) = 22.942389221922603 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.479999999999949 " " y[1] (analytic) = 6.24969705931784 " " y[1] (numeric) = 6.249697059317896 " " absolute error = 5.59552404411078900000000000000E-14 " " relative error = 8.953272440250960000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2241121634703385 " " Order of pole (three term test) = 22.946960555513172 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.489999999999949 " " y[1] (analytic) = 6.2694396020154795 " " y[1] (numeric) = 6.269439602015536 " " absolute error = 5.68434188608080100000000000000E-14 " " relative error = 9.0667463871147560000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.21512872735693092 " " Order of pole (three term test) = 22.951353110840927 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.4999999999999485 " " y[1] (analytic) = 6.289204200569118 " " y[1] (numeric) = 6.289204200569175 " " absolute error = 5.68434188608080100000000000000E-14 " " relative error = 9.0382530202571840000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.20605924262092526 " " Order of pole (three term test) = 22.955565130942315 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.509999999999948 " " y[1] (analytic) = 6.308989878527037 " " y[1] (numeric) = 6.308989878527095 " " absolute error = 5.77315972805081400000000000000E-14 " " relative error = 9.150687890148710000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.19690733693529117 " " Order of pole (three term test) = 22.95959493106544 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.519999999999948 " " y[1] (analytic) = 6.328795657329596 " " y[1] (numeric) = 6.328795657329654 " " absolute error = 5.86197757002082700000000000000E-14 " " relative error = 9.262390330507620000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.18767667094027926 " " Order of pole (three term test) = 22.963440899344 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.529999999999948 " " y[1] (analytic) = 6.348620556407085 " " y[1] (numeric) = 6.348620556407144 " " absolute error = 5.86197757002082700000000000000E-14 " " relative error = 9.2334665742542520000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1783709367792133 " " Order of pole (three term test) = 22.967101497441945 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.539999999999948 " " y[1] (analytic) = 6.368463593277784 " " y[1] (numeric) = 6.368463593277844 " " absolute error = 5.95079541199083900000000000000E-14 " " relative error = 9.3441617822424020000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.16899385662168323 " " Order of pole (three term test) = 22.97057526116885 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.549999999999947 " " y[1] (analytic) = 6.388323783646209 " " y[1] (numeric) = 6.388323783646270 " " absolute error = 6.03961325396085200000000000000E-14 " " relative error = 9.4541439327511260000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.15954918117472566 " " Order of pole (three term test) = 22.973860801065538 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.559999999999947 " " y[1] (analytic) = 6.40820014150154 " " y[1] (numeric) = 6.4082001415016006 " " absolute error = 6.03961325396085200000000000000E-14 " " relative error = 9.4248199503732690000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.15004068818259247 " " Order of pole (three term test) = 22.97695680295986 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.569999999999947 " " y[1] (analytic) = 6.428091679216221 " " y[1] (numeric) = 6.428091679216282 " " absolute error = 6.03961325396085200000000000000E-14 " " relative error = 9.3956551265262330000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.14047218091570202 " " Order of pole (three term test) = 22.97986202849234 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.579999999999947 " " y[1] (analytic) = 6.447997407644724 " " y[1] (numeric) = 6.447997407644785 " " absolute error = 6.03961325396085200000000000000E-14 " " relative error = 9.3666496310936880000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.13084748664938273 " " Order of pole (three term test) = 22.982575315611502 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.589999999999947 " " y[1] (analytic) = 6.46791633622246 " " y[1] (numeric) = 6.467916336222522 " " absolute error = 6.12843109593086400000000000000E-14 " " relative error = 9.4751242554107150000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1211704551330136 " " Order of pole (three term test) = 22.985095579038664 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.599999999999946 " " y[1] (analytic) = 6.487847473064838 " " y[1] (numeric) = 6.4878474730649005 " " absolute error = 6.21724893790087700000000000000E-14 " " relative error = 9.5829147705962760000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.11144495705017576 " " Order of pole (three term test) = 22.987421810702063 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.609999999999946 " " y[1] (analytic) = 6.50778982506645 " " y[1] (numeric) = 6.507789825066513 " " absolute error = 6.30606677987088900000000000000E-14 " " relative error = 9.6900283343223960000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.10167488247043083 " " Order of pole (three term test) = 22.989553080140066 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.619999999999946 " " y[1] (analytic) = 6.52774239800038 " " y[1] (numeric) = 6.527742398000443 " " absolute error = 6.30606677987088900000000000000E-14 " " relative error = 9.6604099784982380000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 9.18641392933447400E-2 " " Order of pole (three term test) = 22.99148853487329 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.629999999999946 " " y[1] (analytic) = 6.547704196617630 " " y[1] (numeric) = 6.547704196617692 " " absolute error = 6.30606677987088900000000000000E-14 " " relative error = 9.6309585627408720000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 8.2016651685380200E-2 " " Order of pole (three term test) = 22.99322740074566 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.6399999999999455 " " y[1] (analytic) = 6.5676742247466375 " " y[1] (numeric) = 6.567674224746700 " " absolute error = 6.30606677987088900000000000000E-14 " " relative error = 9.6016741453313470000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 7.21363585102822600E-2 " " Order of pole (three term test) = 22.99476898223401 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.649999999999945 " " y[1] (analytic) = 6.5876514853928985 " " y[1] (numeric) = 6.587651485392962 " " absolute error = 6.39488462184090200000000000000E-14 " " relative error = 9.7073815092079040000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.222721175358543000E-2 " " Order of pole (three term test) = 22.996112662726294 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.659999999999945 " " y[1] (analytic) = 6.6076349808386645 " " y[1] (numeric) = 6.6076349808387285 " " absolute error = 6.39488462184090200000000000000E-14 " " relative error = 9.6780234386210610000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 5.22931749418723400E-2 " " Order of pole (three term test) = 22.997257904768233 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.669999999999945 " " y[1] (analytic) = 6.627623712742708 " " y[1] (numeric) = 6.627623712742773 " " absolute error = 6.48370246381091400000000000000E-14 " " relative error = 9.7828463787781420000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 4.233822155741559500E-2 " " Order of pole (three term test) = 22.998204250278288 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.679999999999945 " " y[1] (analytic) = 6.647616682240165 " " y[1] (numeric) = 6.64761668224023 " " absolute error = 6.48370246381091400000000000000E-14 " " relative error = 9.7534240822471510000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.23663334488378860E-2 " " Order of pole (three term test) = 22.99895132073087 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.689999999999944 " " y[1] (analytic) = 6.667612890042411 " " y[1] (numeric) = 6.667612890042477 " " absolute error = 6.57252030578092700000000000000E-14 " " relative error = 9.8573813659705730000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.238149923842604200E-2 " " Order of pole (three term test) = 22.999498817307742 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.699999999999944 " " y[1] (analytic) = 6.687611336536998 " " y[1] (numeric) = 6.6876113365370635 " " absolute error = 6.57252030578092700000000000000E-14 " " relative error = 9.8279041275510660000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.23877127267348200E-2 " " Order of pole (three term test) = 22.999846521017606 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.709999999999944 " " y[1] (analytic) = 6.707611021887606 " " y[1] (numeric) = 6.707611021887673 " " absolute error = 6.66133814775093900000000000000E-14 " " relative error = 9.9310143745878020000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.3889712951202105000E-3 " " Order of pole (three term test) = 22.999994292783576 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.719999999999944 " " y[1] (analytic) = 6.727610946134035 " " y[1] (numeric) = 6.727610946134103 " " absolute error = 6.75015598972095200000000000000E-14 " " relative error = 1.0033511217826697000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 7.610725693159915000E-3 " " Order of pole (three term test) = 22.999942073498936 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.729999999999944 " " y[1] (analytic) = 6.747610109292194 " " y[1] (numeric) = 6.747610109292261 " " absolute error = 6.75015598972095200000000000000E-14 " " relative error = 1.0003773010573407000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.760737849263779600E-2 " " Order of pole (three term test) = 22.999689884050717 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.739999999999943 " " y[1] (analytic) = 6.767607511454099 " " y[1] (numeric) = 6.767607511454166 " " absolute error = 6.75015598972095200000000000000E-14 " " relative error = 9.9742131592241290000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.759698857548050000E-2 " " Order of pole (three term test) = 22.999237825311315 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.749999999999943 " " y[1] (analytic) = 6.787602152887863 " " y[1] (numeric) = 6.787602152887931 " " absolute error = 6.83897383169096400000000000000E-14 " " relative error = 1.007568457556288100000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.757556023084797000E-2 " " Order of pole (three term test) = 22.998586078098196 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.759999999999943 " " y[1] (analytic) = 6.807593034137674 " " y[1] (numeric) = 6.807593034137743 " " absolute error = 6.92779167366097700000000000000E-14 " " relative error = 1.0176565548088068000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 4.753910216312385300E-2 " " Order of pole (three term test) = 22.99773490310156 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.769999999999943 " " y[1] (analytic) = 6.827579156123732 " " y[1] (numeric) = 6.827579156123802 " " absolute error = 7.01660951563098900000000000000E-14 " " relative error = 1.0276862933676448000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 5.74836290883807900E-2 " " Order of pole (three term test) = 22.996684640780064 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.7799999999999425 " " y[1] (analytic) = 6.84755952024216 " " y[1] (numeric) = 6.84755952024223 " " absolute error = 7.01660951563098900000000000000E-14 " " relative error = 1.024687627013551000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.74051633284405400E-2 " " Order of pole (three term test) = 22.99543571122464 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.789999999999942 " " y[1] (analytic) = 6.8675331284648635 " " y[1] (numeric) = 6.867533128464934 " " absolute error = 7.01660951563098900000000000000E-14 " " relative error = 1.0217074143476976000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 7.72997364018924700E-2 " " Order of pole (three term test) = 22.993988613990442 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.799999999999942 " " y[1] (analytic) = 6.887498983439330 " " y[1] (numeric) = 6.887498983439402 " " absolute error = 7.10542735760100200000000000000E-14 " " relative error = 1.0316411479240390000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 8.71633906114329200E-2 " " Order of pole (three term test) = 22.992343927897075 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.809999999999942 " " y[1] (analytic) = 6.90745608858837 " " y[1] (numeric) = 6.907456088588441 " " absolute error = 7.10542735760100200000000000000E-14 " " relative error = 1.0286605179205836000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 9.69921806268919600E-2 " " Order of pole (three term test) = 22.99050231079704 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.819999999999942 " " y[1] (analytic) = 6.9274034482097635 " " y[1] (numeric) = 6.9274034482098354 " " absolute error = 7.19424519957101400000000000000E-14 " " relative error = 1.038519735909161000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.10678217506331215 " " Order of pole (three term test) = 22.98846449931264 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.8299999999999415 " " y[1] (analytic) = 6.947340067575839 " " y[1] (numeric) = 6.947340067575910 " " absolute error = 7.19424519957101400000000000000E-14 " " relative error = 1.0355395201031707000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.11652945805345027 " " Order of pole (three term test) = 22.986231308541285 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.839999999999941 " " y[1] (analytic) = 6.96726495303294 " " y[1] (numeric) = 6.967264953033012 " " absolute error = 7.19424519957101400000000000000E-14 " " relative error = 1.032578098876413000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.12623013081407236 " " Order of pole (three term test) = 22.98380363172951 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.849999999999941 " " y[1] (analytic) = 6.98717711210079 " " y[1] (numeric) = 6.987177112100863 " " absolute error = 7.28306304154102700000000000000E-14 " " relative error = 1.0423469914520708000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.13588031320541483 " " Order of pole (three term test) = 22.98118243991567 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.859999999999940 " " y[1] (analytic) = 7.007075553571745 " " y[1] (numeric) = 7.007075553571818 " " absolute error = 7.28306304154102700000000000000E-14 " " relative error = 1.0393869719056477000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.14547614528318847 " " Order of pole (three term test) = 22.978368781541544 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.869999999999940 " " y[1] (analytic) = 7.026959287609905 " " y[1] (numeric) = 7.026959287609980 " " absolute error = 7.3718808835110390000000000000E-14 " " relative error = 1.0490854695158555000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.15501378884250486 " " Order of pole (three term test) = 22.97536378203297 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.87999999999994 " " y[1] (analytic) = 7.046827325850103 " " y[1] (numeric) = 7.0468273258501775 " " absolute error = 7.46069872548105200000000000000E-14 " " relative error = 1.0587315937361956000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.16448942895310736 " " Order of pole (three term test) = 22.972168643349683 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.88999999999994 " " y[1] (analytic) = 7.0666786814967395 " " y[1] (numeric) = 7.066678681496813 " " absolute error = 7.3718808835110390000000000000E-14 " " relative error = 1.0431889174207731000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.17389927548529177 " " Order of pole (three term test) = 22.968784643504545 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.89999999999994 " " y[1] (analytic) = 7.086512369422456 " " y[1] (numeric) = 7.086512369422532 " " absolute error = 7.54951656745106400000000000000E-14 " " relative error = 1.0653359754265614000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.18323956462590796 " " Order of pole (three term test) = 22.965213136052398 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.90999999999994 " " y[1] (analytic) = 7.106327406266658 " " y[1] (numeric) = 7.106327406266733 " " absolute error = 7.54951656745106400000000000000E-14 " " relative error = 1.062365429545729100000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.19250656038383562 " " Order of pole (three term test) = 22.961455549548585 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.9199999999999395 " " y[1] (analytic) = 7.126122810533839 " " y[1] (numeric) = 7.126122810533914 " " absolute error = 7.54951656745106400000000000000E-14 " " relative error = 1.0594143222302266000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2016965560843294 " " Order of pole (three term test) = 22.957513386977606 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.929999999999940 " " y[1] (analytic) = 7.1458976026917345 " " y[1] (numeric) = 7.145897602691810 " " absolute error = 7.63833440942107700000000000000E-14 " " relative error = 1.0689118196353457000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.21080587585164134 " " Order of pole (three term test) = 22.95338822515193 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.939999999999939 " " y[1] (analytic) = 7.165650805269275 " " y[1] (numeric) = 7.165650805269352 " " absolute error = 7.7271522513910900000000000000E-14 " " relative error = 1.0783601463957626000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.21983087607932 " " Order of pole (three term test) = 22.949081714081302 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.949999999999939 " " y[1] (analytic) = 7.185381442954330 " " y[1] (numeric) = 7.185381442954408 " " absolute error = 7.7271522513910900000000000000E-14 " " relative error = 1.0753990324296556000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.22876794688760604 " " Order of pole (three term test) = 22.944595576312707 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.959999999999939 " " y[1] (analytic) = 7.205088542691241 " " y[1] (numeric) = 7.2050885426913185 " " absolute error = 7.7271522513910900000000000000E-14 " " relative error = 1.0724576395704982000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2376135135673361 " " Order of pole (three term test) = 22.93993160624145 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.9699999999999385 " " y[1] (analytic) = 7.2247711337781215 " " y[1] (numeric) = 7.2247711337782 " " absolute error = 7.81597009336110200000000000000E-14 " " relative error = 1.0818294377269523000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24636403800977658 " " Order of pole (three term test) = 22.935091669393373 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.979999999999938 " " y[1] (analytic) = 7.244428247963934 " " y[1] (numeric) = 7.244428247964012 " " absolute error = 7.81597009336110200000000000000E-14 " " relative error = 1.0788939893990669000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2550160201218238 " " Order of pole (three term test) = 22.930077701678695 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.989999999999938 " " y[1] (analytic) = 7.264058919545306 " " y[1] (numeric) = 7.264058919545384 " " absolute error = 7.81597009336110200000000000000E-14 " " relative error = 1.0759783448797168000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2635659992259904 " " Order of pole (three term test) = 22.924891708617626 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.999999999999938 " " y[1] (analytic) = 7.283662185463104 " " y[1] (numeric) = 7.283662185463183 " " absolute error = 7.90478793533111500000000000000E-14 " " relative error = 1.0852765729728195000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.27201055544463265 " " Order of pole (three term test) = 22.91953576453826 " " "NO COMPLEX POLE (six term test) for Equation 1" "Finished!" "diff ( y , x , 1 ) = 1.0 - sin ( x ) ; " Iterations = 491 "Total Elapsed Time "= 13 Seconds "Elapsed Time(since restart) "= 12 Seconds "Time to Timeout "= 9 Minutes 46 Seconds Percent Done = 100.40816326530484 "%" (%o224) true (%o224) diffeq.max