(%i1) batch("diffeq.max") read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max (%i2) load("stringproc") (%i3) alias(convfloat,float) (%i4) alias(int_trunc,truncate) (%i5) alias(elapsed_time_seconds,elapsed_real_time) (%i6) alias(ln,log) (%i7) alias(arcsin,asin) (%i8) alias(arccos,acos) (%i9) alias(arctan,atan) (%i10) alias(float_abs,abs) (%i11) keepfloat:true (%i12) mode_declare(display_poles(),fixnum) (%i13) mode_declare(est_size_answer(),convfloat) (%i14) mode_declare(test_suggested_h(),convfloat) (%i15) mode_declare(reached_interval(),boolean) (%i16) mode_declare(display_alot([iter],fixnum),fixnum) (%i17) mode_declare(prog_report([x_start],convfloat,[x_end],convfloat),fixnum) (%i18) mode_declare(check_for_pole(),fixnum) (%i19) mode_declare(atomall(),fixnum) (%i20) mode_declare(log10([x],convfloat),convfloat) (%i21) mode_declare(logitem_timestr([fd],fixnum,[secs_in],number),fixnum) (%i22) mode_declare(omniout_timestr(secs_in,number),fixnum) (%i23) mode_declare(zero_ats_ar(ar,array([MAX_TERMS],convfloat)),fixnum) (%i24) mode_declare(ats([mmm_ats],fixnum,[arr_a], completearray([MAX_TERMS],convfloat),[arr_b], completearray([MAX_TERMS],convfloat),[jjj_ats], fixnum),convfloat) (%i25) mode_declare(att([mmm_att],fixnum,[arr_a], completearray([MAX_TERMS],convfloat),[arr_b], completearray([MAX_TERMS],convfloat),[jjj_att], fixnum),convfloat) (%i26) mode_declare(logitem_ditto([file],fixnum),fixnum) (%i27) mode_declare(logitem_integer([file],fixnum,[n],fixnum),fixnum) (%i28) mode_declare(logitem_good_digits([file],fixnum,[relerror],convfloat),fixnum) (%i29) mode_declare(logitem_number([file],fixnum,[x],number),fixnum) (%i30) mode_declare(logitem_pole([file],fixnum,[pole],fixnum),fixnum) (%i31) mode_declare(logstart([file],fixnum),fixnum) (%i32) mode_declare(logend([file],fixnum),fixnum) (%i33) mode_declare(chk_data(),fixnum) (%i34) mode_declare(comp_expect_sec([t_end2],convfloat,[t_start2],convfloat, [t2],convfloat,[clock_sec2],convfloat), convfloat) (%i35) mode_declare(comp_percent([t_end2],convfloat,[start2],convfloat,[t2], convfloat),convfloat) (%i36) mode_declare(comp_rad_from_ratio([term1],convfloat,[term2],convfloat, [last_no],fixnum),convfloat) (%i37) mode_declare(comp_ord_from_ratio([term1],convfloat,[term2],convfloat, [last_no],fixnum),convfloat) (%i38) mode_declare(comp_rad_from_three_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [last_no],fixnum),convfloat) (%i39) mode_declare(comp_ord_from_three_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [last_no],fixnum),convfloat) (%i40) mode_declare(comp_rad_from_six_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [term4],convfloat,[term5], convfloat,[term6],convfloat, [last_no],fixnum),convfloat) (%i41) mode_declare(comp_ord_from_six_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [term4],convfloat,[term5], convfloat,[term6],convfloat, [last_no],fixnum),convfloat) (%i42) mode_declare(factorial_2([nnn],fixnum),fixnum) (%i43) mode_declare(factorial_1([nnn],fixnum),fixnum) (%i44) mode_declare(factorial_3([mmm],fixnum,[nnn],fixnum),fixnum) (%i45) mode_declare(convfloat([mmm],fixnum),convfloat) (%i46) mode_declare(elaped_time_seconds(),convfloat) (%i47) mode_declare(Si([x],convfloat),convfloat) (%i48) mode_declare(Ci([x],convfloat),convfloat) (%i49) mode_declare(estimated_needed_step_error([x_start],convfloat,[x_end], convfloat,[estimated_h], convfloat,[estimated_answer], convfloat),convfloat) (%i50) mode_declare(my_check_sign([x0],convfloat,[xf],convfloat),convfloat) (%i51) mode_declare(main_prog(),fixnum) (%i52) define_variable(MAX_TERMS,20,fixnum) (%i53) define_variable(glob_iolevel,5,fixnum) (%i54) define_variable(glob_yes_pole,4,fixnum) (%i55) define_variable(glob_no_pole,3,fixnum) (%i56) define_variable(glob_not_given,0,fixnum) (%i57) define_variable(glob_no_sing_tests,4,fixnum) (%i58) define_variable(glob_ratio_test,1,fixnum) (%i59) define_variable(glob_three_term_test,2,fixnum) (%i60) define_variable(glob_six_term_test,3,fixnum) (%i61) define_variable(glob_log_10,log(10.0),convfloat) (%i62) define_variable(ALWAYS,1,fixnum) (%i63) define_variable(INFO,2,fixnum) (%i64) define_variable(DEBUGL,3,fixnum) (%i65) define_variable(DEBUGMASSIVE,4,fixnum) (%i66) define_variable(MAX_UNCHANGED,10,fixnum) (%i67) define_variable(glob_prec,1.0E-16,convfloat) (%i68) define_variable(glob_est_digits,1,fixnum) (%i69) define_variable(glob_check_sign,1.0,convfloat) (%i70) define_variable(glob_desired_digits_correct,8.0,convfloat) (%i71) define_variable(glob_max_estimated_step_error,0.0,convfloat) (%i72) define_variable(glob_ratio_of_radius,0.1,convfloat) (%i73) define_variable(glob_percent_done,0.0,convfloat) (%i74) define_variable(glob_subiter_method,3,fixnum) (%i75) define_variable(glob_total_exp_sec,0.1,convfloat) (%i76) define_variable(glob_optimal_expect_sec,0.1,convfloat) (%i77) define_variable(glob_estimated_size_answer,100.0,convfloat) (%i78) define_variable(glob_html_log,true,boolean) (%i79) define_variable(glob_good_digits,0,fixnum) (%i80) define_variable(glob_max_opt_iter,10,fixnum) (%i81) define_variable(glob_dump,false,boolean) (%i82) define_variable(glob_djd_debug,true,boolean) (%i83) define_variable(glob_display_flag,true,boolean) (%i84) define_variable(glob_djd_debug2,true,boolean) (%i85) define_variable(glob_h_reason,0,fixnum) (%i86) define_variable(glob_sec_in_minute,60,fixnum) (%i87) define_variable(glob_min_in_hour,60.0,convfloat) (%i88) define_variable(glob_hours_in_day,24.0,convfloat) (%i89) define_variable(glob_days_in_year,365,fixnum) (%i90) define_variable(glob_sec_in_hour,3600,fixnum) (%i91) define_variable(glob_sec_in_day,86400,fixnum) (%i92) define_variable(glob_sec_in_year,31536000,fixnum) (%i93) define_variable(glob_almost_1,0.999,convfloat) (%i94) define_variable(glob_clock_sec,0.0,convfloat) (%i95) define_variable(glob_clock_start_sec,0.0,convfloat) (%i96) define_variable(glob_not_yet_finished,true,boolean) (%i97) define_variable(glob_initial_pass,true,boolean) (%i98) define_variable(glob_not_yet_start_msg,true,boolean) (%i99) define_variable(glob_reached_optimal_h,false,boolean) (%i100) define_variable(glob_optimal_done,false,boolean) (%i101) define_variable(glob_disp_incr,0.1,convfloat) (%i102) define_variable(glob_h,0.1,convfloat) (%i103) define_variable(glob_diff_rc_fm,0.1,convfloat) (%i104) define_variable(glob_diff_rc_fmm1,0.1,convfloat) (%i105) define_variable(glob_diff_rc_fmm2,0.1,convfloat) (%i106) define_variable(glob_diff_ord_fm,0.1,convfloat) (%i107) define_variable(glob_diff_ord_fmm1,0.1,convfloat) (%i108) define_variable(glob_diff_ord_fmm2,0.1,convfloat) (%i109) define_variable(glob_six_term_ord_save,0.1,convfloat) (%i110) define_variable(glob_guess_error_rc,0.1,convfloat) (%i111) define_variable(glob_guess_error_ord,0.1,convfloat) (%i112) define_variable(glob_max_h,0.1,convfloat) (%i113) define_variable(glob_min_h,1.0E-6,convfloat) (%i114) define_variable(glob_type_given_pole,0,fixnum) (%i115) define_variable(glob_large_float,1.0E+100,convfloat) (%i116) define_variable(glob_larger_float,1.1E+100,convfloat) (%i117) define_variable(glob_least_given_sing,9.9E+100,convfloat) (%i118) define_variable(glob_least_ratio_sing,9.9E+100,convfloat) (%i119) define_variable(glob_least_3_sing,9.9E+100,convfloat) (%i120) define_variable(glob_least_6_sing,9.9E+100,convfloat) (%i121) define_variable(glob_last_good_h,0.1,convfloat) (%i122) define_variable(glob_look_poles,false,boolean) (%i123) define_variable(glob_display_interval,0.0,convfloat) (%i124) define_variable(glob_next_display,0.0,convfloat) (%i125) define_variable(glob_dump_analytic,false,boolean) (%i126) define_variable(glob_abserr,1.0E-11,convfloat) (%i127) define_variable(glob_relerr,1.0E-11,convfloat) (%i128) define_variable(glob_min_pole_est,1.0E+9,convfloat) (%i129) define_variable(glob_max_hours,0.0,convfloat) (%i130) define_variable(glob_max_iter,1000,fixnum) (%i131) define_variable(glob_max_rel_trunc_err,1.0E-11,convfloat) (%i132) define_variable(glob_max_trunc_err,1.0E-11,convfloat) (%i133) define_variable(glob_no_eqs,0,fixnum) (%i134) define_variable(glob_optimal_clock_start_sec,0.0,convfloat) (%i135) define_variable(glob_optimal_start,0.0,convfloat) (%i136) define_variable(glob_upper_ratio_limit,1.0001,convfloat) (%i137) define_variable(glob_lower_ratio_limit,0.9999,convfloat) (%i138) define_variable(glob_small_float,0.0,convfloat) (%i139) define_variable(glob_smallish_float,0.0,convfloat) (%i140) define_variable(glob_unchanged_h_cnt,0,fixnum) (%i141) define_variable(glob_warned,false,boolean) (%i142) define_variable(glob_warned2,false,boolean) (%i143) define_variable(glob_max_sec,10000.0,convfloat) (%i144) define_variable(glob_orig_start_sec,0.0,convfloat) (%i145) define_variable(glob_start,0,fixnum) (%i146) define_variable(glob_curr_iter_when_opt,0,fixnum) (%i147) define_variable(glob_current_iter,0,fixnum) (%i148) define_variable(glob_iter,0,fixnum) (%i149) define_variable(glob_normmax,0.0,convfloat) (%i150) define_variable(glob_max_minutes,0.0,convfloat) (%i151) array(array_y_init,MAX_TERMS) (%i152) array(array_norms,MAX_TERMS) (%i153) array(array_fact_1,MAX_TERMS) (%i154) array(array_1st_rel_error,2) (%i155) array(array_last_rel_error,2) (%i156) array(array_est_rel_error,2) (%i157) array(array_max_est_error,2) (%i158) array(array_type_pole,2) (%i159) array(array_type_real_pole,2) (%i160) array(array_type_complex_pole,2) (%i161) array(array_est_digits,2) (%i162) array(array_good_digits,2) (%i163) array(array_y,MAX_TERMS) (%i164) array(array_x,MAX_TERMS) (%i165) array(array_tmp0,MAX_TERMS) (%i166) array(array_tmp1,MAX_TERMS) (%i167) array(array_tmp2,MAX_TERMS) (%i168) array(array_tmp3,MAX_TERMS) (%i169) array(array_tmp4,MAX_TERMS) (%i170) array(array_tmp5,MAX_TERMS) (%i171) array(array_m1,MAX_TERMS) (%i172) array(array_y_higher,2,MAX_TERMS) (%i173) array(array_y_higher_work,2,MAX_TERMS) (%i174) array(array_y_higher_work2,2,MAX_TERMS) (%i175) array(array_y_set_initial,2,MAX_TERMS) (%i176) array(array_given_rad_poles,2,3) (%i177) array(array_given_ord_poles,2,3) (%i178) array(array_rad_test_poles,2,4) (%i179) array(array_ord_test_poles,2,4) (%i180) array(array_fact_2,MAX_TERMS,MAX_TERMS) (%i181) omniout_str(iolevel,str):=if glob_iolevel >= iolevel then printf(true,"~a~%",string(str)) (%i182) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel then printf(true,"~a",string(str)) (%i183) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel then printf(true,"~a = ~a~%",string(label), string(str)) (%i184) 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)) (%i185) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if glob_iolevel >= iolevel then (printf(true,"~a = ~d ~a~%",prelabel,value, postlabel),newline()) (%i186) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen, postlabel):=if glob_iolevel >= iolevel then (sprint(prelabel,"[",elemnt,"]=",value, postlabel),newline()) (%i187) 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) (%i188) 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) (%i189) 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) (%i190) 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) (%i191) 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) (%i192) logditto(file):=(printf(file,""),printf(file,"ditto"), printf(file,""),0) (%i193) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n), printf(file,""),0) (%i194) logitem_str(file,str):=(printf(file,""),printf(file,str), printf(file,""),0) (%i195) 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-33 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) (%i196) log_revs(file,revs):=printf(file,revs) (%i197) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x), printf(file,""),0) (%i198) logitem_h_reason(file):=(printf(file,""), if glob_h_reason = 1 then printf(file,"Max H") elseif glob_h_reason = 2 then printf(file,"Display_interval") elseif glob_h_reason = 3 then printf(file,"Optimal") elseif glob_h_reason = 4 then printf(file,"Pole Accuracy") elseif glob_h_reason = 5 then printf(file,"Min H (Pole)") elseif glob_h_reason = 6 then printf(file,"Pole") else printf(file,"Impossible"), printf(file,""),0) (%i199) logstart(file):=(printf(file,""),0) (%i200) logend(file):=(printf(file,"~%"),0) (%i201) 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) (%i202) 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) (%i203) 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) (%i204) 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) (%i205) 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) (%i206) 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) (%i207) 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) (%i208) 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) (%i209) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save (%i210) factorial_2(nnn):=nnn! (%i211) 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) (%i212) 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) (%i213) log10(x):=log(x)/glob_log_10 (%i214) expt(x,y):=(if x <= 0.0 and y < 0.0 then print("expt error x = ",x,"y = ",y),x^y) (%i215) 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 /sqrt(estimated_steps) /MAX_TERMS), omniout_float(ALWAYS,"step_error",32, step_error,32,""), step_error) (%i216) exact_soln_y(x):=block(1.0/x/x) 1.0 --- x (%o216) exact_soln_y(x) := block(---) x (%i217) display_poles():=( block(mode_declare([[rad_given],convfloat]), if glob_type_given_pole = 1 or glob_type_given_pole = 2 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])), 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," "), if rad_given < glob_least_given_sing then glob_least_given_sing :rad_given) elseif glob_type_given_pole = 3 then omniout_str(ALWAYS, "NO POLE (given) for Equation 1") elseif glob_type_given_pole = 5 then omniout_str(ALWAYS, "SOME 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) (%i218) my_check_sign(x0,xf):=block([ret],if xf > x0 then ret:1.0 else ret:-1.0,ret) (%i219) 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) (%i220) 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) (%i221) track_estimated_error():=block( [hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms, est_tmp],no_terms:MAX_TERMS,hn_div_ho:0.5, hn_div_ho_2:0.25,hn_div_ho_3:0.125, est_tmp:abs(array_y[no_terms])*hn_div_ho_3 +abs(array_y[no_terms-1])*hn_div_ho_2 +abs(array_y[no_terms-2])*hn_div_ho +abs(array_y[no_terms-3]), if glob_prec*abs(array_y[1]) > est_tmp then est_tmp:glob_prec*abs(array_y[1]), if est_tmp >= array_max_est_error[1] then array_max_est_error[1]:est_tmp) (%i222) 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)) (%i223) display_alot(iter):=( block(mode_declare( [[abserr,est_rel_err],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) > 1.0E-33 then ( relerr :abserr*100.0 /abs(analytic_val_y), if relerr > 1.0E-33 then glob_good_digits :3-floor(log10(relerr)) else glob_good_digits:16) else (relerr:-1.0, glob_good_digits:-16), if abs(numeric_val) > 1.0E-33 then ( est_rel_err :array_max_est_error[1] *100.0*sqrt(glob_iter)*22 *MAX_TERMS /abs(numeric_val), if est_rel_err > 1.0E-33 then glob_est_digits :2 -floor( log10(est_rel_err)) else glob_est_digits :16) else (relerr:-1.0, glob_est_digits:-16), array_est_digits[1] :glob_est_digits, array_good_digits[1] :glob_good_digits, if glob_iter = 1 then array_1st_rel_error[1] :relerr else array_last_rel_error[ 1] :relerr, array_est_rel_error[1] :est_rel_err, omniout_float(ALWAYS, "absolute error ", 4,abserr,20," "), omniout_float(ALWAYS, "relative error ", 4,relerr,20,"%"), omniout_int(INFO, "Desired digits ", 32, glob_desired_digits_correct, 4," "), omniout_int(INFO, "Estimated correct digits ", 32,glob_est_digits, 4," "), omniout_int(INFO, "Correct digits ", 32, glob_good_digits,4, " "), omniout_float(ALWAYS, "h ", 4,glob_h,20, " ")))),0) (%i224) 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) (%i225) 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),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)), 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)), 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, omniout_str(ALWAYS, "SETTING H FOR POLE"), glob_h_reason:6, if glob_check_sign*glob_min_h > glob_check_sign*h_new then ( omniout_str(ALWAYS, "SETTING H FOR MIN H"), h_new:glob_min_h,glob_h_reason:5), 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) (%i226) atomall():=( block(mode_declare([[kkk,order_d],fixnum, [adj2,adj3,temporary,term,temp,temp2], convfloat]), array_tmp1[1]:array_m1[1]*array_const_2D0[1], array_tmp2[1]:array_tmp1[1]/array_x[1], array_tmp3[1]:array_tmp2[1]/array_x[1], array_tmp4[1]:array_tmp3[1]/array_x[1], array_tmp5[1]:array_tmp4[1]+array_const_0D0[1], if not array_y_set_initial[1,2] then (if 1 <= MAX_TERMS then ( temporary :array_tmp5[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_tmp1[2]:array_m1[2]*array_const_2D0[1], array_tmp2[2]:(array_tmp1[2]-array_tmp2[1]*array_x[2]) /array_x[1], array_tmp3[2]:(array_tmp2[2]-array_tmp3[1]*array_x[2]) /array_x[1], array_tmp4[2]:(array_tmp3[2]-array_tmp4[1]*array_x[2]) /array_x[1],array_tmp5[2]:array_tmp4[2], if not array_y_set_initial[1,3] then (if 2 <= MAX_TERMS then ( temporary :array_tmp5[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_tmp1[3]:array_m1[3]*array_const_2D0[1], array_tmp2[3]:(array_tmp1[3]-array_tmp2[2]*array_x[2]) /array_x[1], array_tmp3[3]:(array_tmp2[3]-array_tmp3[2]*array_x[2]) /array_x[1], array_tmp4[3]:(array_tmp3[3]-array_tmp4[2]*array_x[2]) /array_x[1],array_tmp5[3]:array_tmp4[3], if not array_y_set_initial[1,4] then (if 3 <= MAX_TERMS then ( temporary :array_tmp5[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_tmp1[4]:array_m1[4]*array_const_2D0[1], array_tmp2[4]:(array_tmp1[4]-array_tmp2[3]*array_x[2]) /array_x[1], array_tmp3[4]:(array_tmp2[4]-array_tmp3[3]*array_x[2]) /array_x[1], array_tmp4[4]:(array_tmp3[4]-array_tmp4[3]*array_x[2]) /array_x[1],array_tmp5[4]:array_tmp4[4], if not array_y_set_initial[1,5] then (if 4 <= MAX_TERMS then ( temporary :array_tmp5[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_tmp1[5]:array_m1[5]*array_const_2D0[1], array_tmp2[5]:(array_tmp1[5]-array_tmp2[4]*array_x[2]) /array_x[1], array_tmp3[5]:(array_tmp2[5]-array_tmp3[4]*array_x[2]) /array_x[1], array_tmp4[5]:(array_tmp3[5]-array_tmp4[4]*array_x[2]) /array_x[1],array_tmp5[5]:array_tmp4[5], if not array_y_set_initial[1,6] then (if 5 <= MAX_TERMS then ( temporary :array_tmp5[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_tmp1[kkk]:array_m1[kkk]*array_const_2D0[1], array_tmp2[kkk] :(-ats(kkk,array_x,array_tmp2,2))/array_x[1], array_tmp3[kkk] :(-ats(kkk,array_x,array_tmp3,2))/array_x[1], array_tmp4[kkk] :(-ats(kkk,array_x,array_tmp4,2))/array_x[1], array_tmp5[kkk]:array_tmp4[kkk],order_d:1, if order_d+kkk <= MAX_TERMS then (if not array_y_set_initial[1,order_d+kkk] then ( temporary :array_tmp5[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) (%i227) exact_soln_y(x):=block(1.0/x/x) 1.0 --- x (%o227) exact_soln_y(x) := block(---) x (%i228) 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,last_min_pole_est], convfloat,[repeat_it],fixnum],[found_h], boolean),Digits:32,max_terms:20, 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_est_rel_error[term]:0.0,term:1+term),term:1, while term <= 2 do (array_max_est_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 <= 2 do (array_est_digits[term]:0,term:1+term), term:1, while term <= 2 do (array_good_digits[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[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_tmp4[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp5[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 <= 4 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 <= 4 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_m1),zero_ats_ar(array_tmp0), zero_ats_ar(array_tmp1),zero_ats_ar(array_tmp2), zero_ats_ar(array_tmp3),zero_ats_ar(array_tmp4), zero_ats_ar(array_tmp5),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_2D0), array_const_2D0[1]:2.0,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,ALWAYS:1,INFO:2,DEBUGL:3, DEBUGMASSIVE:4,MAX_TERMS:20,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/sing3postode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ; "), omniout_str(ALWAYS,"!"), omniout_str(ALWAYS,"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS,"Digits:32,"), omniout_str(ALWAYS,"max_terms:20,"),omniout_str(ALWAYS,"!"), omniout_str(ALWAYS,"/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS,"/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS,"x_start:-2.0,"), omniout_str(ALWAYS,"x_end:-0.7,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS,"glob_look_poles:true,"), omniout_str(ALWAYS,""),omniout_str(ALWAYS,""), omniout_str(ALWAYS,""),omniout_str(ALWAYS,""), omniout_str(ALWAYS,""),omniout_str(ALWAYS,""), omniout_str(ALWAYS,""),omniout_str(ALWAYS,""), omniout_str(ALWAYS,"glob_type_given_pole:1,"), omniout_str(ALWAYS,""), omniout_str(ALWAYS,"array_given_rad_poles[1,1]:0.0,"), omniout_str(ALWAYS,""), omniout_str(ALWAYS,"array_given_rad_poles[1,2]:0.0,"), omniout_str(ALWAYS,""), omniout_str(ALWAYS,"array_given_ord_poles[1,1]:2.0,"), omniout_str(ALWAYS,""), omniout_str(ALWAYS,"array_given_ord_poles[1,2]:0.0,"), 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:100000000,"), 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," (1.0/x/x) "),omniout_str(ALWAYS,"));"), omniout_str(ALWAYS,""),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:-2.0,x_end:-0.7, array_y_init[1+0]:exact_soln_y(x_start), glob_look_poles:true,glob_type_given_pole:1, array_given_rad_poles[1,1]:0.0, array_given_rad_poles[1,2]:0.0, array_given_ord_poles[1,1]:2.0, array_given_ord_poles[1,2]:0.0, glob_desired_digits_correct:10,glob_display_interval:0.01, glob_look_poles:true,glob_max_iter:100000000, 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_min_pole_est:glob_larger_float, last_min_pole_est:glob_larger_float, glob_least_given_sing:glob_larger_float, glob_least_ratio_sing:glob_larger_float, glob_least_3_sing:glob_larger_float, glob_least_6_sing:glob_larger_float, glob_min_h:abs(glob_min_h)*glob_check_sign, glob_max_h:abs(glob_max_h)*glob_check_sign, glob_h:abs(glob_min_h)*glob_check_sign, glob_display_interval:abs(glob_display_interval) *glob_check_sign,chk_data(), 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(), if glob_check_sign*glob_max_h <= glob_check_sign*glob_h then (omniout_str(ALWAYS,"SETTING H FOR MAX H"), glob_h:glob_check_sign*abs(glob_max_h), glob_h_reason:1,found_h:true), if glob_check_sign*glob_display_interval <= glob_check_sign*glob_h then (omniout_str(ALWAYS, "SETTING H FOR DISPLAY INTERVAL"), glob_h_reason:2, glob_h:glob_display_interval,found_h:true), if glob_look_poles then (check_for_pole(), if opt_iter > 2 and not found_h and (glob_min_pole_est < 0.999*last_min_pole_est or glob_min_pole_est > 1.111 *last_min_pole_est) then ( omniout_str(ALWAYS, "SETTING H FOR POLE ACCURACY"), glob_h_reason:4,found_h:true, glob_h:glob_h/2.0, last_min_pole_est:glob_min_pole_est) else last_min_pole_est :glob_min_pole_est), if not found_h then (est_answer:est_size_answer(), 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:test_suggested_h(), omniout_float(ALWAYS, "estimated_step_error",32, estimated_step_error,32,""), if estimated_step_error < est_needed_step_err then ( omniout_str(ALWAYS, "Double H and LOOP"), glob_h:glob_h*2.0) else ( omniout_str(ALWAYS, "Found H for OPTIMAL"), found_h:true,glob_h_reason:3, glob_h:glob_h/2.0)), 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 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, glob_min_pole_est:glob_larger_float, glob_least_given_sing:glob_larger_float, glob_least_ratio_sing:glob_larger_float, glob_least_3_sing:glob_larger_float, glob_least_6_sing:glob_larger_float,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(), track_estimated_error(), glob_current_iter:1+glob_current_iter, atomall(),track_estimated_error(), display_alot(current_iter), 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 ) = m1 * 2.0 / x / x / 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, "2014-01-31T14:02:35-06:00"), logitem_str(html_log_file,"Maxima"), logitem_str(html_log_file, "sing3"), logitem_str(html_log_file, "diff ( y , x , 1 ) = m1 * 2.0 / x / x / 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_h_reason(html_log_file), logitem_str(html_log_file,"16"), logitem_float(html_log_file, glob_desired_digits_correct), if array_est_digits[1] # -16 then ( logitem_integer(html_log_file, array_est_digits[ 1]),0) else ( logitem_str(html_log_file, "Unknown"),0), if array_good_digits[1] # -16 then ( logitem_integer(html_log_file, array_good_digits[ 1]),0) else ( logitem_str(html_log_file, "Unknown"),0), logitem_integer(html_log_file, MAX_TERMS), if glob_type_given_pole = 0 then ( logitem_str(html_log_file, "Not Given"), logitem_str(html_log_file,"NA"),0) elseif glob_type_given_pole = 4 then ( logitem_str(html_log_file, "No Solution"), logitem_str(html_log_file,"NA"),0) elseif glob_type_given_pole = 5 then ( logitem_str(html_log_file, "Some Pole"), logitem_str(html_log_file,"????"),0) elseif glob_type_given_pole = 3 then ( logitem_str(html_log_file, "No Pole"), logitem_str(html_log_file,"NA"),0) elseif glob_type_given_pole = 1 then ( logitem_str(html_log_file, "Real Sing"), logitem_float(html_log_file, glob_least_given_sing), 0) elseif glob_type_given_pole = 2 then ( logitem_str(html_log_file, "Complex Sing"), logitem_float(html_log_file, glob_least_given_sing), 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, " 257 "), logitem_str(html_log_file, "sing3 diffeq.max"), logitem_str(html_log_file, "sing3 maxima results"), logitem_str(html_log_file,"OK"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%i229) main():=(alias(convfloat,convfloat),compile(all),main_prog()) (%i230) 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. warning: encountered undefined variable glob_h_reason 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. 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_x in translation. warning: encountered undefined variable array_given_rad_poles in translation. warning: encountered undefined variable ALWAYS in translation. warning: encountered undefined variable rad_given in translation. warning: encountered undefined variable array_given_ord_poles 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 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. warning: encountered undefined variable MAX_TERMS in translation. warning: encountered undefined variable glob_prec in translation. warning: encountered undefined variable array_max_est_error 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 glob_iter in translation. warning: encountered undefined variable MAX_TERMS in translation. warning: encountered undefined variable est_rel_err in translation. warning: variable glob_est_digits (declared type fixnum) assigned type any. warning: encountered undefined variable glob_est_digits in translation. warning: encountered undefined variable array_est_digits in translation. warning: encountered undefined variable glob_good_digits in translation. warning: encountered undefined variable array_good_digits in translation. warning: encountered undefined variable array_1st_rel_error in translation. warning: encountered undefined variable array_last_rel_error in translation. warning: encountered undefined variable array_est_rel_error in translation. warning: encountered undefined variable INFO in translation. warning: encountered undefined variable glob_desired_digits_correct 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 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: encountered undefined variable array_y_higher 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 ALWAYS in translation. warning: encountered undefined variable glob_min_h in translation. warning: encountered undefined variable h_new in translation. warning: encountered undefined variable term in translation. warning: encountered undefined variable ratio 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_m1 in translation. warning: encountered undefined variable array_const_2D0 in translation. warning: encountered undefined variable array_tmp1 in translation. warning: encountered undefined variable array_tmp2 in translation. warning: encountered undefined variable array_tmp3 in translation. warning: encountered undefined variable array_tmp4 in translation. warning: encountered undefined variable array_const_0D0 in translation. warning: encountered undefined variable array_tmp5 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: [found_h] is not a built-in type; assuming it is a Maxima extension type. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: variable term (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable MAX_TERMS in translation. warning: encountered undefined variable array_y_init in translation. warning: variable term (declared type [found_h]) assigned type any. 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: variable ord (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable ord in translation. warning: variable ord (declared type [found_h]) assigned type any. 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: variable iiif (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable iiif in translation. warning: variable jjjf (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable jjjf in translation. warning: variable jjjf (declared type [found_h]) assigned type any. warning: variable iiif (declared type [found_h]) assigned type any. warning: encountered undefined variable INFO in translation. warning: variable glob_orig_start_sec (declared type convfloat) assigned type any. warning: variable opt_iter (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable ALWAYS in translation. warning: variable x_start (declared type [found_h]) assigned type convfloat. warning: variable x_end (declared type [found_h]) assigned type convfloat. 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_larger_float in translation. warning: variable last_min_pole_est (declared type [found_h]) assigned type convfloat. 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: variable min_value (declared type [found_h]) assigned type convfloat. warning: variable est_answer (declared type [found_h]) assigned type any. warning: encountered undefined variable est_answer in translation. warning: variable est_needed_step_err (declared type [found_h]) assigned type any. warning: encountered undefined variable est_needed_step_err in translation. warning: variable estimated_step_error (declared type [found_h]) assigned type convfloat. 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 [found_h]. warning: variable order_diff (declared type [found_h]) assigned type fixnum. warning: variable term_no (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable order_diff in translation. warning: variable term_no (declared type [found_h]) assigned type any. warning: variable r_order (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable r_order in translation. warning: encountered undefined variable rows in translation. warning: variable it (declared type [found_h]) assigned type any. warning: encountered undefined variable it in translation. warning: variable r_order (declared type [found_h]) assigned type any. warning: encountered undefined variable glob_min_pole_est in translation. warning: encountered undefined variable last_min_pole_est in translation. warning: encountered undefined variable glob_look_poles in translation. warning: variable estimated_step_error (declared type [found_h]) assigned type any. warning: encountered undefined variable estimated_step_error in translation. warning: variable opt_iter (declared type [found_h]) assigned type any. warning: variable html_log_file (declared type [found_h]) assigned type any. warning: encountered undefined variable glob_html_log in translation. warning: variable current_iter (declared type [found_h]) assigned type fixnum. 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_next_display in translation. warning: variable calc_term (declared type [found_h]) assigned type fixnum. warning: variable iii (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable calc_term in translation. warning: variable iii (declared type [found_h]) assigned type any. warning: variable temp_sum (declared type [found_h]) assigned type convfloat. warning: encountered undefined variable temp_sum in translation. warning: variable temp_sum (declared type [found_h]) assigned type any. warning: encountered undefined variable html_log_file in translation. warning: encountered undefined variable glob_desired_digits_correct in translation. warning: encountered undefined variable glob_type_given_pole in translation. warning: encountered undefined variable glob_least_given_sing in translation. warning: encountered undefined variable glob_least_ratio_sing in translation. warning: encountered undefined variable glob_large_float 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 $MAIN_PROG : |$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 : $MIN_VALUE is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_REACHED_OPTIMAL_H 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/sing3postode.ode#################" "diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ; " "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:20," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:-2.0," "x_end:-0.7," "array_y_init[0 + 1] : exact_soln_y(x_start)," "glob_look_poles:true," "" "" "" "" "" "" "" "" "glob_type_given_pole:1," "" "array_given_rad_poles[1,1]:0.0," "" "array_given_rad_poles[1,2]:0.0," "" "array_given_ord_poles[1,1]:2.0," "" "array_given_ord_poles[1,2]:0.0," "/* END SECOND INPUT BLOCK */" "/* BEGIN OVERRIDE BLOCK */" "glob_desired_digits_correct:10," "glob_display_interval:0.01," "glob_look_poles:true," "glob_max_iter:100000000," "glob_max_minutes:10.0," "glob_subiter_method:3," "/* END OVERRIDE BLOCK */" "!" "/* BEGIN USER DEF BLOCK */" "exact_soln_y (x) := (block(" " (1.0/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 = 1.3 "" estimated_steps = 1300000. "" step_error = 4.385290096535146000000000000000E-15 "" est_needed_step_err = 4.385290096535146000000000000000E-15 "" opt_iter = 1 Radius of convergence (given) for eq 1 = 2. " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.000000000000008 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" min_size = 0.25 "" min_size = 1. "" glob_desired_digits_correct = 10. "" estimated_h = 1.000000E-6 "" estimated_answer = 1. "" desired_abs_gbl_error = 1.0000000000E-10 "" range = 1.3 "" estimated_steps = 1300000. "" step_error = 4.385290096535146000000000000000E-15 "" est_needed_step_err = 4.385290096535146000000000000000E-15 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 7.152559056001943000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-102 "" estimated_step_error = 7.152559056001943000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-102 "" "Double H and LOOP" opt_iter = 2 Radius of convergence (given) for eq 1 = 2. " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.000000000000008 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" min_size = 0.25 "" min_size = 1. "" glob_desired_digits_correct = 10. "" estimated_h = 2.000000E-6 "" estimated_answer = 1. "" desired_abs_gbl_error = 1.0000000000E-10 "" range = 1.3 "" estimated_steps = 650000. "" step_error = 6.201736729460423000000000000000E-15 "" est_needed_step_err = 6.201736729460423000000000000000E-15 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 4.687502205883390400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-97 "" estimated_step_error = 4.687502205883390400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-97 "" "Double H and LOOP" opt_iter = 3 Radius of convergence (given) for eq 1 = 2. " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.000000000000008 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" min_size = 0.25 "" min_size = 1. "" glob_desired_digits_correct = 10. "" estimated_h = 4.000000E-6 "" estimated_answer = 1. "" desired_abs_gbl_error = 1.0000000000E-10 "" range = 1.3 "" estimated_steps = 325000. "" step_error = 8.770580193070292000000000000000E-15 "" est_needed_step_err = 8.770580193070292000000000000000E-15 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 3.07200289129684600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-92 "" estimated_step_error = 3.07200289129684600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-92 "" "Double H and LOOP" opt_iter = 4 Radius of convergence (given) for eq 1 = 2. " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.000000000000008 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" min_size = 0.25 "" min_size = 1. "" glob_desired_digits_correct = 10. "" estimated_h = 8.000000E-6 "" estimated_answer = 1. "" desired_abs_gbl_error = 1.0000000000E-10 "" range = 1.3 "" estimated_steps = 162500. "" step_error = 1.240347345892084700000000000000E-14 "" est_needed_step_err = 1.240347345892084700000000000000E-14 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 2.0132697096841826000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-87 "" estimated_step_error = 2.0132697096841826000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-87 "" "Double H and LOOP" opt_iter = 5 Radius of convergence (given) for eq 1 = 2. " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.000000000000008 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" min_size = 0.25 "" min_size = 1. "" glob_desired_digits_correct = 10. "" estimated_h = 1.600000E-5 "" estimated_answer = 1. "" desired_abs_gbl_error = 1.0000000000E-10 "" range = 1.3 "" estimated_steps = 81250. "" step_error = 1.754116038614058300000000000000E-14 "" est_needed_step_err = 1.754116038614058300000000000000E-14 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.31941892055543550000000000000000000000000000000000000000000000000000000000000000000000000000000000E-82 "" estimated_step_error = 1.31941892055543550000000000000000000000000000000000000000000000000000000000000000000000000000000000E-82 "" "Double H and LOOP" opt_iter = 6 Radius of convergence (given) for eq 1 = 2. " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.000000000000008 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" min_size = 0.25 "" min_size = 1. "" glob_desired_digits_correct = 10. "" estimated_h = 3.200000E-5 "" estimated_answer = 1. "" desired_abs_gbl_error = 1.0000000000E-10 "" range = 1.3 "" estimated_steps = 40625. "" step_error = 2.480694691784169300000000000000E-14 "" est_needed_step_err = 2.480694691784169300000000000000E-14 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 8.646976391198815000000000000000000000000000000000000000000000000000000000000000000000000000000E-78 "" estimated_step_error = 8.646976391198815000000000000000000000000000000000000000000000000000000000000000000000000000000E-78 "" "Double H and LOOP" opt_iter = 7 Radius of convergence (given) for eq 1 = 2. " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.000000000000008 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" min_size = 0.25 "" min_size = 1. "" glob_desired_digits_correct = 10. "" estimated_h = 6.400000E-5 "" estimated_answer = 1. "" desired_abs_gbl_error = 1.0000000000E-10 "" range = 1.3 "" estimated_steps = 20312.5 "" step_error = 3.50823207722811670000000000000E-14 "" est_needed_step_err = 3.50823207722811670000000000000E-14 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 5.6669251166733180000000000000000000000000000000000000000000000000000000000000000000000000E-73 "" estimated_step_error = 5.6669251166733180000000000000000000000000000000000000000000000000000000000000000000000000E-73 "" "Double H and LOOP" opt_iter = 8 Radius of convergence (given) for eq 1 = 2. " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.000000000000008 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" min_size = 0.25 "" min_size = 1. "" glob_desired_digits_correct = 10. "" estimated_h = 1.280000E-4 "" estimated_answer = 1. "" desired_abs_gbl_error = 1.0000000000E-10 "" range = 1.3 "" estimated_steps = 10156.25 "" step_error = 4.961389383568338700000000000000E-14 "" est_needed_step_err = 4.961389383568338700000000000000E-14 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 3.71393197276019100000000000000000000000000000000000000000000000000000000000000000000E-68 "" estimated_step_error = 3.71393197276019100000000000000000000000000000000000000000000000000000000000000000000E-68 "" "Double H and LOOP" opt_iter = 9 Radius of convergence (given) for eq 1 = 2. " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.000000000000008 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" min_size = 0.25 "" min_size = 1. "" glob_desired_digits_correct = 10. "" estimated_h = 2.560000E-4 "" estimated_answer = 1. "" desired_abs_gbl_error = 1.0000000000E-10 "" range = 1.3 "" estimated_steps = 5078.125 "" step_error = 7.01646415445623300000000000000E-14 "" est_needed_step_err = 7.01646415445623300000000000000E-14 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 2.4340357673292026000000000000000000000000000000000000000000000000000000000000000E-63 "" estimated_step_error = 2.4340357673292026000000000000000000000000000000000000000000000000000000000000000E-63 "" "Double H and LOOP" opt_iter = 10 Radius of convergence (given) for eq 1 = 2. " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.000000000000008 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" min_size = 0.25 "" min_size = 1. "" glob_desired_digits_correct = 10. "" estimated_h = 5.120000E-4 "" estimated_answer = 1. "" desired_abs_gbl_error = 1.0000000000E-10 "" range = 1.3 "" estimated_steps = 2539.0625 "" step_error = 9.92277876713667700000000000000E-14 "" est_needed_step_err = 9.92277876713667700000000000000E-14 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.59526577762891840000000000000000000000000000000000000000000000000000000000E-58 "" estimated_step_error = 1.59526577762891840000000000000000000000000000000000000000000000000000000000E-58 "" "Double H and LOOP" opt_iter = 11 Radius of convergence (given) for eq 1 = 2. " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.000000000000008 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" min_size = 0.25 "" min_size = 1. "" glob_desired_digits_correct = 10. "" estimated_h = 1.024000E-3 "" estimated_answer = 1. "" desired_abs_gbl_error = 1.0000000000E-10 "" range = 1.3 "" estimated_steps = 1269.53125 "" step_error = 1.40329283089124680000000000000E-13 "" est_needed_step_err = 1.40329283089124680000000000000E-13 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.045599359331681700000000000000000000000000000000000000000000000000000E-53 "" estimated_step_error = 1.045599359331681700000000000000000000000000000000000000000000000000000E-53 "" "Double H and LOOP" opt_iter = 12 Radius of convergence (given) for eq 1 = 2. " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.000000000000008 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" min_size = 0.25 "" min_size = 1. "" glob_desired_digits_correct = 10. "" estimated_h = 2.048000E-3 "" estimated_answer = 1. "" desired_abs_gbl_error = 1.0000000000E-10 "" range = 1.3 "" estimated_steps = 634.765625 "" step_error = 1.98455575342733560000000000000E-13 "" est_needed_step_err = 1.98455575342733560000000000000E-13 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 6.8540917963991140000000000000000000000000000000000000000000000000E-49 "" estimated_step_error = 6.8540917963991140000000000000000000000000000000000000000000000000E-49 "" "Double H and LOOP" opt_iter = 13 Radius of convergence (given) for eq 1 = 2. " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.000000000000008 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" min_size = 0.25 "" min_size = 1. "" glob_desired_digits_correct = 10. "" estimated_h = 4.096000E-3 "" estimated_answer = 1. "" desired_abs_gbl_error = 1.0000000000E-10 "" range = 1.3 "" estimated_steps = 317.3828125 "" step_error = 2.80658566178249360000000000000E-13 "" est_needed_step_err = 2.80658566178249360000000000000E-13 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 4.49406426490768600000000000000000000000000000000000000000000E-44 "" estimated_step_error = 4.49406426490768600000000000000000000000000000000000000000000E-44 "" "Double H and LOOP" opt_iter = 14 Radius of convergence (given) for eq 1 = 2. " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.000000000000008 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" min_size = 0.25 "" min_size = 1. "" glob_desired_digits_correct = 10. "" estimated_h = 8.192000E-3 "" estimated_answer = 1. "" desired_abs_gbl_error = 1.0000000000E-10 "" range = 1.3 "" estimated_steps = 158.69140625 "" step_error = 3.9691115068546710000000000000E-13 "" est_needed_step_err = 3.9691115068546710000000000000E-13 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 2.948073975815616000000000000000000000000000000000000000E-39 "" estimated_step_error = 2.948073975815616000000000000000000000000000000000000000E-39 "" "Double H and LOOP" opt_iter = 15 "SETTING H FOR DISPLAY INTERVAL" Radius of convergence (given) for eq 1 = 2. " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.2207031250000049 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" "START of Soultion" " " "TOP MAIN SOLVE Loop" x[1] = -2. " " y[1] (analytic) = 0.25 " " y[1] (numeric) = 0.25 " " absolute error = 0.0 " " relative error = 0.0 "%" Desired digits = 10 Estimated correct digits = 14 Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2. " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.0000000000000084 " " Order of pole (three term test) = 6.58359363706014900000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.99 " " y[1] (analytic) = 0.25251887578596494 " " y[1] (numeric) = 0.2525188757859571 " " absolute error = 7.827072323607354000000000000000E-15 " " relative error = 3.099598910871749000000000000E-12 "%" Desired digits = 10 Estimated correct digits = 14 Correct digits = 15 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.99 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.9900000000000033 " " Order of pole (three term test) = 2.832209945658366000000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.98 " " y[1] (analytic) = 0.25507601265177027 " " y[1] (numeric) = 0.2550760126517541 " " absolute error = 1.615374500829602800000000000000E-14 " " relative error = 6.332914193052374000000000000E-12 "%" Desired digits = 10 Estimated correct digits = 14 Correct digits = 15 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.98 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.9799999999999944 " " Order of pole (three term test) = 2.434943335785029700000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.97 " " y[1] (analytic) = 0.25767218944059367 " " y[1] (numeric) = 0.257672189440569 " " absolute error = 2.464695114667847500000000000000E-14 " " relative error = 9.565235270514449000000000000E-12 "%" Desired digits = 10 Estimated correct digits = 14 Correct digits = 15 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.97 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.970000000000003 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.96 " " y[1] (analytic) = 0.2603082049146189 " " y[1] (numeric) = 0.26030820491458534 " " absolute error = 3.358424649491098500000000000000E-14 " " relative error = 1.290172413348500400000000000E-11 "%" Desired digits = 10 Estimated correct digits = 14 Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.96 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.9600000000000055 " " Order of pole (three term test) = 3.591247094202294500000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.95 " " y[1] (analytic) = 0.2629848783694938 " " y[1] (numeric) = 0.2629848783694509 " " absolute error = 4.2910119901762300000000000000E-14 " " relative error = 1.63165730926451120000000000E-11 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.95 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.9500000000000048 " " Order of pole (three term test) = 3.08036008903220140000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.94 " " y[1] (analytic) = 0.26570305027101715 " " y[1] (numeric) = 0.2657030502709646 " " absolute error = 5.25690602160011600000000000000E-14 " " relative error = 1.978489150289419500000000000E-11 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.94 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.9400000000000068 " " Order of pole (three term test) = 7.92020275463060600000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.93 " " y[1] (analytic) = 0.2684635829149776 " " y[1] (numeric) = 0.268463582914915 " " absolute error = 6.26165785888588300000000000000E-14 " " relative error = 2.33240493585640200000000000E-11 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.93 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.9300000000000084 " " Order of pole (three term test) = 9.04362214155689300000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.92 " " y[1] (analytic) = 0.27126736111111116 " " y[1] (numeric) = 0.27126736111103805 " " absolute error = 7.31081861715665600000000000000E-14 " " relative error = 2.695060175028629000000000000E-11 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.92 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.9200000000000075 " " Order of pole (three term test) = 3.86927862035032160000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.91 " " y[1] (analytic) = 0.27411529289219044 " " y[1] (numeric) = 0.27411529289210645 " " absolute error = 8.39883718128930900000000000000E-14 " " relative error = 3.06397979210615300000000000E-11 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.91 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.9100000000000044 " " Order of pole (three term test) = 3.30821830232209800000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.9 " " y[1] (analytic) = 0.27700831024930744 " " y[1] (numeric) = 0.2770083102492121 " " absolute error = 9.53681578153009500000000000000E-14 " " relative error = 3.44279049713236400000000000E-11 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.9 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.900000000000003 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.89 " " y[1] (analytic) = 0.27994736989445995 " " y[1] (numeric) = 0.27994736989435254 " " absolute error = 1.0741407763248390000000000000E-13 " " relative error = 3.83693826710995560000000000E-11 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.89 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.8900000000000015 " " Order of pole (three term test) = 2.412388601478813700000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.88 " " y[1] (analytic) = 0.282933454051607 " " y[1] (numeric) = 0.28293345405148734 " " absolute error = 1.19682042054591880000000000000E-13 " " relative error = 4.23004209437749600000000000E-11 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.88 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.8800000000000021 " " Order of pole (three term test) = 4.11489365805531640000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.8699999999999999 " " y[1] (analytic) = 0.2859675712774172 " " y[1] (numeric) = 0.2859675712772845 " " absolute error = 1.3267165144270620000000000000E-13 " " relative error = 4.63939497929999330000000000E-11 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.8699999999999999 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.8700000000000034 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.8599999999999999 " " y[1] (analytic) = 0.28905075731298424 " " y[1] (numeric) = 0.289050757312838 " " absolute error = 1.46216372343133120000000000000E-13 " " relative error = 5.05850161758303200000000000E-11 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.8599999999999999 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.8600000000000003 " " Order of pole (three term test) = 2.98546142989950300000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.8499999999999999 " " y[1] (analytic) = 0.2921840759678598 " " y[1] (numeric) = 0.2921840759676995 " " absolute error = 1.60260693604641350000000000000E-13 " " relative error = 5.4849222386188500000000000E-11 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.8499999999999999 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.8500000000000068 " " Order of pole (three term test) = 2.539656558584166000000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.8399999999999999 " " y[1] (analytic) = 0.2953686200378073 " " y[1] (numeric) = 0.2953686200376322 " " absolute error = 1.75082170983387200000000000000E-13 " " relative error = 5.92758198081355400000000000E-11 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.8399999999999999 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.8400000000000045 " " Order of pole (three term test) = 4.31705741060590230000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.8299999999999998 " " y[1] (analytic) = 0.29860551225775633 " " y[1] (numeric) = 0.29860551225756593 " " absolute error = 1.90403248723214350000000000000E-13 " " relative error = 6.37641439649172500000000000E-11 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.8299999999999998 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.8300000000000074 " " Order of pole (three term test) = 3.66594399409455100000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.8199999999999998 " " y[1] (analytic) = 0.30189590629151075 " " y[1] (numeric) = 0.30189590629130425 " " absolute error = 2.06501482580279120000000000000E-13 " " relative error = 6.84015510898916400000000000E-11 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.8199999999999998 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.8200000000000023 " " Order of pole (three term test) = 3.110246237949861300000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.8099999999999998 " " y[1] (analytic) = 0.30524098775983644 " " y[1] (numeric) = 0.30524098775961317 " " absolute error = 2.23265850252118980000000000000E-13 " " relative error = 7.3144125201096700000000000E-11 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.8099999999999998 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.8100000000000085 " " Order of pole (three term test) = 5.272788793840947000000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.7999999999999998 " " y[1] (analytic) = 0.308641975308642 " " y[1] (numeric) = 0.3086419753084012 " " absolute error = 2.40807374041196450000000000000E-13 " " relative error = 7.80215891893476500000000000E-11 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.7999999999999998 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.8000000000000034 " " Order of pole (three term test) = 4.465378558213156700000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.7899999999999998 " " y[1] (analytic) = 0.31210012171904755 " " y[1] (numeric) = 0.31210012171878837 " " absolute error = 2.5918156509874280000000000000E-13 " " relative error = 8.30443652732881600000000000E-11 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.7899999999999998 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.7900000000000014 " " Order of pole (three term test) = 3.77810530810207200000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.7799999999999998 " " y[1] (analytic) = 0.3156167150612297 " " y[1] (numeric) = 0.31561671506095135 " " absolute error = 2.78332912273526740000000000000E-13 " " relative error = 8.8186999924744200000000000E-11 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.7799999999999998 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.780000000000005 " " Order of pole (three term test) = 6.38723940358978400000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.7699999999999998 " " y[1] (analytic) = 0.3191930798940279 " " y[1] (numeric) = 0.3191930798937295 " " absolute error = 2.9837243786801080000000000000E-13 " " relative error = 9.34771010596691100000000000E-11 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.7699999999999998 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.7700000000000067 " " Order of pole (three term test) = 5.39400216062058600000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.7599999999999998 " " y[1] (analytic) = 0.32283057851239677 " " y[1] (numeric) = 0.32283057851207736 " " absolute error = 3.19411164184657540000000000000E-13 " " relative error = 9.89408022178395100000000000E-11 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.7599999999999998 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.7600000000000073 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.7499999999999998 " " y[1] (analytic) = 0.32653061224489804 " " y[1] (numeric) = 0.32653061224455665 " " absolute error = 3.41393580072235640000000000000E-13 " " relative error = 1.04551783897122140000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.7499999999999998 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.75 " " Order of pole (three term test) = 3.835787908616166000000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.7399999999999998 " " y[1] (analytic) = 0.3302946228035408 " " y[1] (numeric) = 0.33029462280317645 " " absolute error = 3.6437519668197640000000000000E-13 " " relative error = 1.10318234547435140000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.7399999999999998 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.7400000000000015 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.7299999999999998 " " y[1] (analytic) = 0.3341240936883959 " " y[1] (numeric) = 0.3341240936880075 " " absolute error = 3.884115251651110000000000000E-13 " " relative error = 1.16247685366666060000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.7299999999999998 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.7300000000000058 " " Order of pole (three term test) = 5.43408233958992600000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.7199999999999998 " " y[1] (analytic) = 0.3380205516495403 " " y[1] (numeric) = 0.3380205516491267 " " absolute error = 4.13613587824102070000000000000E-13 " " relative error = 1.22363443821882340000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.7199999999999998 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.7200000000000046 " " Order of pole (three term test) = 4.566637389221818700000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.7099999999999997 " " y[1] (analytic) = 0.34198556820902165 " " y[1] (numeric) = 0.3419855682085816 " " absolute error = 4.4003689581018080000000000000E-13 " " relative error = 1.28671188703854940000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.7099999999999997 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.709999999999998 " " Order of pole (three term test) = 3.833773337088652000000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.6999999999999997 " " y[1] (analytic) = 0.3460207612456749 " " y[1] (numeric) = 0.34602076124520714 " " absolute error = 4.6773696027457845000000000000E-13 " " relative error = 1.35175981519353120000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.6999999999999997 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.7000000000000064 " " Order of pole (three term test) = 6.43044100021650400000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.6899999999999997 " " y[1] (analytic) = 0.35012779664577587 " " y[1] (numeric) = 0.35012779664527915 " " absolute error = 4.967137812172950400000000000E-13 " " relative error = 1.41866423053471580000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.6899999999999997 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.690000000000004 " " Order of pole (three term test) = 8.08100757781193200000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.6799999999999997 " " y[1] (analytic) = 0.3543083900226759 " " y[1] (numeric) = 0.3543083900221488 " " absolute error = 5.2707838094079310000000000000E-13 " " relative error = 1.48762602236729380000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.6799999999999997 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.6800000000000013 " " Order of pole (three term test) = 4.508702379035131600000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.6699999999999997 " " y[1] (analytic) = 0.3585643085087311 " " y[1] (numeric) = 0.3585643085081722 " " absolute error = 5.5888627059630380000000000000E-13 " " relative error = 1.55867792006603140000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.6699999999999997 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.670000000000005 " " Order of pole (three term test) = 3.76935681832030600000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.6599999999999997 " " y[1] (analytic) = 0.3628973726230224 " " y[1] (numeric) = 0.36289737262242994 " " absolute error = 5.9247051709121480000000000000E-13 " " relative error = 1.63261175689655060000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.6599999999999997 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.6600000000000084 " " Order of pole (three term test) = 3.147862527712467000000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.6499999999999997 " " y[1] (analytic) = 0.36730945821854927 " " y[1] (numeric) = 0.36730945821792177 " " absolute error = 6.2749805351813850000000000000E-13 " " relative error = 1.70836345070313120000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.6499999999999997 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.6500000000000037 " " Order of pole (three term test) = 2.625980174613245500000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.6399999999999997 " " y[1] (analytic) = 0.3718024985127901 " " y[1] (numeric) = 0.3718024985121258 " " absolute error = 6.6430194678446240000000000000E-13 " " relative error = 1.78670651607148960000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.6399999999999997 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.640000000000009 " " Order of pole (three term test) = 4.37641556184025400000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.6299999999999997 " " y[1] (analytic) = 0.3763784862057286 " " y[1] (numeric) = 0.3763784862050256 " " absolute error = 7.0299321919264910000000000000E-13 " " relative error = 1.86778268407294900000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.6299999999999997 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.630000000000009 " " Order of pole (three term test) = 3.64276574776413560000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.6199999999999997 " " y[1] (analytic) = 0.38103947568968155 " " y[1] (numeric) = 0.381039475688938 " " absolute error = 7.4357187074269860000000000000E-13 " " relative error = 1.95143001757713760000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.6199999999999997 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.619999999999997 " " Order of pole (three term test) = 3.028681107519511400000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.6099999999999997 " " y[1] (analytic) = 0.38578758535550345 " " y[1] (numeric) = 0.38578758535471713 " " absolute error = 7.8631545719076710000000000000E-13 " " relative error = 2.03820829658418630000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.6099999999999997 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.610000000000001 " " Order of pole (three term test) = 2.51523978077699200000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.5999999999999996 " " y[1] (analytic) = 0.39062500000000017 " " y[1] (numeric) = 0.39062499999916905 " " absolute error = 8.3111295623439220000000000000E-13 " " relative error = 2.1276491679600430000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.5999999999999996 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.6000000000000074 " " Order of pole (three term test) = 4.17284821283900400000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.5899999999999996 " " y[1] (analytic) = 0.3955539733396624 " " y[1] (numeric) = 0.3955539733387841 " " absolute error = 8.7829743478096130000000000000E-13 " " relative error = 2.2204237448697470000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.5899999999999996 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.5900000000000043 " " Order of pole (three term test) = 6.91475557533758800000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.5799999999999996 " " y[1] (analytic) = 0.4005768306361162 " " y[1] (numeric) = 0.4005768306351884 " " absolute error = 9.2781338167924330000000000000E-13 " " relative error = 2.31619332602406160000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.5799999999999996 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.5800000000000054 " " Order of pole (three term test) = 2.86118353057751630000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.5699999999999996 " " y[1] (analytic) = 0.4056959714390039 " " y[1] (numeric) = 0.4056959714380239 " " absolute error = 9.7999386383662570000000000000E-13 " " relative error = 2.4155868749708970000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.5699999999999996 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.570000000000004 " " Order of pole (three term test) = 2.364953903779426200000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.5599999999999996 " " y[1] (analytic) = 0.4109138724523342 " " y[1] (numeric) = 0.41091387245129946 " " absolute error = 1.0347278589506459000000000000E-12 " " relative error = 2.51811371754229100000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.5599999999999996 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.5600000000000012 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.5499999999999996 " " y[1] (analytic) = 0.41623309053069746 " " y[1] (numeric) = 0.41623309052960494 " " absolute error = 1.0925149673823853000000000000E-12 " " relative error = 2.6247672091361790000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.5499999999999996 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.5500000000000045 " " Order of pole (three term test) = 3.219689925334966500000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.5399999999999996 " " y[1] (analytic) = 0.42165626581211024 " " y[1] (numeric) = 0.42165626581095694 " " absolute error = 1.1532996779806126000000000000E-12 " " relative error = 2.73516551629881900000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.5399999999999996 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.5400000000000023 " " Order of pole (three term test) = 2.651457856535144000000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.5299999999999996 " " y[1] (analytic) = 0.42718612499466047 " " y[1] (numeric) = 0.42718612499344316 " " absolute error = 1.2173040353502529000000000000E-12 " " relative error = 2.84958701635140500000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.5299999999999996 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.5300000000000036 " " Order of pole (three term test) = 8.72300295102771100000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.5199999999999996 " " y[1] (analytic) = 0.43282548476454313 " " y[1] (numeric) = 0.4328254847632585 " " absolute error = 1.2846390617937686000000000000E-12 " " relative error = 2.9680300883683220000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.5199999999999996 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.5200000000000005 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.5099999999999996 " " y[1] (analytic) = 0.43857725538353604 " " y[1] (numeric) = 0.4385772553821803 " " absolute error = 1.35574884652101000000000000E-12 " " relative error = 3.0912429449525530000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.5099999999999996 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.510000000000002 " " Order of pole (three term test) = 2.939013073974215400000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.4999999999999996 " " y[1] (analytic) = 0.4444444444444447 " " y[1] (numeric) = 0.444444444443014 " " absolute error = 1.430688900683208000000000000E-12 " " relative error = 3.2190500265372160000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.4999999999999996 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.4999999999999962 " " Order of pole (three term test) = 4.81571599374825200000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.4899999999999995 " " y[1] (analytic) = 0.45043016080356774 " " y[1] (numeric) = 0.45043016080205794 " " absolute error = 1.5097922911877504000000000000E-12 " " relative error = 3.3518898656659220000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.4899999999999995 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.4900000000000047 " " Order of pole (three term test) = 3.940135408449061400000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.4799999999999995 " " y[1] (analytic) = 0.45653761869978116 " " y[1] (numeric) = 0.45653761869818804 " " absolute error = 1.5931145291858684000000000000E-12 " " relative error = 3.4895580647287240000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.4799999999999995 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.4800000000000022 " " Order of pole (three term test) = 3.21939716086274750000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.4699999999999995 " " y[1] (analytic) = 0.4627701420704339 " " y[1] (numeric) = 0.46277014206875283 " " absolute error = 1.6810441927361808000000000000E-12 " " relative error = 3.63256839608361140000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.4699999999999995 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.470000000000004 " " Order of pole (three term test) = 5.25379512237778200000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.4599999999999995 " " y[1] (analytic) = 0.46913116907487357 " " y[1] (numeric) = 0.46913116907309965 " " absolute error = 1.7739143487460750000000000000E-12 " " relative error = 3.78127582578713150000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.4599999999999995 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.4600000000000017 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.4499999999999995 " " y[1] (analytic) = 0.4756242568370991 " " y[1] (numeric) = 0.4756242568352269 " " absolute error = 1.8721690864254015000000000000E-12 " " relative error = 3.93623550420940300000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.4499999999999995 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.4500000000000006 " " Order of pole (three term test) = 6.96663653880109900000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.4399999999999995 " " y[1] (analytic) = 0.48225308641975334 " " y[1] (numeric) = 0.48225308641777764 " " absolute error = 1.9756973834716973000000000000E-12 " " relative error = 4.09680609436690930000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.4399999999999995 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.440000000000008 " " Order of pole (three term test) = 8.49080971434773200000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.4299999999999995 " " y[1] (analytic) = 0.4890214680424475 " " y[1] (numeric) = 0.48902146804036206 " " absolute error = 2.085442929455894000000000000E-12 " " relative error = 4.2645222464443533000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.4299999999999995 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.4299999999999997 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.4199999999999995 " " y[1] (analytic) = 0.49593334655822296 " " y[1] (numeric) = 0.4959333465560217 " " absolute error = 2.201239190924298000000000000E-12 " " relative error = 4.43857870457975030000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.4199999999999995 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.4200000000000013 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.4099999999999995 " " y[1] (analytic) = 0.5029928072028573 " " y[1] (numeric) = 0.5029928072005336 " " absolute error = 2.3236967905404526000000000000E-12 " " relative error = 4.61974158927347060000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.4099999999999995 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.4100000000000033 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.3999999999999995 " " y[1] (analytic) = 0.5102040816326534 " " y[1] (numeric) = 0.5102040816301999 " " absolute error = 2.4534818621191334000000000000E-12 " " relative error = 4.8088244497534980000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.3999999999999995 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.4000000000000044 " " Order of pole (three term test) = 9.72487768941091600000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.3899999999999995 " " y[1] (analytic) = 0.5175715542673779 " " y[1] (numeric) = 0.517571554264787 " " absolute error = 2.590927472567728000000000000E-12 " " relative error = 5.0059309697481020000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.3899999999999995 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.390000000000006 " " Order of pole (three term test) = 7.84308795120640800000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.3799999999999994 " " y[1] (analytic) = 0.5250997689561021 " " y[1] (numeric) = 0.5250997689533657 " " absolute error = 2.7363666887936233000000000000E-12 " " relative error = 5.2111367221385720000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.3799999999999994 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.379999999999999 " " Order of pole (three term test) = 3.15780766011369060000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.3699999999999994 " " y[1] (analytic) = 0.5327934359848692 " " y[1] (numeric) = 0.5327934359819786 " " absolute error = 2.8905766669140576000000000000E-12 " " relative error = 5.4253233461309890000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.3699999999999994 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.3699999999999983 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.3599999999999994 " " y[1] (analytic) = 0.5406574394463672 " " y[1] (numeric) = 0.5406574394433133 " " absolute error = 3.053890473836418000000000000E-12 " " relative error = 5.6484758204078330000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.3599999999999994 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.3600000000000063 " " Order of pole (three term test) = 4.07577619682831570000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.3499999999999994 " " y[1] (analytic) = 0.5486968449931418 " " y[1] (numeric) = 0.5486968449899147 " " absolute error = 3.2270852656779425000000000000E-12 " " relative error = 5.8813628966980450000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.3499999999999994 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.3499999999999959 " " Order of pole (three term test) = 3.26630046239154200000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.3399999999999994 " " y[1] (analytic) = 0.5569169079973274 " " y[1] (numeric) = 0.5569169079939164 " " absolute error = 3.411049220858331000000000000E-12 " " relative error = 6.1248799809732120000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.3399999999999994 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.3399999999999992 " " Order of pole (three term test) = 2.613286521256572000000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.3299999999999994 " " y[1] (analytic) = 0.5653230821414442 " " y[1] (numeric) = 0.5653230821378383 " " absolute error = 3.605893361680046000000000000E-12 " " relative error = 6.3784647674758290000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.3299999999999994 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.3299999999999983 " " Order of pole (three term test) = 4.17467145350279500000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.3199999999999994 " " y[1] (analytic) = 0.5739210284664835 " " y[1] (numeric) = 0.5739210284626703 " " absolute error = 3.813172000377562700000000000E-12 " " relative error = 6.6440708934578590000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.3199999999999994 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.3200000000000056 " " Order of pole (three term test) = 6.65765068907179500000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.3099999999999994 " " y[1] (analytic) = 0.5827166249053092 " " y[1] (numeric) = 0.5827166249012758 " " absolute error = 4.033329226160731000000000000E-12 " " relative error = 6.9215962850144230000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.3099999999999994 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.3100000000000034 " " Order of pole (three term test) = 2.64979296575635500000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.2999999999999994 " " y[1] (analytic) = 0.5917159763313615 " " y[1] (numeric) = 0.5917159763270944 " " absolute error = 4.267142195146789000000000000E-12 " " relative error = 7.2114703097980660000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2999999999999994 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.300000000000005 " " Order of pole (three term test) = 4.211178381020225000000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.2899999999999994 " " y[1] (analytic) = 0.6009254251547389 " " y[1] (numeric) = 0.6009254251502231 " " absolute error = 4.515832152662824000000000000E-12 " " relative error = 7.5147962852461980000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2899999999999994 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.2900000000000054 " " Order of pole (three term test) = 3.34036848646456330000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.2799999999999994 " " y[1] (analytic) = 0.6103515625000007 " " y[1] (numeric) = 0.6103515624952202 " " absolute error = 4.7805093217334615000000000000E-12 " " relative error = 7.8323864727280960000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2799999999999994 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.2800000000000002 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.2699999999999994 " " y[1] (analytic) = 0.6200012400024806 " " y[1] (numeric) = 0.6200012399974185 " " absolute error = 5.062061880778401000000000000E-12 " " relative error = 8.1645996075074760000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2699999999999994 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.270000000000007 " " Order of pole (three term test) = 4.18065849851660600000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.2599999999999993 " " y[1] (analytic) = 0.6298815822625353 " " y[1] (numeric) = 0.6298815822571733 " " absolute error = 5.3620441420321190000000000000E-12 " " relative error = 8.5127812798901830000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2599999999999993 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.2600000000000076 " " Order of pole (three term test) = 6.59598126942297100000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.2499999999999993 " " y[1] (analytic) = 0.6400000000000006 " " y[1] (numeric) = 0.6399999999943191 " " absolute error = 5.681455306216776000000000000E-12 " " relative error = 8.8772739159637050000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2499999999999993 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.2500000000000029 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.2399999999999993 " " y[1] (analytic) = 0.650364203954215 " " y[1] (numeric) = 0.6503642039481929 " " absolute error = 6.022071730171774000000000000E-12 " " relative error = 9.259537492312111000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2399999999999993 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.2400000000000087 " " Order of pole (three term test) = 8.16288373279930200000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.2299999999999993 " " y[1] (analytic) = 0.6609822195782941 " " y[1] (numeric) = 0.6609822195719087 " " absolute error = 6.385336703829125000000000000E-12 " " relative error = 9.6603758992230740000000000E-10 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2299999999999993 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.2300000000000073 " " Order of pole (three term test) = 3.201226500038671400000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.2199999999999993 " " y[1] (analytic) = 0.6718624025799524 " " y[1] (numeric) = 0.6718624025731794 " " absolute error = 6.77302658402823000000000000E-12 " " relative error = 1.0080972767667604000000000E-9 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 12 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2199999999999993 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.2200000000000049 " " Order of pole (three term test) = 2.505866789556440000000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.2099999999999993 " " y[1] (analytic) = 0.6830134553650714 " " y[1] (numeric) = 0.6830134553578847 " " absolute error = 7.186695683003563000000000000E-12 " " relative error = 1.0522041149485506000000000E-9 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 12 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2099999999999993 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.2100000000000055 " " Order of pole (three term test) = 3.91520192321579800000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.1999999999999993 " " y[1] (analytic) = 0.6944444444444452 " " y[1] (numeric) = 0.6944444444368165 " " absolute error = 7.628675469106838000000000000E-12 " " relative error = 1.0985292675513834000000000E-9 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 12 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1999999999999993 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.200000000000003 " " Order of pole (three term test) = 3.05232263500181600000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.1899999999999993 " " y[1] (analytic) = 0.7061648188687247 " " y[1] (numeric) = 0.7061648188606237 " " absolute error = 8.101075366084842000000000000E-12 " " relative error = 1.1471932825912731000000000E-9 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 12 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1899999999999993 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.189999999999999 " " Order of pole (three term test) = 2.374662519572028300000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.1799999999999993 " " y[1] (analytic) = 0.7181844297615636 " " y[1] (numeric) = 0.7181844297529573 " " absolute error = 8.606337864591751000000000000E-12 " " relative error = 1.198346484265754000000000E-9 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 12 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1799999999999993 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.1800000000000055 " " Order of pole (three term test) = 3.687086027192090000000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.1699999999999993 " " y[1] (analytic) = 0.7305135510263724 " " y[1] (numeric) = 0.7305135510172255 " " absolute error = 9.14690545528174000000000000E-12 " " relative error = 1.252119887773516000000000E-9 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 12 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1699999999999993 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.1700000000000021 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.1599999999999993 " " y[1] (analytic) = 0.7431629013079676 " " y[1] (numeric) = 0.7431629012982419 " " absolute error = 9.725664718018834000000000000E-12 " " relative error = 1.3086854444566126000000000E-9 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 12 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1599999999999993 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.1600000000000021 " " Order of pole (three term test) = 4.41563049499154400000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.1499999999999992 " " y[1] (analytic) = 0.7561436672967873 " " y[1] (numeric) = 0.7561436672864417 " " absolute error = 1.034561325496952100000000000E-11 " " relative error = 1.3682073529697175000000000E-9 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 12 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1499999999999992 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.1500000000000032 " " Order of pole (three term test) = 3.40555781682160300000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.1399999999999992 " " y[1] (analytic) = 0.7694675284702996 " " y[1] (numeric) = 0.7694675284592893 " " absolute error = 1.101030377981260200000000000E-11 " " relative error = 1.4308990792244436000000000E-9 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 12 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1399999999999992 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.140000000000001 " " Order of pole (three term test) = 2.620587030127345000000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.1299999999999992 " " y[1] (analytic) = 0.783146683373797 " " y[1] (numeric) = 0.783146683362074 " " absolute error = 1.17229559393194900000000000E-11 " " relative error = 1.4969042438917035000000000E-9 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 12 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1299999999999992 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.1300000000000017 " " Order of pole (three term test) = 4.023799639060053300000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.1199999999999992 " " y[1] (analytic) = 0.7971938775510214 " " y[1] (numeric) = 0.7971938775385338 " " absolute error = 1.248767755868129800000000000E-11 " " relative error = 1.56645427296097980000000E-9 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 12 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1199999999999992 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.1200000000000014 " " Order of pole (three term test) = 3.081936760031930000000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.1099999999999992 " " y[1] (analytic) = 0.8116224332440561 " " y[1] (numeric) = 0.8116224332307469 " " absolute error = 1.330924259690391400000000000E-11 " " relative error = 1.6398317803645285000000000E-9 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 12 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1099999999999992 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.1099999999999968 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.0999999999999992 " " y[1] (analytic) = 0.8264462809917367 " " y[1] (numeric) = 0.826446280977545 " " absolute error = 1.419164785687598900000000000E-11 " " relative error = 1.7171893906819924000000000E-9 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 12 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0999999999999992 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.100000000000006 " " Order of pole (three term test) = 1.07699787888694980000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.0899999999999992 " " y[1] (analytic) = 0.8416799932665614 " " y[1] (numeric) = 0.8416799932514206 " " absolute error = 1.514077752062803500000000000E-11 " " relative error = 1.798875777225814000000000E-9 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 12 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0899999999999992 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.0900000000000034 " " Order of pole (three term test) = 2.729656360872823600000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.0799999999999992 " " y[1] (analytic) = 0.8573388203017845 " " y[1] (numeric) = 0.8573388202856228 " " absolute error = 1.61617386140733300000000000E-11 " " relative error = 1.8851051919455103000000000E-9 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 12 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0799999999999992 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.0800000000000007 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.0699999999999992 " " y[1] (analytic) = 0.8734387282732131 " " y[1] (numeric) = 0.8734387282559518 " " absolute error = 1.726130349766208400000000000E-11 " " relative error = 1.9762466374473284000000000E-9 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 12 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0699999999999992 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.0700000000000027 " " Order of pole (three term test) = 6.2644992328184400000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.0599999999999992 " " y[1] (analytic) = 0.8899964400142414 " " y[1] (numeric) = 0.8899964399957957 " " absolute error = 1.8445689420332200000000000E-11 " " relative error = 2.0725576632685228000000000E-9 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 12 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0599999999999992 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.060000000000003 " " Order of pole (three term test) = 2.363300746281365200000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.0499999999999992 " " y[1] (analytic) = 0.9070294784580513 " " y[1] (numeric) = 0.9070294784383286 " " absolute error = 1.972266794325605600000000000E-11 " " relative error = 2.174424140743976800000000E-9 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 12 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0499999999999992 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.0500000000000016 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.0399999999999991 " " y[1] (analytic) = 0.924556213017753 " " y[1] (numeric) = 0.9245562129966522 " " absolute error = 2.110078778372326300000000000E-11 " " relative error = 2.282261206687504200000000E-9 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 12 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0399999999999991 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.0400000000000027 " " Order of pole (three term test) = 5.33830280236837100000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.0299999999999991 " " y[1] (analytic) = 0.9425959091337559 " " y[1] (numeric) = 0.9425959091111673 " " absolute error = 2.258859765902343500000000000E-11 " " relative error = 2.396424325645792000000000E-9 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 12 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0299999999999991 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.0300000000000014 " " Order of pole (three term test) = 7.9900548803993600000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.0199999999999991 " " y[1] (analytic) = 0.9611687812379871 " " y[1] (numeric) = 0.9611687812137907 " " absolute error = 2.419642264328558700000000000E-11 " " relative error = 2.5173958118074280000000000E-9 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 12 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0199999999999991 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.0199999999999998 " " Order of pole (three term test) = 2.98131714987942160000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.0099999999999991 " " y[1] (analytic) = 0.9802960494069226 " " y[1] (numeric) = 0.9802960493809877 " " absolute error = 2.59349208775461200000000000E-11 " " relative error = 2.645621278718474600000000E-9 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 12 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0099999999999991 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.0100000000000018 " " Order of pole (three term test) = 8.87368954270389300000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.9999999999999991 " " y[1] (analytic) = 1.0000000000000018 " " y[1] (numeric) = 0.9999999999721855 " " absolute error = 2.78163048150759100000000000E-11 " " relative error = 2.781630481507586000000000E-9 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 12 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 0.9999999999999991 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.000000000000003 " " Order of pole (three term test) = 6.58359363705997300000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.9899999999999991 " " y[1] (analytic) = 1.0203040506070828 " " y[1] (numeric) = 1.0203040505772287 " " absolute error = 2.985411917677538400000000000E-11 " " relative error = 2.92600222051575000000000E-9 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 12 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 0.9899999999999991 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.9899999999999984 " " Order of pole (three term test) = 2.434943335784968400000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.9799999999999991 " " y[1] (analytic) = 1.0412328196584775 " " y[1] (numeric) = 1.041232819626415 " " absolute error = 3.206257481735974600000000000E-11 " " relative error = 3.0792896854592244000000000E-9 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 12 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 0.9799999999999991 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.9799999999999964 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.9699999999999991 " " y[1] (analytic) = 1.0628122010840706 " " y[1] (numeric) = 1.0628122010496117 " " absolute error = 3.445888019371068400000000000E-11 " " relative error = 3.2422360374262316000000000E-9 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 12 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 0.9699999999999991 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.9700000000000027 " " Order of pole (three term test) = 5.28013516975360300000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.9599999999999991 " " y[1] (analytic) = 1.0850694444444464 " " y[1] (numeric) = 1.0850694444073863 " " absolute error = 3.706013274040742500000000000E-11 " " relative error = 3.4154618333559420000000000E-9 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 12 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 0.9599999999999991 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.9600000000000007 " " Order of pole (three term test) = 3.869278620350216600000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.9499999999999991 " " y[1] (analytic) = 1.1080332409972322 " " y[1] (numeric) = 1.108033240957345 " " absolute error = 3.988720465031292400000000000E-11 " " relative error = 3.5998202196907336000000000E-9 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 12 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 0.9499999999999991 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.9500000000000021 " " Order of pole (three term test) = 2.826188801122272400000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.9399999999999991 " " y[1] (analytic) = 1.1317338162064305 " " y[1] (numeric) = 1.131733816163469 " " absolute error = 4.29616342501049100000000000E-11 " " relative error = 3.796090002339262000000000E-9 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 12 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 0.9399999999999991 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.9400000000000022 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.929999999999999 " " y[1] (analytic) = 1.156203029251939 " " y[1] (numeric) = 1.1562030292056305 " " absolute error = 4.630851258013990400000000000E-11 " " relative error = 4.005223253056292000000000E-9 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 12 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 0.929999999999999 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.930000000000005 " " Order of pole (three term test) = 5.9709228597988900000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.919999999999999 " " y[1] (analytic) = 1.181474480151231 " " y[1] (numeric) = 1.181474480101276 " " absolute error = 4.99549290822187700000000000E-11 " " relative error = 4.228185197518989400000000E-9 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 12 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 0.919999999999999 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.9200000000000014 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.909999999999999 " " y[1] (analytic) = 1.2075836251660454 " " y[1] (numeric) = 1.2075836251121133 " " absolute error = 5.39321920456359300000000000E-11 " " relative error = 4.466124823299101300000000E-9 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 12 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 0.909999999999999 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.9100000000000038 " " Order of pole (three term test) = 9.33073871384933800000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.899999999999999 " " y[1] (analytic) = 1.2345679012345705 " " y[1] (numeric) = 1.2345679011762973 " " absolute error = 5.82731640719202900000000000E-11 " " relative error = 4.720126289825533600000000E-9 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 12 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 0.899999999999999 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.9000000000000056 " " Order of pole (three term test) = 4.46537855821304200000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.889999999999999 " " y[1] (analytic) = 1.2624668602449212 " " y[1] (numeric) = 1.2624668601819047 " " absolute error = 6.30164809223288100000000000E-11 " " relative error = 4.9915354538576545000000000E-9 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 12 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 0.889999999999999 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.8900000000000012 " " Order of pole (three term test) = 3.19361970179479600000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.879999999999999 " " y[1] (analytic) = 1.2913223140495895 " " y[1] (numeric) = 1.2913223139813848 " " absolute error = 6.82047751610070900000000000E-11 " " relative error = 5.281777788468378000000000E-9 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 12 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 0.879999999999999 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.879999999999998 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.869999999999999 " " y[1] (analytic) = 1.321178491214166 " " y[1] (numeric) = 1.3211784911402806 " " absolute error = 7.38853422888041700000000000E-11 " " relative error = 5.592381557839575000000000E-9 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 12 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 0.869999999999999 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.8700000000000025 " " Order of pole (three term test) = 6.45982227016938300000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.859999999999999 " " y[1] (analytic) = 1.3520822065981644 " " y[1] (numeric) = 1.352082206518053 " " absolute error = 8.01112509662971200000000000E-11 " " relative error = 5.925028121467322000000000E-9 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 12 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 0.859999999999999 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.8600000000000004 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.849999999999999 " " y[1] (analytic) = 1.3840830449827022 " " y[1] (numeric) = 1.3840830448957602 " " absolute error = 8.69420091476058600000000000E-11 " " relative error = 6.281560160914509000000000E-9 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 12 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 0.849999999999999 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.850000000000002 " " Order of pole (three term test) = 6.43044100021632300000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.839999999999999 " " y[1] (analytic) = 1.4172335600907067 " " y[1] (numeric) = 1.4172335599962615 " " absolute error = 9.44451183926275900000000000E-11 " " relative error = 6.664047553783785000000000E-9 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 12 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 0.839999999999999 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.8400000000000034 " " Order of pole (three term test) = 4.508702379035005600000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.829999999999999 " " y[1] (analytic) = 1.4515894904920923 " " y[1] (numeric) = 1.4515894903893976 " " absolute error = 1.02694741599407280000000000E-10 " " relative error = 7.074640748783151000000000E-9 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 12 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 0.829999999999999 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.830000000000002 " " Order of pole (three term test) = 3.147862527712372000000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.819999999999999 " " y[1] (analytic) = 1.4872099940511638 " " y[1] (numeric) = 1.4872099939393868 " " absolute error = 1.11777032074655840000000000E-10 " " relative error = 7.51588763669984000000000E-9 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 12 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 0.819999999999999 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.819999999999998 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.8099999999999989 " " y[1] (analytic) = 1.52415790275873 " " y[1] (numeric) = 1.5241579026369432 " " absolute error = 1.21786802864676250000000000E-10 " " relative error = 7.990432135951386000000000E-9 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 12 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 0.8099999999999989 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.8100000000000006 " " Order of pole (three term test) = 3.02868110751940700000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.7999999999999989 " " y[1] (analytic) = 1.5625000000000044 " " y[1] (numeric) = 1.5624999998671725 " " absolute error = 1.32831967647462080000000000E-10 " " relative error = 8.501245929437549000000000E-9 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 12 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 0.7999999999999989 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.8000000000000002 " " Order of pole (three term test) = 4.1728482128388400000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.7899999999999989 " " y[1] (analytic) = 1.6023073225444682 " " y[1] (numeric) = 1.602307322399434 " " absolute error = 1.45034206866512250000000000E-10 " " relative error = 9.051584850539007000000000E-9 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 12 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 0.7899999999999989 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.789999999999998 " " Order of pole (three term test) = 2.86118353057741140000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.7799999999999989 " " y[1] (analytic) = 1.6436554898093407 " " y[1] (numeric) = 1.6436554896508075 " " absolute error = 1.5853318657832460000000000E-10 " " relative error = 9.645159071425242000000000E-9 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 12 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 0.7799999999999989 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.7799999999999985 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.7699999999999989 " " y[1] (analytic) = 1.6866250632484445 " " y[1] (numeric) = 1.6866250630749604 " " absolute error = 1.73484115961741740000000000E-10 " " relative error = 1.028587323537163800000000E-8 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 11 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 0.7699999999999989 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.770000000000001 " " Order of pole (three term test) = 5.30291571307012900000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.7599999999999989 " " y[1] (analytic) = 1.7313019390581768 " " y[1] (numeric) = 1.7313019388681101 " " absolute error = 1.900666291021480000000000E-10 " " relative error = 1.097824849694003700000000E-8 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 11 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 0.7599999999999989 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.759999999999999 " " Order of pole (three term test) = 3.582619930100892600000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.7499999999999989 " " y[1] (analytic) = 1.777777777777783 " " y[1] (numeric) = 1.7777777775693 " " absolute error = 2.0848300863463010000000000E-10 " " relative error = 1.172716923569790800000000E-8 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 11 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 0.7499999999999989 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.7500000000000041 " " Order of pole (three term test) = 7.22357399062218900000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.7399999999999989 " " y[1] (analytic) = 1.8261504747991288 " " y[1] (numeric) = 1.8261504745701642 " " absolute error = 2.2896462503751990000000000E-10 " " relative error = 1.253810286705455400000000E-8 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 11 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 0.7399999999999989 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.7399999999999984 " " Order of pole (three term test) = 3.21939716086262600000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.7299999999999989 " " y[1] (analytic) = 1.8765246762994992 " " y[1] (numeric) = 1.8765246760477232 " " absolute error = 2.51775933435283150000000000E-10 " " relative error = 1.341713949276619700000000E-8 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 11 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 0.7299999999999989 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.7299999999999985 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.7199999999999989 " " y[1] (analytic) = 1.9290123456790185 " " y[1] (numeric) = 1.9290123454017993 " " absolute error = 2.7721913653522280000000000E-10 " " relative error = 1.437104003798590200000000E-8 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 11 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 0.7199999999999989 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.7199999999999984 " " Order of pole (three term test) = 2.8302699047824500000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.7099999999999989 " " y[1] (analytic) = 1.983733386232897 " " y[1] (numeric) = 1.983733385927256 " " absolute error = 3.0564106801023170000000000E-10 " " relative error = 1.54073662383957300000000E-8 "%" Desired digits = 10 Estimated correct digits = 13 Correct digits = 11 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 0.7099999999999989 " " Order of pole (given) = 2. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.7100000000000022 " " Order of pole (three term test) = 7.44155015790851700000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" "Finished!" "diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ; " Iterations = 130 "Total Elapsed Time "= 7 Seconds "Elapsed Time(since restart) "= 6 Seconds "Time to Timeout "= 9 Minutes 52 Seconds Percent Done = 100.76923076923084 "%" (%o230) diffeq.max