(%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,30,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_check_sign,1.0,convfloat) (%i68) define_variable(glob_desired_digits_correct,8.0,convfloat) (%i69) define_variable(glob_max_estimated_step_error,0.0,convfloat) (%i70) define_variable(glob_ratio_of_radius,0.1,convfloat) (%i71) define_variable(glob_percent_done,0.0,convfloat) (%i72) define_variable(glob_subiter_method,3,fixnum) (%i73) define_variable(glob_total_exp_sec,0.1,convfloat) (%i74) define_variable(glob_optimal_expect_sec,0.1,convfloat) (%i75) define_variable(glob_estimated_size_answer,100.0,convfloat) (%i76) define_variable(glob_html_log,true,boolean) (%i77) define_variable(glob_good_digits,0,fixnum) (%i78) define_variable(glob_max_opt_iter,10,fixnum) (%i79) define_variable(glob_dump,false,boolean) (%i80) define_variable(glob_djd_debug,true,boolean) (%i81) define_variable(glob_display_flag,true,boolean) (%i82) define_variable(glob_djd_debug2,true,boolean) (%i83) define_variable(glob_h_reason,0,fixnum) (%i84) define_variable(glob_sec_in_minute,60,fixnum) (%i85) define_variable(glob_min_in_hour,60.0,convfloat) (%i86) define_variable(glob_hours_in_day,24.0,convfloat) (%i87) define_variable(glob_days_in_year,365,fixnum) (%i88) define_variable(glob_sec_in_hour,3600,fixnum) (%i89) define_variable(glob_sec_in_day,86400,fixnum) (%i90) define_variable(glob_sec_in_year,31536000,fixnum) (%i91) define_variable(glob_almost_1,0.999,convfloat) (%i92) define_variable(glob_clock_sec,0.0,convfloat) (%i93) define_variable(glob_clock_start_sec,0.0,convfloat) (%i94) define_variable(glob_not_yet_finished,true,boolean) (%i95) define_variable(glob_initial_pass,true,boolean) (%i96) define_variable(glob_not_yet_start_msg,true,boolean) (%i97) define_variable(glob_reached_optimal_h,false,boolean) (%i98) define_variable(glob_optimal_done,false,boolean) (%i99) define_variable(glob_disp_incr,0.1,convfloat) (%i100) define_variable(glob_h,0.1,convfloat) (%i101) define_variable(glob_diff_rc_fm,0.1,convfloat) (%i102) define_variable(glob_diff_rc_fmm1,0.1,convfloat) (%i103) define_variable(glob_diff_rc_fmm2,0.1,convfloat) (%i104) define_variable(glob_diff_ord_fm,0.1,convfloat) (%i105) define_variable(glob_diff_ord_fmm1,0.1,convfloat) (%i106) define_variable(glob_diff_ord_fmm2,0.1,convfloat) (%i107) define_variable(glob_six_term_ord_save,0.1,convfloat) (%i108) define_variable(glob_guess_error_rc,0.1,convfloat) (%i109) define_variable(glob_guess_error_ord,0.1,convfloat) (%i110) define_variable(glob_max_h,0.1,convfloat) (%i111) define_variable(glob_min_h,1.0E-6,convfloat) (%i112) define_variable(glob_type_given_pole,0,fixnum) (%i113) define_variable(glob_large_float,1.0E+100,convfloat) (%i114) define_variable(glob_larger_float,1.1E+100,convfloat) (%i115) define_variable(glob_least_given_sing,9.9E+100,convfloat) (%i116) define_variable(glob_least_ratio_sing,9.9E+100,convfloat) (%i117) define_variable(glob_least_3_sing,9.9E+100,convfloat) (%i118) define_variable(glob_least_6_sing,9.9E+100,convfloat) (%i119) define_variable(glob_last_good_h,0.1,convfloat) (%i120) define_variable(glob_look_poles,false,boolean) (%i121) define_variable(glob_display_interval,0.0,convfloat) (%i122) define_variable(glob_next_display,0.0,convfloat) (%i123) define_variable(glob_dump_analytic,false,boolean) (%i124) define_variable(glob_abserr,1.0E-11,convfloat) (%i125) define_variable(glob_relerr,1.0E-11,convfloat) (%i126) define_variable(glob_min_pole_est,1.0E+9,convfloat) (%i127) define_variable(glob_max_hours,0.0,convfloat) (%i128) define_variable(glob_max_iter,1000,fixnum) (%i129) define_variable(glob_max_rel_trunc_err,1.0E-11,convfloat) (%i130) define_variable(glob_max_trunc_err,1.0E-11,convfloat) (%i131) define_variable(glob_no_eqs,0,fixnum) (%i132) define_variable(glob_optimal_clock_start_sec,0.0,convfloat) (%i133) define_variable(glob_optimal_start,0.0,convfloat) (%i134) define_variable(glob_upper_ratio_limit,1.0001,convfloat) (%i135) define_variable(glob_lower_ratio_limit,0.9999,convfloat) (%i136) define_variable(glob_small_float,0.0,convfloat) (%i137) define_variable(glob_smallish_float,0.0,convfloat) (%i138) define_variable(glob_unchanged_h_cnt,0,fixnum) (%i139) define_variable(glob_warned,false,boolean) (%i140) define_variable(glob_warned2,false,boolean) (%i141) define_variable(glob_max_sec,10000.0,convfloat) (%i142) define_variable(glob_orig_start_sec,0.0,convfloat) (%i143) define_variable(glob_start,0,fixnum) (%i144) define_variable(glob_curr_iter_when_opt,0,fixnum) (%i145) define_variable(glob_current_iter,0,fixnum) (%i146) define_variable(glob_iter,0,fixnum) (%i147) define_variable(glob_normmax,0.0,convfloat) (%i148) define_variable(glob_max_minutes,0.0,convfloat) (%i149) array(array_y_init,MAX_TERMS) (%i150) array(array_norms,MAX_TERMS) (%i151) array(array_fact_1,MAX_TERMS) (%i152) array(array_1st_rel_error,2) (%i153) array(array_last_rel_error,2) (%i154) array(array_type_pole,2) (%i155) array(array_type_real_pole,2) (%i156) array(array_type_complex_pole,2) (%i157) array(array_y,MAX_TERMS) (%i158) array(array_x,MAX_TERMS) (%i159) array(array_tmp0,MAX_TERMS) (%i160) array(array_tmp1,MAX_TERMS) (%i161) array(array_tmp2,MAX_TERMS) (%i162) array(array_tmp3,MAX_TERMS) (%i163) array(array_tmp4,MAX_TERMS) (%i164) array(array_tmp5,MAX_TERMS) (%i165) array(array_tmp6,MAX_TERMS) (%i166) array(array_tmp7,MAX_TERMS) (%i167) array(array_tmp8,MAX_TERMS) (%i168) array(array_tmp9,MAX_TERMS) (%i169) array(array_tmp10,MAX_TERMS) (%i170) array(array_tmp11,MAX_TERMS) (%i171) array(array_tmp12,MAX_TERMS) (%i172) array(array_tmp13,MAX_TERMS) (%i173) array(array_tmp14,MAX_TERMS) (%i174) array(array_m1,MAX_TERMS) (%i175) array(array_y_higher,2,MAX_TERMS) (%i176) array(array_y_higher_work,2,MAX_TERMS) (%i177) array(array_y_higher_work2,2,MAX_TERMS) (%i178) array(array_y_set_initial,2,MAX_TERMS) (%i179) array(array_given_rad_poles,2,3) (%i180) array(array_given_ord_poles,2,3) (%i181) array(array_rad_test_poles,2,4) (%i182) array(array_ord_test_poles,2,4) (%i183) array(array_fact_2,MAX_TERMS,MAX_TERMS) (%i184) omniout_str(iolevel,str):=if glob_iolevel >= iolevel then printf(true,"~a~%",string(str)) (%i185) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel then printf(true,"~a",string(str)) (%i186) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel then printf(true,"~a = ~a~%",string(label), string(str)) (%i187) 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)) (%i188) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if glob_iolevel >= iolevel then (printf(true,"~a = ~d ~a~%",prelabel,value, postlabel),newline()) (%i189) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen, postlabel):=if glob_iolevel >= iolevel then (sprint(prelabel,"[",elemnt,"]=",value, postlabel),newline()) (%i190) 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) (%i191) 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) (%i192) 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) (%i193) 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) (%i194) 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) (%i195) logditto(file):=(printf(file,""),printf(file,"ditto"), printf(file,""),0) (%i196) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n), printf(file,""),0) (%i197) logitem_str(file,str):=(printf(file,""),printf(file,str), printf(file,""),0) (%i198) logitem_good_digits(file,rel_error):=( block(mode_declare([[good_digits],fixnum]), printf(file,""), if rel_error # -1.0 then (if rel_error > +1.0E-34 then ( good_digits :3-floor(log10(rel_error)), printf(file,"~d",good_digits)) else (good_digits:16, printf(file,"~d", good_digits))) else printf(file,"Unknown"), printf(file,"")),0) (%i199) log_revs(file,revs):=printf(file,revs) (%i200) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x), printf(file,""),0) (%i201) 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) (%i202) logstart(file):=(printf(file,""),0) (%i203) logend(file):=(printf(file,"~%"),0) (%i204) 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) (%i205) 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) (%i206) 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) (%i207) 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) (%i208) 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) (%i209) 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) (%i210) 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) (%i211) 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) (%i212) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save (%i213) factorial_2(nnn):=nnn! (%i214) 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) (%i215) 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) (%i216) log10(x):=log(x)/glob_log_10 (%i217) expt(x,y):=(if x <= 0.0 and y < 0.0 then print("expt error x = ",x,"y = ",y),x^y) (%i218) 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)), omniout_float(ALWAYS,"step_error",32, step_error,32,""), step_error) (%i219) exact_soln_y(x):=block(1.0/(x-6.0)/(x-6.0)/(x-6.0)/(x-6.0)/(x-6.0)) 1.0 ------- x - 6.0 ------- x - 6.0 ------- x - 6.0 ------- x - 6.0 (%o219) exact_soln_y(x) := block(-------) x - 6.0 (%i220) 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) (%i221) my_check_sign(x0,xf):=block([ret],if xf > x0 then ret:1.0 else ret:-1.0,ret) (%i222) 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) (%i223) 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) (%i224) 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)) (%i225) display_alot(iter):=( block(mode_declare( [[abserr],convfloat,[analytic_val_y],convfloat, [ind_var],convfloat,[numeric_val],convfloat, [relerr],convfloat,[term_no],fixnum]), if reached_interval() then (if iter >= 0 then (ind_var:array_x[1], omniout_float(ALWAYS, "x[1] ", 33,ind_var,20, " "), analytic_val_y :exact_soln_y(ind_var), omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20," "), term_no:1, numeric_val:array_y[term_no], abserr :abs( numeric_val-analytic_val_y), omniout_float(ALWAYS, "y[1] (numeric) ", 33,numeric_val, 20," "), if abs(analytic_val_y) # 0.0 then ( relerr :abserr*100.0 /abs(analytic_val_y), if relerr > 1.0E-34 then glob_good_digits :3-floor(log10(relerr)) else glob_good_digits :16) else (relerr:-1.0, glob_good_digits:-1), if glob_iter = 1 then array_1st_rel_error[1] :relerr else array_last_rel_error[ 1] :relerr, omniout_float(ALWAYS, "absolute error ", 4,abserr,20," "), omniout_float(ALWAYS, "relative error ", 4,relerr,20,"%"), omniout_int(INFO, "Correct digits ", 32, glob_good_digits,4, " "), omniout_float(ALWAYS, "h ", 4,glob_h,20, " ")))),0) (%i226) 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) (%i227) 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) (%i228) atomall():=( block(mode_declare([[kkk,order_d],fixnum, [adj2,adj3,temporary,term,temp,temp2], convfloat]), array_tmp1[1]:array_m1[1]*array_const_5D0[1], array_tmp2[1]:array_x[1]-array_const_6D0[1], array_tmp3[1]:array_tmp1[1]/array_tmp2[1], array_tmp4[1]:array_x[1]-array_const_6D0[1], array_tmp5[1]:array_tmp3[1]/array_tmp4[1], array_tmp6[1]:array_x[1]-array_const_6D0[1], array_tmp7[1]:array_tmp5[1]/array_tmp6[1], array_tmp8[1]:array_x[1]-array_const_6D0[1], array_tmp9[1]:array_tmp7[1]/array_tmp8[1], array_tmp10[1]:array_x[1]-array_const_6D0[1], array_tmp11[1]:array_tmp9[1]/array_tmp10[1], array_tmp12[1]:array_x[1]-array_const_6D0[1], array_tmp13[1]:array_tmp11[1]/array_tmp12[1], array_tmp14[1]:array_tmp13[1]+array_const_0D0[1], if not array_y_set_initial[1,2] then (if 1 <= MAX_TERMS then ( temporary :array_tmp14[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_5D0[1], array_tmp2[2]:array_x[2], array_tmp3[2]:(array_tmp1[2] -array_tmp3[1]*array_tmp2[2]) /array_tmp2[1],array_tmp4[2]:array_x[2], array_tmp5[2]:(array_tmp3[2] -array_tmp5[1]*array_tmp4[2]) /array_tmp4[1],array_tmp6[2]:array_x[2], array_tmp7[2]:(array_tmp5[2] -array_tmp7[1]*array_tmp6[2]) /array_tmp6[1],array_tmp8[2]:array_x[2], array_tmp9[2]:(array_tmp7[2] -array_tmp9[1]*array_tmp8[2]) /array_tmp8[1],array_tmp10[2]:array_x[2], array_tmp11[2]:(array_tmp9[2] -array_tmp11[1]*array_tmp10[2]) /array_tmp10[1], array_tmp12[2]:array_x[2], array_tmp13[2]:(array_tmp11[2] -array_tmp13[1]*array_tmp12[2]) /array_tmp12[1], array_tmp14[2]:array_tmp13[2], if not array_y_set_initial[1,3] then (if 2 <= MAX_TERMS then ( temporary :array_tmp14[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_5D0[1], array_tmp3[3]:(array_tmp1[3] -array_tmp3[2]*array_tmp2[2]) /array_tmp2[1], array_tmp5[3]:(array_tmp3[3] -array_tmp5[2]*array_tmp4[2]) /array_tmp4[1], array_tmp7[3]:(array_tmp5[3] -array_tmp7[2]*array_tmp6[2]) /array_tmp6[1], array_tmp9[3]:(array_tmp7[3] -array_tmp9[2]*array_tmp8[2]) /array_tmp8[1], array_tmp11[3]:(array_tmp9[3] -array_tmp11[2]*array_tmp10[2]) /array_tmp10[1], array_tmp13[3]:(array_tmp11[3] -array_tmp13[2]*array_tmp12[2]) /array_tmp12[1], array_tmp14[3]:array_tmp13[3], if not array_y_set_initial[1,4] then (if 3 <= MAX_TERMS then ( temporary :array_tmp14[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_5D0[1], array_tmp3[4]:(array_tmp1[4] -array_tmp3[3]*array_tmp2[2]) /array_tmp2[1], array_tmp5[4]:(array_tmp3[4] -array_tmp5[3]*array_tmp4[2]) /array_tmp4[1], array_tmp7[4]:(array_tmp5[4] -array_tmp7[3]*array_tmp6[2]) /array_tmp6[1], array_tmp9[4]:(array_tmp7[4] -array_tmp9[3]*array_tmp8[2]) /array_tmp8[1], array_tmp11[4]:(array_tmp9[4] -array_tmp11[3]*array_tmp10[2]) /array_tmp10[1], array_tmp13[4]:(array_tmp11[4] -array_tmp13[3]*array_tmp12[2]) /array_tmp12[1], array_tmp14[4]:array_tmp13[4], if not array_y_set_initial[1,5] then (if 4 <= MAX_TERMS then ( temporary :array_tmp14[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_5D0[1], array_tmp3[5]:(array_tmp1[5] -array_tmp3[4]*array_tmp2[2]) /array_tmp2[1], array_tmp5[5]:(array_tmp3[5] -array_tmp5[4]*array_tmp4[2]) /array_tmp4[1], array_tmp7[5]:(array_tmp5[5] -array_tmp7[4]*array_tmp6[2]) /array_tmp6[1], array_tmp9[5]:(array_tmp7[5] -array_tmp9[4]*array_tmp8[2]) /array_tmp8[1], array_tmp11[5]:(array_tmp9[5] -array_tmp11[4]*array_tmp10[2]) /array_tmp10[1], array_tmp13[5]:(array_tmp11[5] -array_tmp13[4]*array_tmp12[2]) /array_tmp12[1], array_tmp14[5]:array_tmp13[5], if not array_y_set_initial[1,6] then (if 5 <= MAX_TERMS then ( temporary :array_tmp14[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_5D0[1], array_tmp3[kkk] :(-ats(kkk,array_tmp2,array_tmp3,2)) /array_tmp2[1], array_tmp5[kkk] :(-ats(kkk,array_tmp4,array_tmp5,2)) /array_tmp4[1], array_tmp7[kkk] :(-ats(kkk,array_tmp6,array_tmp7,2)) /array_tmp6[1], array_tmp9[kkk] :(-ats(kkk,array_tmp8,array_tmp9,2)) /array_tmp8[1], array_tmp11[kkk] :(-ats(kkk,array_tmp10,array_tmp11,2)) /array_tmp10[1], array_tmp13[kkk] :(-ats(kkk,array_tmp12,array_tmp13,2)) /array_tmp12[1], array_tmp14[kkk]:array_tmp13[kkk],order_d:1, if order_d+kkk <= MAX_TERMS then (if not array_y_set_initial[1,order_d+kkk] then ( temporary :array_tmp14[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) (%i229) exact_soln_y(x):=block(1.0/(x-6.0)/(x-6.0)/(x-6.0)/(x-6.0)/(x-6.0)) 1.0 ------- x - 6.0 ------- x - 6.0 ------- x - 6.0 ------- x - 6.0 (%o229) exact_soln_y(x) := block(-------) x - 6.0 (%i230) 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:64,max_terms:30, glob_html_log:true,term:1, while term <= MAX_TERMS do (array_y_init[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_norms[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_fact_1[term]:0.0,term:1+term),term:1, while term <= 2 do (array_1st_rel_error[term]:0.0,term:1+term),term:1, while term <= 2 do (array_last_rel_error[term]:0.0,term:1+term),term:1, while term <= 2 do (array_type_pole[term]:0,term:1+term), term:1, while term <= 2 do (array_type_real_pole[term]:0,term:1+term),term:1, while term <= 2 do (array_type_complex_pole[term]:0,term:1+term),term:1, while term <= MAX_TERMS do (array_y[term]:0.0,term:1+term), term:1, while term <= MAX_TERMS do (array_x[term]:0.0,term:1+term), term:1, while term <= MAX_TERMS do (array_tmp0[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp1[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp2[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_tmp6[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp7[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp8[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp9[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp10[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp11[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp12[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp13[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp14[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_tmp6), zero_ats_ar(array_tmp7),zero_ats_ar(array_tmp8), zero_ats_ar(array_tmp9),zero_ats_ar(array_tmp10), zero_ats_ar(array_tmp11),zero_ats_ar(array_tmp12), zero_ats_ar(array_tmp13),zero_ats_ar(array_tmp14), 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_5D0),array_const_5D0[1]:5.0, zero_ats_ar(array_const_6D0),array_const_6D0[1]:6.0, zero_ats_ar(array_m1),array_m1[1]:-1.0,iiif:0, while iiif <= MAX_TERMS do (jjjf:0, while jjjf <= MAX_TERMS do (array_fact_1[iiif]:0, array_fact_2[iiif,jjjf]:0,jjjf:1+jjjf), iiif:1+iiif),array_y_set_initial[1,1]:true, array_y_set_initial[1,2]:false, array_y_set_initial[1,3]:false, array_y_set_initial[1,4]:false, array_y_set_initial[1,5]:false, array_y_set_initial[1,6]:false, array_y_set_initial[1,7]:false, array_y_set_initial[1,8]:false, array_y_set_initial[1,9]:false, array_y_set_initial[1,10]:false, array_y_set_initial[1,11]:false, array_y_set_initial[1,12]:false, array_y_set_initial[1,13]:false, array_y_set_initial[1,14]:false, array_y_set_initial[1,15]:false, array_y_set_initial[1,16]:false, array_y_set_initial[1,17]:false, array_y_set_initial[1,18]:false, array_y_set_initial[1,19]:false, array_y_set_initial[1,20]:false, array_y_set_initial[1,21]:false, array_y_set_initial[1,22]:false, array_y_set_initial[1,23]:false, array_y_set_initial[1,24]:false, array_y_set_initial[1,25]:false, array_y_set_initial[1,26]:false, array_y_set_initial[1,27]:false, array_y_set_initial[1,28]:false, array_y_set_initial[1,29]:false, array_y_set_initial[1,30]:false,ALWAYS:1,INFO:2,DEBUGL:3, DEBUGMASSIVE:4,MAX_TERMS:30,glob_iolevel:INFO, glob_orig_start_sec:elapsed_time_seconds(), glob_curr_iter_when_opt:0,glob_display_flag:true, glob_no_eqs:1,glob_iter:-1,opt_iter:-1,glob_max_iter:50000, glob_max_hours:0.0,glob_max_minutes:15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "##############temp/sing7postode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = m1 * 5.0 / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; "), omniout_str(ALWAYS,"!"), omniout_str(ALWAYS,"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS,"Digits:64,"), omniout_str(ALWAYS,"max_terms:30,"),omniout_str(ALWAYS,"!"), omniout_str(ALWAYS,"/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS,"/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS,"x_start:2.0,"), omniout_str(ALWAYS,"x_end:3.0,"), 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,"glob_type_given_pole:1,"), omniout_str(ALWAYS,""), omniout_str(ALWAYS,"array_given_rad_poles[1,1]:6.0,"), omniout_str(ALWAYS,""),omniout_str(ALWAYS,""), omniout_str(ALWAYS,""),omniout_str(ALWAYS,""), omniout_str(ALWAYS,""),omniout_str(ALWAYS,""), 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 - 6.0 ) / ( x - 6.0 )/ ( x - 6.0 )/ ( x - 6.0 )/ ( x - 6.0 )) "), 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:3.0, 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]:6.0, 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(), glob_current_iter:1+glob_current_iter, atomall(),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 * 5.0 / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; "), 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, "2014-01-20T02:41:09-06:00"), logitem_str(html_log_file,"Maxima"), logitem_str(html_log_file, "sing7"), logitem_str(html_log_file, "diff ( y , x , 1 ) = m1 * 5.0 / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; "), 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_good_digits(html_log_file, array_last_rel_error[ 1]), 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, " 249 "), logitem_str(html_log_file, "sing7 diffeq.max"), logitem_str(html_log_file, "sing7 maxima results"), logitem_str(html_log_file, "All Tests - Maxima only - to save time"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%i231) main():=(alias(convfloat,convfloat),compile(all),main_prog()) (%i232) 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. 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. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob_check_sign in translation. warning: encountered undefined variable glob_next_display in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable ALWAYS in translation. warning: encountered undefined variable ind_var in translation. warning: encountered undefined variable analytic_val_y in translation. warning: encountered undefined variable term_no in translation. warning: encountered undefined variable numeric_val in translation. warning: encountered undefined variable abserr in translation. warning: encountered undefined variable relerr in translation. warning: variable glob_good_digits (declared type fixnum) assigned type any. warning: encountered undefined variable array_1st_rel_error in translation. warning: encountered undefined variable glob_iter in translation. warning: encountered undefined variable array_last_rel_error in translation. warning: encountered undefined variable INFO in translation. warning: encountered undefined variable glob_good_digits in translation. warning: encountered undefined variable glob_h in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable 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_5D0 in translation. warning: encountered undefined variable array_tmp1 in translation. warning: encountered undefined variable array_const_6D0 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_tmp5 in translation. warning: encountered undefined variable array_tmp6 in translation. warning: encountered undefined variable array_tmp7 in translation. warning: encountered undefined variable array_tmp8 in translation. warning: encountered undefined variable array_tmp9 in translation. warning: encountered undefined variable array_tmp10 in translation. warning: encountered undefined variable array_tmp11 in translation. warning: encountered undefined variable array_tmp12 in translation. warning: encountered undefined variable array_tmp13 in translation. warning: encountered undefined variable array_const_0D0 in translation. warning: encountered undefined variable array_tmp14 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_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/sing7postode.ode#################" "diff ( y , x , 1 ) = m1 * 5.0 / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; " "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:64," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:2.0," "x_end:3.0," "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]:6.0," "" "" "" "" "" "" "/* 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 - 6.0 ) / ( x - 6.0 )/ ( x - 6.0 )/ ( x - 6.0 )/ ( x - 6.0 )) " "));" "" "" "/* 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. "" estimated_steps = 1000000. "" step_error = 1.0000000000000E-13 "" est_needed_step_err = 1.0000000000000E-13 "" opt_iter = 1 Radius of convergence (given) for eq 1 = 4. " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.9999999999999964 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" min_size = 9.7656250000E-4 "" 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. "" estimated_steps = 1000000. "" step_error = 1.0000000000000E-13 "" est_needed_step_err = 1.0000000000000E-13 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 5.254211160650322000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-174 "" estimated_step_error = 5.254211160650322000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-174 "" "Double H and LOOP" opt_iter = 2 Radius of convergence (given) for eq 1 = 4. " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.9999999999999964 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" min_size = 9.7656250000E-4 "" 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. "" estimated_steps = 500000. "" step_error = 1.4142135623730950000000000000E-13 "" est_needed_step_err = 1.4142135623730950000000000000E-13 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 3.52604184650466060000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-166 "" estimated_step_error = 3.52604184650466060000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-166 "" "Double H and LOOP" opt_iter = 3 Radius of convergence (given) for eq 1 = 4. " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.9999999999999964 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" min_size = 9.7656250000E-4 "" 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. "" estimated_steps = 250000. "" step_error = 2.0000000000000E-13 "" est_needed_step_err = 2.0000000000000E-13 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 2.366287197015771700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-158 "" estimated_step_error = 2.366287197015771700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-158 "" "Double H and LOOP" opt_iter = 4 Radius of convergence (given) for eq 1 = 4. " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.9999999999999964 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" min_size = 9.7656250000E-4 "" 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. "" estimated_steps = 125000. "" step_error = 2.828427124746190000000000000E-13 "" est_needed_step_err = 2.828427124746190000000000000E-13 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.587989221482499000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-150 "" estimated_step_error = 1.587989221482499000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-150 "" "Double H and LOOP" opt_iter = 5 Radius of convergence (given) for eq 1 = 4. " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.9999999999999964 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" min_size = 9.7656250000E-4 "" 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. "" estimated_steps = 62500. "" step_error = 4.0000000000000E-13 "" est_needed_step_err = 4.0000000000000E-13 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.065682553193170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-142 "" estimated_step_error = 1.065682553193170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-142 "" "Double H and LOOP" opt_iter = 6 Radius of convergence (given) for eq 1 = 4. " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.9999999999999964 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" min_size = 9.7656250000E-4 "" 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. "" estimated_steps = 31250. "" step_error = 5.656854249492380000000000000E-13 "" est_needed_step_err = 5.656854249492380000000000000E-13 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 7.15168832658992000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-135 "" estimated_step_error = 7.15168832658992000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-135 "" "Double H and LOOP" opt_iter = 7 Radius of convergence (given) for eq 1 = 4. " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.9999999999999964 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" min_size = 9.7656250000E-4 "" 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. "" estimated_steps = 15625. "" step_error = 8.0000000000000E-13 "" est_needed_step_err = 8.0000000000000E-13 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 4.7994352795802770000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-127 "" estimated_step_error = 4.7994352795802770000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-127 "" "Double H and LOOP" opt_iter = 8 Radius of convergence (given) for eq 1 = 4. " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.9999999999999964 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" min_size = 9.7656250000E-4 "" 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. "" estimated_steps = 7812.5 "" step_error = 1.131370849898476000000000000E-12 "" est_needed_step_err = 1.131370849898476000000000000E-12 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 3.22087130737170600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-119 "" estimated_step_error = 3.22087130737170600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-119 "" "Double H and LOOP" opt_iter = 9 Radius of convergence (given) for eq 1 = 4. " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.9999999999999964 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" min_size = 9.7656250000E-4 "" 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. "" estimated_steps = 3906.25 "" step_error = 1.6000000000000E-12 "" est_needed_step_err = 1.6000000000000E-12 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 2.161523449266746200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-111 "" estimated_step_error = 2.161523449266746200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-111 "" "Double H and LOOP" opt_iter = 10 Radius of convergence (given) for eq 1 = 4. " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.9999999999999964 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" min_size = 9.7656250000E-4 "" 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. "" estimated_steps = 1953.125 "" step_error = 2.262741699796952000000000000E-12 "" est_needed_step_err = 2.262741699796952000000000000E-12 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.45061853382117440000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-103 "" estimated_step_error = 1.45061853382117440000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-103 "" "Double H and LOOP" opt_iter = 11 Radius of convergence (given) for eq 1 = 4. " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.9999999999999964 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" min_size = 9.7656250000E-4 "" 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. "" estimated_steps = 976.5625 "" step_error = 3.2000000000000E-12 "" est_needed_step_err = 3.2000000000000E-12 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 9.735536224832557000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-96 "" estimated_step_error = 9.735536224832557000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-96 "" "Double H and LOOP" opt_iter = 12 Radius of convergence (given) for eq 1 = 4. " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.9999999999999964 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" min_size = 9.7656250000E-4 "" 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. "" estimated_steps = 488.28125 "" step_error = 4.525483399593904000000000000E-12 "" est_needed_step_err = 4.525483399593904000000000000E-12 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 6.5342132667754950000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-88 "" estimated_step_error = 6.5342132667754950000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-88 "" "Double H and LOOP" opt_iter = 13 Radius of convergence (given) for eq 1 = 4. " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.9999999999999964 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" min_size = 9.7656250000E-4 "" 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. "" estimated_steps = 244.140625 "" step_error = 6.4000000000000E-12 "" est_needed_step_err = 6.4000000000000E-12 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 4.386117821653052000000000000000000000000000000000000000000000000000000000000000000000000000000000E-80 "" estimated_step_error = 4.386117821653052000000000000000000000000000000000000000000000000000000000000000000000000000000000E-80 "" "Double H and LOOP" opt_iter = 14 Radius of convergence (given) for eq 1 = 4. " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.9999999999999964 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" min_size = 9.7656250000E-4 "" 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. "" estimated_steps = 122.0703125 "" step_error = 9.050966799187808000000000000E-12 "" est_needed_step_err = 9.050966799187808000000000000E-12 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 2.944926520833646000000000000000000000000000000000000000000000000000000000000000000000000E-72 "" estimated_step_error = 2.944926520833646000000000000000000000000000000000000000000000000000000000000000000000000E-72 "" "Double H and LOOP" opt_iter = 15 "SETTING H FOR DISPLAY INTERVAL" Radius of convergence (given) for eq 1 = 4. " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.4414062499999982 " " 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) = -9.7656250000E-4 " " y[1] (numeric) = -9.7656250000E-4 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 4. " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.9999999999999862 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.01 " " y[1] (analytic) = -9.8886162072434670000E-4 " " y[1] (numeric) = -9.8886162072432170000E-4 " " absolute error = 2.493664996716660200000000000000000E-17 " " relative error = 2.5217532407517610000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.99 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.9899999999999807 " " Order of pole (three term test) = 1.9790352399601110000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.0199999999999996 " " y[1] (analytic) = -1.0013470890107976000E-3 " " y[1] (numeric) = -1.001347089010747000E-3 " " absolute error = 5.052382123782451000000000000000000E-17 " " relative error = 5.045585271310427000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.9800000000000004 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.9799999999999995 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.0299999999999994 " " y[1] (analytic) = -1.0140222071652674000E-3 " " y[1] (numeric) = -1.0140222071651908000E-3 " " absolute error = 7.65446733774766100000000000000000E-17 " " relative error = 7.548619037788115000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.9700000000000006 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.969999999999987 " " Order of pole (three term test) = 7.46809359568548100000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.039999999999999 " " y[1] (analytic) = -1.0268903445442867000E-3 " " y[1] (numeric) = -1.0268903445441821000E-3 " " absolute error = 1.04517089427602630000000000000000E-16 " " relative error = 1.017801851803224600000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.960000000000001 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.9600000000000177 " " Order of pole (three term test) = 1.29688593710732820000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.049999999999999 " " y[1] (analytic) = -1.0399549390904728000E-3 " " y[1] (numeric) = -1.0399549390903413000E-3 " " absolute error = 1.31405303305243140000000000000000E-16 " " relative error = 1.263567279368546800000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.950000000000001 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.95000000000001 " " Order of pole (three term test) = 1.12566386298358970000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.0599999999999987 " " y[1] (analytic) = -1.0532194989071875000E-3 " " y[1] (numeric) = -1.0532194989070268000E-3 " " absolute error = 1.60678761962351760000000000000000E-16 " " relative error = 1.525596156632789400000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.9400000000000013 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.940000000000014 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.0699999999999985 " " y[1] (analytic) = -1.0666876038734437000E-3 " " y[1] (numeric) = -1.066687603873254000E-3 " " absolute error = 1.89735380184963280000000000000000E-16 " " relative error = 1.77873427511466900000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.9300000000000015 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.9299999999999877 " " Order of pole (three term test) = 8.47138052422208600000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.0799999999999983 " " y[1] (analytic) = -1.0803629073002406000E-3 " " y[1] (numeric) = -1.0803629073000201000E-3 " " absolute error = 2.2052672188355160000000000000000E-16 " " relative error = 2.04122818724528500000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.9200000000000017 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.9200000000000172 " " Order of pole (three term test) = 1.46899770721117040000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.089999999999998 " " y[1] (analytic) = -1.094249137629459100E-3 " " y[1] (numeric) = -1.0942491376292082000E-3 " " absolute error = 2.50884382713145700000000000000000E-16 " " relative error = 2.29275376224332600000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.910000000000002 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.910000000000018 " " Order of pole (three term test) = 1.27320923187586480000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.099999999999998 " " y[1] (analytic) = -1.1083501001765582000E-3 " " y[1] (numeric) = -1.1083501001762748000E-3 " " absolute error = 2.83410447887710860000000000000000E-16 " " relative error = 2.557048064890002400000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.900000000000002 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.9000000000000075 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.1099999999999977 " " y[1] (analytic) = -1.122669678918285100E-3 " " y[1] (numeric) = -1.1226696789179691000E-3 " " absolute error = 3.159365130622760000000000000000E-16 " " relative error = 2.814153788910440700000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.8900000000000023 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.8900000000000374 " " Order of pole (three term test) = 9.55386365394589400000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.1199999999999974 " " y[1] (analytic) = -1.1372118383267135000E-3 " " y[1] (numeric) = -1.1372118383263638000E-3 " " absolute error = 3.49763620843823730000000000000000E-16 " " relative error = 3.075624163027213500000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.8800000000000026 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.8800000000000257 " " Order of pole (three term test) = 1.65427609384210440000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.1299999999999972 " " y[1] (analytic) = -1.1519806252509066000E-3 " " y[1] (numeric) = -1.1519806252505214000E-3 " " absolute error = 3.85108611666851200000000000000000E-16 " " relative error = 3.34301292248706700000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.8700000000000028 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.8699999999999872 " " Order of pole (three term test) = 7.15839082644994900000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.139999999999997 " " y[1] (analytic) = -1.1669801708475837000E-3 " " y[1] (numeric) = -1.1669801708471625000E-3 " " absolute error = 4.2110412379336990000000000000000E-16 " " relative error = 3.60849425134207600000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.860000000000003 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.859999999999986 " " Order of pole (three term test) = 1.23856961653769780000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.149999999999997 " " y[1] (analytic) = -1.1822146925621997000E-3 " " y[1] (numeric) = -1.1822146925617412000E-3 " " absolute error = 4.5840067852687130000000000000000E-16 " " relative error = 3.877474044358093500000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.850000000000003 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.8499999999999974 " " Order of pole (three term test) = 1.07110541017189430000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.1599999999999966 " " y[1] (analytic) = -1.197688496161876100E-3 " " y[1] (numeric) = -1.1976884961613794000E-3 " " absolute error = 4.965645949983610300000000000000E-16 " " relative error = 4.146024584770219000000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.8400000000000034 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.8400000000000105 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.1699999999999964 " " y[1] (analytic) = -1.2134059778216935000E-3 " " y[1] (numeric) = -1.2134059778211585000E-3 " " absolute error = 5.3494535190434790000000000000000E-16 " " relative error = 4.408626310418231600000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.8300000000000036 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.8299999999999863 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.179999999999996 " " y[1] (analytic) = -1.229371626265886000E-3 " " y[1] (numeric) = -1.2293716262653112000E-3 " " absolute error = 5.7484399185181450000000000000000E-16 " " relative error = 4.67591718866861400000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.820000000000004 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.820000000000003 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.189999999999996 " " y[1] (analytic) = -1.2455900249655255000E-3 " " y[1] (numeric) = -1.2455900249649086000E-3 " " absolute error = 6.169110361442520000000000000000E-16 " " relative error = 4.95276153292353470000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.810000000000004 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.8100000000000076 " " Order of pole (three term test) = 1.19360325362720330000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.1999999999999957 " " y[1] (analytic) = -1.262065854394345000E-3 " " y[1] (numeric) = -1.2620658543936852000E-3 " " absolute error = 6.5962860174018090000000000000000E-16 " " relative error = 5.22657830764886000000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.8000000000000043 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.800000000000027 " " Order of pole (three term test) = 2.06050068072723770000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.2099999999999955 " " y[1] (analytic) = -1.278803894344402000E-3 " " y[1] (numeric) = -1.278803894343698800E-3 " " absolute error = 7.0299668863960110000000000000000E-16 " " relative error = 5.49729862216288300000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.7900000000000045 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.78999999999998 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.2199999999999953 " " y[1] (analytic) = -1.2958090263033237000E-3 " " y[1] (numeric) = -1.2958090263025754000E-3 " " absolute error = 7.4831633944949520000000000000000E-16 " " relative error = 5.77489679620682600000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.7800000000000047 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.7799999999999674 " " Order of pole (three term test) = 1.53331767760829400000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.229999999999995 " " y[1] (analytic) = -1.3130862358949397000E-3 " " y[1] (numeric) = -1.313086235894145000E-3 " " absolute error = 7.94720192431874800000000000000000E-16 " " relative error = 6.05230769089761800000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.770000000000005 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.770000000000012 " " Order of pole (three term test) = 1.32192544854879830000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.239999999999995 " " y[1] (analytic) = -1.3306406153851785000E-3 " " y[1] (numeric) = -1.3306406153843348000E-3 " " absolute error = 8.43726130628219600000000000000000E-16 " " relative error = 6.34075137097771100000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.760000000000005 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.7599999999999927 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.2499999999999947 " " y[1] (analytic) = -1.3484773662551341000E-3 " " y[1] (numeric) = -1.348477366254242000E-3 " " absolute error = 8.920815475210730000000000000000E-16 " " relative error = 6.61547290184394400000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.7500000000000053 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.749999999999992 " " Order of pole (three term test) = 9.81391618381043600000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.2599999999999945 " " y[1] (analytic) = -1.3666018018433168000E-3 " " y[1] (numeric) = -1.366601801842372800E-3 " " absolute error = 9.4390641136588020000000000000000E-16 " " relative error = 6.90696009688197900000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.7400000000000055 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.740000000000026 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.2699999999999942 " " y[1] (analytic) = -1.385019350059096000E-3 " " y[1] (numeric) = -1.3850193500581007000E-3 " " absolute error = 9.952975943416931000000000000000E-16 " " relative error = 7.1861638200161290000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.7300000000000058 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.7299999999999907 " " Order of pole (three term test) = 7.27421164960446700000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.279999999999994 " " y[1] (analytic) = -1.4037355561695067000E-3 " " y[1] (numeric) = -1.4037355561684564000E-3 " " absolute error = 1.0501582242694596000000000000000E-15 " " relative error = 7.48116851250185800000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.720000000000006 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.7200000000000126 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.289999999999994 " " y[1] (analytic) = -1.4227560856615470000E-3 " " y[1] (numeric) = -1.4227560856604426000E-3 " " absolute error = 1.104585173328231900000000000000E-15 " " relative error = 7.7637002186121500000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.710000000000006 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.7099999999999973 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.2999999999999936 " " y[1] (analytic) = -1.442086727182285100E-3 " " y[1] (numeric) = -1.4420867271811233000E-3 " " absolute error = 1.1618310480354666000000000000000E-15 " " relative error = 8.05659622362370400000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.7000000000000064 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.699999999999991 " " Order of pole (three term test) = 1.8511767661570820000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.3099999999999934 " " y[1] (analytic) = -1.4617333955590467000E-3 " " y[1] (numeric) = -1.4617333955578250000E-3 " " absolute error = 1.2218958483911635000000000000000E-15 " " relative error = 8.3592250960637290000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.6900000000000066 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.689999999999995 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.319999999999993 " " y[1] (analytic) = -1.4817021349021348000E-3 " " y[1] (numeric) = -1.4817021349008527000E-3 " " absolute error = 1.2819606487468604000000000000000E-15 " " relative error = 8.65194574907954000000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.680000000000007 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.6799999999999855 " " Order of pole (three term test) = 6.83280761985263700000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.329999999999993 " " y[1] (analytic) = -1.5019991217925570000E-3 " " y[1] (numeric) = -1.5019991217912124000E-3 " " absolute error = 1.3446275343165226000000000000000E-15 " " relative error = 8.95225246677761200000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.670000000000007 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.6700000000000212 " " Order of pole (three term test) = 1.17341312395242760000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.3399999999999928 " " y[1] (analytic) = -1.5226306685573116000E-3 " " y[1] (numeric) = -1.5226306685559020000E-3 " " absolute error = 1.4094628242311558000000000000000E-15 " " relative error = 9.25676103428691700000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.6600000000000072 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.659999999999998 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.3499999999999925 " " y[1] (analytic) = -1.543603226634907000E-3 " " y[1] (numeric) = -1.5436032266334315000E-3 " " absolute error = 1.4753823163182744000000000000000E-15 " " relative error = 9.5580411524187100000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.6500000000000075 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.6500000000000283 " " Order of pole (three term test) = 8.6407562209259900000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.3599999999999923 " " y[1] (analytic) = -1.5649233900338538000E-3 " " y[1] (numeric) = -1.5649233900323095000E-3 " " absolute error = 1.5441207340538554000000000000000E-15 " " relative error = 9.86706917340184800000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.6400000000000077 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.640000000000005 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.369999999999992 " " y[1] (analytic) = -1.5865978988869445000E-3 " " y[1] (numeric) = -1.5865978988853300000E-3 " " absolute error = 1.6145938752654132000000000000000E-15 " " relative error = 1.01764528769268430000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.630000000000008 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.630000000000018 " " Order of pole (three term test) = 1.27043468089842930000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.379999999999992 " " y[1] (analytic) = -1.6086336431042747000E-3 " " y[1] (numeric) = -1.6086336431025863000E-3 " " absolute error = 1.6883196229944275000000000000000E-15 " " relative error = 1.04953643748018240000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.620000000000008 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.6199999999999695 " " Order of pole (three term test) = 2.17716470074936660000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.3899999999999917 " " y[1] (analytic) = -1.6310376661280016000E-3 " " y[1] (numeric) = -1.6310376661262390000E-3 " " absolute error = 1.762479051592436000000000000000E-15 " " relative error = 1.08058758432996170000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.6100000000000083 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.6100000000000048 " " Order of pole (three term test) = 9.32362173265952500000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.3999999999999915 " " y[1] (analytic) = -1.6538171687920006000E-3 " " y[1] (numeric) = -1.6538171687901607000E-3 " " absolute error = 1.839891086707901000000000000000E-15 " " relative error = 1.11251178269712540000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.6000000000000085 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.600000000000011 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.4099999999999913 " " y[1] (analytic) = -1.6769795132896115000E-3 " " y[1] (numeric) = -1.6769795132876908000E-3 " " absolute error = 1.9207725687753197000000000000000E-15 " " relative error = 1.14537628727942930000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.5900000000000087 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.589999999999999 " " Order of pole (three term test) = 1.3661565064724920000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.419999999999991 " " y[1] (analytic) = -1.7005322272528467000E-3 " " y[1] (numeric) = -1.700532227250844000E-3 " " absolute error = 2.0025214125807267000000000000000E-15 " " relative error = 1.17758509982238540000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.580000000000009 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.5799999999999845 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.429999999999991 " " y[1] (analytic) = -1.7244830079465068000E-3 " " y[1] (numeric) = -1.7244830079444196000E-3 " " absolute error = 2.087089182034596000000000000000E-15 " " relative error = 1.21026949666490270000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.570000000000009 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.5700000000000167 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.4399999999999906 " " y[1] (analytic) = -1.74883972658076000E-3 " " y[1] (numeric) = -1.7488397265785857000E-3 " " absolute error = 2.1742590367024306000000000000000E-15 " " relative error = 1.24325803197153360000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.5600000000000094 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.5600000000000107 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.4499999999999904 " " y[1] (analytic) = -1.7736104327458957000E-3 " " y[1] (numeric) = -1.773610432743630800E-3 " " absolute error = 2.2646814978877217000000000000000E-15 " " relative error = 1.2768765091111650000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.5500000000000096 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.550000000000016 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.45999999999999 " " y[1] (analytic) = -1.7988033589730557000E-3 " " y[1] (numeric) = -1.7988033589706975000E-3 " " absolute error = 2.358139725155972100000000000000E-15 " " relative error = 1.31094914482606050000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.54000000000001 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.540000000000037 " " Order of pole (three term test) = 1.24573023002248080000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.46999999999999 " " y[1] (analytic) = -1.824426925424901000E-3 " " y[1] (numeric) = -1.824426925422448000E-3 " " absolute error = 2.4531158354657023000000000000000E-15 " " relative error = 1.34459528155362130000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.53000000000001 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.5299999999999936 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.4799999999999898 " " y[1] (analytic) = -1.8504897447202992000E-3 " " y[1] (numeric) = -1.8504897447177454000E-3 " " absolute error = 2.553729797072357000000000000000E-15 " " relative error = 1.38002915409744830000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.5200000000000102 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.5200000000000284 " " Order of pole (three term test) = 9.07048448683247500000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.4899999999999896 " " y[1] (analytic) = -1.8770006268972297000E-3 " " y[1] (numeric) = -1.8770006268945738000E-3 " " absolute error = 2.6558616417204917000000000000000E-15 " " relative error = 1.41494978939392030000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.5100000000000104 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.509999999999996 " " Order of pole (three term test) = 7.73463550197141700000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.4999999999999893 " " y[1] (analytic) = -1.9039685845183270000E-3 " " y[1] (numeric) = -1.9039685845155657000E-3 " " absolute error = 2.7614629333205800000000000000000E-15 " " relative error = 1.450372110009990000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.5000000000000107 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.500000000000002 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.509999999999989 " " y[1] (analytic) = -1.931402837923529000E-3 " " y[1] (numeric) = -1.9314028379206596000E-3 " " absolute error = 2.869232629265639000000000000000E-15 " " relative error = 1.48556923130048840000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.490000000000011 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.4900000000000015 " " Order of pole (three term test) = 1.1232986462589220000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.519999999999989 " " y[1] (analytic) = -1.9593128206345464000E-3 " " y[1] (numeric) = -1.959312820631564000E-3 " " absolute error = 2.9824233360731256000000000000000E-15 " " relative error = 1.52217823752474250000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.480000000000011 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.4799999999999898 " " Order of pole (three term test) = 9.56552886973204100000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.5299999999999887 " " y[1] (analytic) = -1.987708184915964000E-3 " " y[1] (numeric) = -1.9877081849128658000E-3 " " absolute error = 3.0982161280945775000000000000000E-15 " " relative error = 1.5586876140098820000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.4700000000000113 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.4700000000000037 " " Order of pole (three term test) = 1.62836556478406530000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.5399999999999885 " " y[1] (analytic) = -2.0165988074980143000E-3 " " y[1] (numeric) = -2.016598807494797000E-3 " " absolute error = 3.217478367067983000000000000000E-15 " " relative error = 1.5954975055548581000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.4600000000000115 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.460000000000021 " " Order of pole (three term test) = 6.92680334781322500000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.5499999999999883 " " y[1] (analytic) = -2.045994795466177800E-3 " " y[1] (numeric) = -2.045994795462836900E-3 " " absolute error = 3.3410774147313305000000000000000E-15 " " relative error = 1.63298431752367660000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.4500000000000117 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.450000000000027 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.559999999999988 " " y[1] (analytic) = -2.075906492322994200E-3 " " y[1] (numeric) = -2.0759064923195242000E-3 " " absolute error = 3.4698806328226084000000000000000E-15 " " relative error = 1.67150141186741040000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.440000000000012 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.4399999999999884 " " Order of pole (three term test) = 1.00132280078266090000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.569999999999988 " " y[1] (analytic) = -2.106344484227627200E-3 " " y[1] (numeric) = -2.1063444842240264000E-3 " " absolute error = 3.600852255258857300000000000000E-15 " " relative error = 1.709526757005870000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.430000000000012 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.4300000000000166 " " Order of pole (three term test) = 1.70138280579825360000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.5799999999999876 " " y[1] (analytic) = -2.137319606418954800E-3 " " y[1] (numeric) = -2.1373196064152183000E-3 " " absolute error = 3.7365943672540425000000000000000E-15 " " relative error = 1.7482618678236180000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.4200000000000124 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.4199999999999915 " " Order of pole (three term test) = 7.22375920011809400000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.5899999999999874 " " y[1] (analytic) = -2.168842949828109200E-3 " " y[1] (numeric) = -2.168842949824232000E-3 " " absolute error = 3.877106968808164000000000000000E-15 " " relative error = 1.787638412968279900000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.4100000000000126 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.409999999999996 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.599999999999987 " " y[1] (analytic) = -2.2009258678866547000E-3 " " y[1] (numeric) = -2.2009258678826316000E-3 " " absolute error = 4.02325742165921000000000000000E-15 " " relative error = 1.82798406814236370000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.400000000000013 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.4000000000000186 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.609999999999987 " " y[1] (analytic) = -2.233579983536781700E-3 " " y[1] (numeric) = -2.2335799835326084000E-3 " " absolute error = 4.173311002331203700000000000000E-15 " " relative error = 1.86844036617974050000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.390000000000013 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.3900000000000268 " " Order of pole (three term test) = 8.82093082885417700000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.619999999999987 " " y[1] (analytic) = -2.2668171964501350000E-3 " " y[1] (numeric) = -2.2668171964458067000E-3 " " absolute error = 4.328135072562133700000000000000E-15 " " relative error = 1.90934455559100660000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.380000000000013 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.380000000000011 " " Order of pole (three term test) = 7.47595248831648700000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.6299999999999866 " " y[1] (analytic) = -2.300649690462113000E-3 " " y[1] (numeric) = -2.3006496904576257000E-3 " " absolute error = 4.487295951483006000000000000000E-15 " " relative error = 1.95044728890545640000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.3700000000000134 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.3700000000000117 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.6399999999999864 " " y[1] (analytic) = -2.3350899412287562000E-3 " " y[1] (numeric) = -2.3350899412241033000E-3 " " absolute error = 4.652962043438791000000000000000E-15 " " relative error = 1.9926264771584510000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.3600000000000136 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.3600000000000025 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.649999999999986 " " y[1] (analytic) = -2.370150724113549200E-3 " " y[1] (numeric) = -2.3701507241087252000E-3 " " absolute error = 4.823832305822506300000000000000E-15 " " relative error = 2.03524284626525140000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.350000000000014 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.350000000000008 " " Order of pole (three term test) = 1.81509977312701850000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.659999999999986 " " y[1] (analytic) = -2.4058451223117847000E-3 " " y[1] (numeric) = -2.4058451223067834000E-3 " " absolute error = 5.001207781241135000000000000000E-15 " " relative error = 2.0787737892435310000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.340000000000014 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.340000000000017 " " Order of pole (three term test) = 1.5353007069053650000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.6699999999999857 " " y[1] (analytic) = -2.4421865352203545000E-3 " " y[1] (numeric) = -2.442186535215171200E-3 " " absolute error = 5.1833537462187000000000000000000E-15 " " relative error = 2.12242335770269690000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.3300000000000143 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.3300000000000125 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.6799999999999855 " " y[1] (analytic) = -2.4791886870611776000E-3 " " y[1] (numeric) = -2.4791886870558058000E-3 " " absolute error = 5.372004924231177000000000000000E-15 " " relative error = 2.1668398828485840000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.3200000000000145 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.3200000000000136 " " Order of pole (three term test) = 1.09679129745240510000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.6899999999999853 " " y[1] (analytic) = -2.516865635766714000E-3 " " y[1] (numeric) = -2.5168656357611480000E-3 " " absolute error = 5.5658602726715860000000000000000E-15 " " relative error = 2.21142527180480770000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.3100000000000147 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.3100000000000214 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.699999999999985 " " y[1] (analytic) = -2.555231782136383000E-3 " " y[1] (numeric) = -2.555231782130615000E-3 " " absolute error = 5.7679555576228840000000000000000E-15 " " relative error = 2.25731207554110830000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.300000000000015 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.3000000000000083 " " Order of pole (three term test) = 7.81937320245144200000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.709999999999985 " " y[1] (analytic) = -2.5943018792729694000E-3 " " y[1] (numeric) = -2.594301879266992500E-3 " " absolute error = 5.976556055609095000000000000000E-15 " " relative error = 2.3037242131914010000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.290000000000015 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.29000000000002 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.7199999999999847 " " y[1] (analytic) = -2.634091042308497000E-3 " " y[1] (numeric) = -2.6340910423023056000E-3 " " absolute error = 6.1912280857612250000000000000000E-15 " " relative error = 2.3504229680441420000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.2800000000000153 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.2800000000000082 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.7299999999999844 " " y[1] (analytic) = -2.6746147584293417000E-3 " " y[1] (numeric) = -2.6746147584229263000E-3 " " absolute error = 6.415007414162233000000000000000E-15 " " relative error = 2.3984790310247980000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.2700000000000156 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.2700000000000204 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.7399999999999842 " " y[1] (analytic) = -2.7158888972107414000E-3 " " y[1] (numeric) = -2.7158888972040970000E-3 " " absolute error = 6.6448582747291600000000000000000E-15 " " relative error = 2.4466605690510862000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.2600000000000158 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.260000000000005 " " Order of pole (three term test) = 7.89963286423728500000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.749999999999984 " " y[1] (analytic) = -2.7579297212712720000E-3 " " y[1] (numeric) = -2.757929721264389000E-3 " " absolute error = 6.8833827526759700000000000000000E-15 " " relative error = 2.49585139881775660000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.250000000000016 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.2500000000000093 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.759999999999984 " " y[1] (analytic) = -2.800753897258174700E-3 " " y[1] (numeric) = -2.8007538972510426000E-3 " " absolute error = 7.132315571478642000000000000000E-15 " " relative error = 2.5465698997905140000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.240000000000016 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.240000000000044 " " Order of pole (three term test) = 2.23873076268213840000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.7699999999999836 " " y[1] (analytic) = -2.844378507174893000E-3 " " y[1] (numeric) = -2.844378507167508000E-3 " " absolute error = 7.385151518102262000000000000000E-15 " " relative error = 2.59640251797478850000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.2300000000000164 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.2300000000000204 " " Order of pole (three term test) = 9.41439791019074700000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.7799999999999834 " " y[1] (analytic) = -2.8888210600626150000E-3 " " y[1] (numeric) = -2.8888210600549640000E-3 " " absolute error = 7.650997890795708000000000000000E-15 " " relative error = 2.64848453113598950000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.2200000000000166 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.2200000000000224 " " Order of pole (three term test) = 7.91370969653500200000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.789999999999983 " " y[1] (analytic) = -2.9340995040479410000E-3 " " y[1] (numeric) = -2.9340995040400186000E-3 " " absolute error = 7.922915795655072000000000000000E-15 " " relative error = 2.7002887205169634000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.210000000000017 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.210000000000031 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.799999999999983 " " y[1] (analytic) = -2.980232238769452000E-3 " " y[1] (numeric) = -2.980232238761246000E-3 " " absolute error = 8.205675722239292000000000000000E-15 " " relative error = 2.75336788035936530000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.200000000000017 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.2000000000000015 " " Order of pole (three term test) = 1.11655489882301050000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.8099999999999827 " " y[1] (analytic) = -3.0272381281962235000E-3 " " y[1] (numeric) = -3.027238128187725000E-3 " " absolute error = 8.498410308810378000000000000000E-15 " " relative error = 2.80731476974166700000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.1900000000000173 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.1900000000000195 " " Order of pole (three term test) = 9.37043055948971400000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.8199999999999825 " " y[1] (analytic) = -3.075136513852002000E-3 " " y[1] (numeric) = -3.0751365138432013000E-3 " " absolute error = 8.800685874499337000000000000000E-15 " " relative error = 2.86188461385584200000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.1800000000000175 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.1799999999999873 " " Order of pole (three term test) = 7.85959222862795800000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.8299999999999823 " " y[1] (analytic) = -3.123947228459174000E-3 " " y[1] (numeric) = -3.1239472284500586000E-3 " " absolute error = 9.115538185389127000000000000000E-15 " " relative error = 2.9179552401994920000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.1700000000000177 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.1700000000000115 " " Order of pole (three term test) = 1.31774074684002730000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.839999999999982 " " y[1] (analytic) = -3.1736906100172270000E-3 " " y[1] (numeric) = -3.1736906100077883000E-3 " " absolute error = 9.438196751920813000000000000000E-15 " " relative error = 2.9738868439572264000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.160000000000018 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.1600000000000197 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.849999999999982 " " y[1] (analytic) = -3.2243875163310126000E-3 " " y[1] (numeric) = -3.2243875163212393000E-3 " " absolute error = 9.773432063653331000000000000000E-15 " " relative error = 3.03109722828054760000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.150000000000018 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.1500000000000163 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.8599999999999817 " " y[1] (analytic) = -3.2760593400046184000E-3 " " y[1] (numeric) = -3.2760593399944954000E-3 " " absolute error = 1.012341252493165200000000000000E-14 " " relative error = 3.0901187903749566000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.1400000000000183 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.1400000000000206 " " Order of pole (three term test) = 7.7369819414828510000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.8699999999999815 " " y[1] (analytic) = -3.328728023917339000E-3 " " y[1] (numeric) = -3.3287280239068556000E-3 " " absolute error = 1.04833676461968400000000000000E-14 " " relative error = 3.14936142901207140000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.1300000000000185 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.130000000000012 " " Order of pole (three term test) = 1.29426792764883340000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.8799999999999812 " " y[1] (analytic) = -3.3824160771988776000E-3 " " y[1] (numeric) = -3.38241607718802000E-3 " " absolute error = 1.085763423613883600000000000000E-14 " " relative error = 3.21002324620290440000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.1200000000000188 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.1199999999999912 " " Order of pole (three term test) = 2.1638569537863840000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.889999999999981 " " y[1] (analytic) = -3.4371465917214960000E-3 " " y[1] (numeric) = -3.4371465917102520000E-3 " " absolute error = 1.12440438904126700000000000000E-14 " " relative error = 3.2713309107893140000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.110000000000019 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.110000000000015 " " Order of pole (three term test) = 9.03905590129690100000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.899999999999981 " " y[1] (analytic) = -3.492943259127624000E-3 " " y[1] (numeric) = -3.492943259115981000E-3 " " absolute error = 1.164303028988733500000000000000E-14 " " relative error = 3.3333007226676870000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.100000000000019 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.100000000000008 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.9099999999999806 " " y[1] (analytic) = -3.549830388412087000E-3 " " y[1] (numeric) = -3.549830388400027000E-3 " " absolute error = 1.206023128585975700000000000000E-14 " " relative error = 3.3974105707215350000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.0900000000000194 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.09000000000001 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.9199999999999804 " " y[1] (analytic) = -3.607832924078878000E-3 " " y[1] (numeric) = -3.607832924066388000E-3 " " absolute error = 1.249000902703301100000000000000E-14 " " relative error = 3.4619144760484870000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.0800000000000196 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.080000000000004 " " Order of pole (three term test) = 1.05053712952721120000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.92999999999998 " " y[1] (analytic) = -3.6669764648932446000E-3 " " y[1] (numeric) = -3.666976464880308000E-3 " " absolute error = 1.293670032209704000000000000000E-14 " " relative error = 3.5278929237615547000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.07000000000002 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.070000000000034 " " Order of pole (three term test) = 8.75629347975569500000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.93999999999998 " " y[1] (analytic) = -3.727287283250559000E-3 " " y[1] (numeric) = -3.7272872832371634000E-3 " " absolute error = 1.339553468149290400000000000000E-14 " " relative error = 3.5939099037761020000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.06000000000002 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.0600000000000103 " " Order of pole (three term test) = 7.29409080154892900000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.9499999999999797 " " y[1] (analytic) = -3.7887923451844396000E-3 " " y[1] (numeric) = -3.7887923451705646000E-3 " " absolute error = 1.387518572260049200000000000000E-14 " " relative error = 3.66216579281149370000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.0500000000000203 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.0500000000000314 " " Order of pole (three term test) = 1.21448535309297140000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.9599999999999795 " " y[1] (analytic) = -3.851519331037322000E-3 " " y[1] (numeric) = -3.851519331022948000E-3 " " absolute error = 1.437391872194382400000000000000E-14 " " relative error = 3.73201261281805000000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.0400000000000205 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.0400000000000227 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.9699999999999793 " " y[1] (analytic) = -3.915496656817760700E-3 " " y[1] (numeric) = -3.915496656802875400E-3 " " absolute error = 1.488566214735698200000000000000E-14 " " relative error = 3.8017302661816077000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.0300000000000207 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.0300000000000327 " " Order of pole (three term test) = 8.4021121515970200000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.979999999999979 " " y[1] (analytic) = -3.98075349626962950E-3 " " y[1] (numeric) = -3.980753496254209000E-3 " " absolute error = 1.542082433969582700000000000000E-14 " " relative error = 3.8738455807792930000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.020000000000021 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.020000000000019 " " Order of pole (three term test) = 6.98216461408108600000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.989999999999979 " " y[1] (analytic) = -4.047319803679339000E-3 " " y[1] (numeric) = -4.047319803663363000E-3 " " absolute error = 1.597593585200840500000000000000E-14 " " relative error = 3.9472877427390330000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.010000000000021 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.0100000000000082 " " Order of pole (three term test) = 1.15972502063308140000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.9999999999999787 " " y[1] (analytic) = -4.115226337448415000E-3 " " y[1] (numeric) = -4.115226337431863000E-3 " " absolute error = 1.655186404603270500000000000000E-14 " " relative error = 4.02210296318608830000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 3.0000000000000213 " " Order of pole (given) = 0.0 " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.0000000000000164 " " Order of pole (three term test) = 9.62546098568050500000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" "Finished!" "diff ( y , x , 1 ) = m1 * 5.0 / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; " Iterations = 101 "Total Elapsed Time "= 14 Seconds "Elapsed Time(since restart) "= 13 Seconds "Time to Timeout "= 9 Minutes 45 Seconds Percent Done = 101.99999999999783 "%" (%o232) diffeq.max