(%i1) batch("temp/diffeq.diff_B.max") read and interpret file: /home/dennis/src/mine/omni/testtar/omnisode0060dir/temp/diffeq.diff_B.max (%i2) load("stringproc") (%i3) keepfloat:true (%i4) alias(convfloat,float) (%i5) alias(int_trunc,truncate) (%i6) alias(elapsed_time_seconds,elapsed_real_time) (%i7) alias(ln,log) (%i8) alias(arcsin,asin) (%i9) alias(arccos,acos) (%i10) alias(arctan,atan) (%i11) alias(float_abs,abs) (%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([30],convfloat)),fixnum) (%i24) mode_declare(ats([mmm_ats],fixnum,[arr_a], completearray([30],convfloat),[arr_b], completearray([30],convfloat),[jjj_ats],fixnum), convfloat) (%i25) mode_declare(att([mmm_att],fixnum,[arr_a], completearray([30],convfloat),[arr_b], completearray([30],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(neg([nnn],convfloat),convfloat) (%i43) mode_declare(factorial_2([nnn],fixnum),convfloat) (%i44) mode_declare(factorial_1([nnn],fixnum),convfloat) (%i45) mode_declare(factorial_3([mmm],fixnum,[nnn],fixnum),convfloat) (%i46) mode_declare(convfloat([mmm],fixnum),convfloat) (%i47) mode_declare(elaped_time_seconds(),convfloat) (%i48) mode_declare(Si([x],convfloat),convfloat) (%i49) mode_declare(Ci([x],convfloat),convfloat) (%i50) mode_declare(estimated_needed_step_error([x_start],convfloat,[x_end], convfloat,[estimated_h], convfloat,[estimated_answer], convfloat),convfloat) (%i51) mode_declare(my_check_sign([x0],convfloat,[xf],convfloat),convfloat) (%i52) mode_declare(main_prog(),fixnum) (%i53) define_variable(always,1,fixnum) (%i54) define_variable(info,2,fixnum) (%i55) define_variable(debugl,3,fixnum) (%i56) define_variable(debugmassive,4,fixnum) (%i57) define_variable(glob_iolevel,5,fixnum) (%i58) define_variable(glob_yes_pole,4,fixnum) (%i59) define_variable(glob_no_pole,3,fixnum) (%i60) define_variable(glob_not_given,0,fixnum) (%i61) define_variable(glob_no_sing_tests,4,fixnum) (%i62) define_variable(glob_ratio_test,1,fixnum) (%i63) define_variable(glob_three_term_test,2,fixnum) (%i64) define_variable(glob_six_term_test,3,fixnum) (%i65) define_variable(ats_max_terms,30,fixnum) (%i66) define_variable(glob_log_10,0.0,convfloat) (%i67) define_variable(max_unchanged,10,fixnum) (%i68) define_variable(glob__small,1.0E-51,convfloat) (%i69) define_variable(glob_small_float,1.0E-51,convfloat) (%i70) define_variable(glob_smallish_float,1.0E-61,convfloat) (%i71) define_variable(glob_large_float,1.0E+100,convfloat) (%i72) define_variable(glob_larger_float,1.1E+100,convfloat) (%i73) define_variable(glob__m2,-2.0,convfloat) (%i74) define_variable(glob__m1,-1.0,convfloat) (%i75) define_variable(glob__0,0.0,convfloat) (%i76) define_variable(glob__1,1.0,convfloat) (%i77) define_variable(glob__2,2.0,convfloat) (%i78) define_variable(glob__3,3.0,convfloat) (%i79) define_variable(glob__4,4.0,convfloat) (%i80) define_variable(glob__5,5.0,convfloat) (%i81) define_variable(glob__8,8.0,convfloat) (%i82) define_variable(glob__10,10.0,convfloat) (%i83) define_variable(glob__100,100.0,convfloat) (%i84) define_variable(glob__pi,0.0,convfloat) (%i85) define_variable(glob__0_5,0.5,convfloat) (%i86) define_variable(glob__0_8,0.8,convfloat) (%i87) define_variable(glob__m0_8,-0.8,convfloat) (%i88) define_variable(glob__0_25,0.25,convfloat) (%i89) define_variable(glob__0_125,0.125,convfloat) (%i90) define_variable(glob_prec,1.0E-16,convfloat) (%i91) define_variable(glob_check_sign,1.0,convfloat) (%i92) define_variable(glob_desired_digits_correct,8.0,convfloat) (%i93) define_variable(glob_max_estimated_step_error,0.0,convfloat) (%i94) define_variable(glob_ratio_of_radius,0.1,convfloat) (%i95) define_variable(glob_percent_done,0.0,convfloat) (%i96) define_variable(glob_total_exp_sec,0.1,convfloat) (%i97) define_variable(glob_optimal_expect_sec,0.1,convfloat) (%i98) define_variable(glob_estimated_size_answer,100.0,convfloat) (%i99) define_variable(glob_almost_1,0.999,convfloat) (%i100) define_variable(glob_clock_sec,0.0,convfloat) (%i101) define_variable(glob_clock_start_sec,0.0,convfloat) (%i102) define_variable(glob_disp_incr,0.1,convfloat) (%i103) define_variable(glob_h,0.1,convfloat) (%i104) define_variable(glob_diff_rc_fm,0.1,convfloat) (%i105) define_variable(glob_diff_rc_fmm1,0.1,convfloat) (%i106) define_variable(glob_diff_rc_fmm2,0.1,convfloat) (%i107) define_variable(glob_diff_ord_fm,0.1,convfloat) (%i108) define_variable(glob_diff_ord_fmm1,0.1,convfloat) (%i109) define_variable(glob_diff_ord_fmm2,0.1,convfloat) (%i110) define_variable(glob_six_term_ord_save,0.1,convfloat) (%i111) define_variable(glob_guess_error_rc,0.1,convfloat) (%i112) define_variable(glob_guess_error_ord,0.1,convfloat) (%i113) define_variable(glob_least_given_sing,9.9E+200,convfloat) (%i114) define_variable(glob_least_ratio_sing,9.9E+200,convfloat) (%i115) define_variable(glob_least_3_sing,9.9E+100,convfloat) (%i116) define_variable(glob_least_6_sing,9.9E+100,convfloat) (%i117) define_variable(glob_last_good_h,0.1,convfloat) (%i118) define_variable(glob_max_h,0.1,convfloat) (%i119) define_variable(glob_min_h,1.0E-6,convfloat) (%i120) define_variable(glob_display_interval,0.1,convfloat) (%i121) define_variable(glob_abserr,1.0E-11,convfloat) (%i122) define_variable(glob_relerr,1.0E-11,convfloat) (%i123) define_variable(glob_min_pole_est,1.0E+9,convfloat) (%i124) define_variable(glob_max_rel_trunc_err,1.0E-11,convfloat) (%i125) define_variable(glob_max_trunc_err,1.0E-11,convfloat) (%i126) define_variable(glob_max_hours,0.0,convfloat) (%i127) define_variable(glob_optimal_clock_start_sec,0.0,convfloat) (%i128) define_variable(glob_optimal_start,0.0,convfloat) (%i129) define_variable(glob_upper_ratio_limit,1.0001,convfloat) (%i130) define_variable(glob_lower_ratio_limit,0.9999,convfloat) (%i131) define_variable(glob_max_sec,10000.0,convfloat) (%i132) define_variable(glob_orig_start_sec,0.0,convfloat) (%i133) define_variable(glob_normmax,0.0,convfloat) (%i134) define_variable(glob_max_minutes,0.0,convfloat) (%i135) define_variable(glob_next_display,0.0,convfloat) (%i136) define_variable(glob_est_digits,1,fixnum) (%i137) define_variable(glob_subiter_method,3,fixnum) (%i138) define_variable(glob_html_log,true,boolean) (%i139) define_variable(glob_min_good_digits,99999,fixnum) (%i140) define_variable(glob_good_digits,0,fixnum) (%i141) define_variable(glob_min_apfp_est_good_digits,99999,fixnum) (%i142) define_variable(glob_apfp_est_good_digits,0,fixnum) (%i143) define_variable(glob_max_opt_iter,10,fixnum) (%i144) define_variable(glob_dump,false,boolean) (%i145) define_variable(glob_djd_debug,true,boolean) (%i146) define_variable(glob_display_flag,true,boolean) (%i147) define_variable(glob_djd_debug2,true,boolean) (%i148) define_variable(glob_h_reason,0,fixnum) (%i149) define_variable(glob_sec_in_minute,60,fixnum) (%i150) define_variable(glob_min_in_hour,60,fixnum) (%i151) define_variable(glob_hours_in_day,24,fixnum) (%i152) define_variable(glob_days_in_year,365,fixnum) (%i153) define_variable(glob_sec_in_hour,3600,fixnum) (%i154) define_variable(glob_sec_in_day,86400,fixnum) (%i155) define_variable(glob_sec_in_year,31536000,fixnum) (%i156) define_variable(glob_not_yet_finished,true,boolean) (%i157) define_variable(glob_initial_pass,true,boolean) (%i158) define_variable(glob_not_yet_start_msg,true,boolean) (%i159) define_variable(glob_reached_optimal_h,false,boolean) (%i160) define_variable(glob_optimal_done,false,boolean) (%i161) define_variable(glob_type_given_pole,0,fixnum) (%i162) define_variable(glob_optimize,false,boolean) (%i163) define_variable(glob_look_poles,false,boolean) (%i164) define_variable(glob_dump_closed_form,false,boolean) (%i165) define_variable(glob_max_iter,1000,fixnum) (%i166) define_variable(glob_no_eqs,0,fixnum) (%i167) define_variable(glob_unchanged_h_cnt,0,fixnum) (%i168) define_variable(glob_warned,false,boolean) (%i169) define_variable(glob_warned2,false,boolean) (%i170) define_variable(glob_start,0,fixnum) (%i171) define_variable(glob_iter,0,fixnum) (%i172) completearray(array_y_init,[30],convfloat) (%i173) completearray(array_norms,[30],convfloat) (%i174) completearray(array_fact_1,[30],convfloat) (%i175) completearray(array_1st_rel_error,[2],convfloat) (%i176) completearray(array_last_rel_error,[2],convfloat) (%i177) completearray(array_est_rel_error,[2],convfloat) (%i178) completearray(array_max_est_error,[2],convfloat) (%i179) completearray(array_type_pole,[2],convfloat) (%i180) completearray(array_type_real_pole,[2],convfloat) (%i181) completearray(array_type_complex_pole,[2],convfloat) (%i182) completearray(array_est_digits,[2],convfloat) (%i183) completearray(array_y,[30],convfloat) (%i184) completearray(array_x,[30],convfloat) (%i185) completearray(array_tmp0,[30],convfloat) (%i186) completearray(array_tmp1,[30],convfloat) (%i187) completearray(array_tmp2,[30],convfloat) (%i188) completearray(array_m1,[30],convfloat) (%i189) completearray(array_y_higher,[3,30],convfloat) (%i190) completearray(array_y_higher_work,[3,30],convfloat) (%i191) completearray(array_y_higher_work2,[3,30],convfloat) (%i192) completearray(array_y_set_initial,[2,30],convfloat) (%i193) completearray(array_given_rad_poles,[2,3],convfloat) (%i194) completearray(array_given_ord_poles,[2,3],convfloat) (%i195) completearray(array_rad_test_poles,[2,4],convfloat) (%i196) completearray(array_ord_test_poles,[2,4],convfloat) (%i197) completearray(array_fact_2,[30,30],convfloat) (%i198) omniout_str(iolevel,str):=if glob_iolevel >= iolevel then printf(true,"~a~%",string(str)) (%i199) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel then printf(true,"~a",string(str)) (%i200) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel then printf(true,"~a = ~a~%",string(label), string(str)) (%i201) 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)) (%i202) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if glob_iolevel >= iolevel then (printf(true,"~a = ~d ~a~%",prelabel,value, postlabel),newline()) (%i203) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen, postlabel):=if glob_iolevel >= iolevel then (sprint(prelabel,"[",elemnt,"]=",value, postlabel),newline()) (%i204) 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) (%i205) 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) (%i206) zero_ats_ar(arr_a):=( block(mode_declare([iii],fixnum),iii:1, while iii <= ats_max_terms do (arr_a[iii]:glob__0,iii:1+iii)),0) (%i207) ats(mmm_ats,arr_a,arr_b,jjj_ats):=block( mode_declare([[iii_ats,lll_ats,ma_ats],fixnum,[ret_ats], convfloat]),ret_ats:glob__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 <= ats_max_terms and iii_ats <= ats_max_terms then ret_ats :c(arr_a[iii_ats])*c(arr_b[lll_ats])+ret_ats, iii_ats:1+iii_ats)),ret_ats) (%i208) 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:glob__0, if jjj_att < mmm_att then (ma_att:2+mmm_att,iii_att:jjj_att, while iii_att < mmm_att and iii_att <= ats_max_terms do (lll_att:ma_att-iii_att,al_att:lll_att-1, if lll_att <= ats_max_terms and iii_att <= ats_max_terms then ret_att :c(arr_aa[iii_att])*c(arr_bb[lll_att]) *c(al_att) +ret_att,iii_att:1+iii_att), ret_att:ret_att/c(mmm_att)),ret_att) (%i209) logditto(file):=(printf(file,""),printf(file,"ditto"), printf(file,""),0) (%i210) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n), printf(file,""),0) (%i211) logitem_str(file,str):=(printf(file,""),printf(file,str), printf(file,""),0) (%i212) logitem_good_digits(file,rel_error):=( block(mode_declare([[good_digits],fixnum]), printf(file,""), printf(file,"~d",glob_min_good_digits), printf(file,"")),0) (%i213) log_revs(file,revs):=printf(file,revs) (%i214) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x), printf(file,""),0) (%i215) 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") elseif glob_h_reason = 7 then printf(file,"Opt Iter") else printf(file,"Impossible"), printf(file,""),0) (%i216) logstart(file):=(printf(file,""),0) (%i217) logend(file):=(printf(file,"~%"),0) (%i218) 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) (%i219) comp_expect_sec(t_end2,t_start2,t2,clock_sec2):=block( mode_declare([[ms2,rrr,sec_left,sub1,sub2], convfloat]),ms2:c(clock_sec2), sub1:c(t_end2-t_start2),sub2:c(t2-t_start2), if sub1 = glob__0 then sec_left:glob__0 else (if sub2 > glob__0 then (rrr:sub1/sub2, sec_left:rrr*c(ms2)-c(ms2)) else sec_left:glob__0),sec_left) (%i220) 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:glob__100*sub2/sub1 else rrr:0.0,rrr) (%i221) comp_rad_from_ratio(term1,term2,last_no):=( if abs(term2) > glob__0 then ret:abs(term1*glob_h/term2) else ret:glob_larger_float,ret) (%i222) comp_ord_from_ratio(term1,term2,last_no):=( if abs(term2) > glob__0 then ret :abs(term2)*c(last_no) *log(abs(term1*glob_h/term2)) /log(c(last_no)) +glob__1 else ret:glob_larger_float,ret) (%i223) c(in_val):=(ret:in_val,ret) (%i224) comp_rad_from_three_terms(term1,term2,term3,last_no):=( temp:abs( term1*term3-term1*term3*c(last_no) +glob__m2*term2*term2 +term2*term2*c(last_no)), if abs(temp) > glob__0 then ret:abs(term2*glob_h*term1/temp) else ret:glob_larger_float,ret) (%i225) comp_ord_from_three_terms(term1,term2,term3,last_no):=( ret:abs( (-term1*term3*c(last_no*last_no) +term2*term2*c(last_no*last_no) +glob__4*term2*term2 -glob__4*term2*term2*c(last_no) -glob__3*term1*term3 +glob__4*term1*term3*c(last_no)) /(term1*term3-term1*term3*c(last_no) -glob__2*term2*term2 +term2*term2*c(last_no))), ret) (%i226) comp_rad_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):= ( if term5 # glob__0 and term4 # glob__0 and term3 # glob__0 and term2 # glob__0 and term1 # glob__0 then (rm0:term6/term5,rm1:term5/term4, rm2:term4/term3,rm3:term3/term2, rm4:term2/term1, nr1 :c(last_no-3)*rm2 -glob__2*c(last_no-2)*rm1 +c(last_no-1)*rm0, nr2 :c(last_no-4)*rm3 -glob__2*c(last_no-3)*rm2 +c(last_no-2)*rm1, dr1 :(-glob__1)/rm3+glob__2/rm2 +glob__m1/rm1, dr2 :(-glob__1)/rm4+glob__2/rm3 +glob__m1/rm2, ds1 :glob__5/rm3-glob__8/rm2 +glob__3/rm1, ds2 :glob__5/rm4-glob__8/rm3 +glob__3/rm2, if abs(nr1*dr2-nr2*dr1) = glob__0 or abs(dr1) = glob__0 then (rad_c:glob_larger_float, ord_no:glob_larger_float) else (if abs(nr1*dr2-nr2*dr1) > glob__0 then ( rcs :(dr1*dr2-ds2*dr1+ds1*dr2) /(nr1*dr2-nr2*dr1), ord_no :(rcs*nr1-ds1)/(glob__2*dr1) -c(last_no)/glob__2, if abs(rcs) # glob__0 then (if rcs > glob__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) (%i227) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save (%i228) factorial_2(nnn):=block(mode_declare([[ret],convfloat]),ret:nnn!,ret) (%i229) factorial_1(nnn):=block(mode_declare([[ret],convfloat]), if nnn <= ats_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) (%i230) factorial_1(in):=block(mode_declare([[ret],convfloat]),ret:in!,ret) (%i231) neg(in):=block(mode_declare([[ret],convfloat]),ret:-in,ret) (%i232) factorial_3(mmm,nnn):=block(mode_declare([[ret],convfloat]), if nnn <= ats_max_terms and mmm <= ats_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) (%i233) log10(x):=log(x)/glob_log_10 (%i234) c(x):=x (%i235) expt(x,y):=if y = 0.0 then 1.0 elseif x <= 0.0 and y < 0.0 then print("expt error x = ",x,"y = ",y) else x^y (%i236) 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(glob__10, c(-glob_desired_digits_correct)) *c(abs(c(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 :c( abs(desired_abs_gbl_error) /sqrt(c(estimated_steps)) /c(ats_max_terms)), omniout_float(always,"step_error",32, step_error,32,""), step_error) (%i237) exact_soln_y(x):=block(exp(c(x))+c(1.0)) (%o237) exact_soln_y(x) := block(exp(c(x)) + c(1.0)) (%i238) exact_soln_yp(x):=block(exp(c(x))) (%o238) exact_soln_yp(x) := block(exp(c(x))) (%i239) exact_soln_ypp(x):=block(exp(c(x))) (%o239) exact_soln_ypp(x) := block(exp(c(x))) (%i240) 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] > glob__small 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] > glob__small 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) (%i241) my_check_sign(x0,xf):=block([ret], if xf > x0 then ret:glob__1 else ret:glob__m1,ret) (%i242) 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 < glob__1 then (min_size:glob__1, omniout_float(always,"min_size",32,min_size, 32,"")),min_size) (%i243) 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:glob__small, no_terms:ats_max_terms,hn_div_ho:glob__0_5, hn_div_ho_2:glob__0_25,hn_div_ho_3:glob__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) (%i244) track_estimated_error():=block( [hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms, est_tmp],no_terms:ats_max_terms, hn_div_ho:glob__0_5,hn_div_ho_2:glob__0_25, hn_div_ho_3:glob__0_125, est_tmp:c(abs(array_y[no_terms]))*c(hn_div_ho_3) +c(abs(array_y[no_terms-1])) *c(hn_div_ho_2) +c(abs(array_y[no_terms-2])) *c(hn_div_ho) +c(abs(array_y[no_terms-3])), if glob_prec*c(abs(array_y[1])) > c(est_tmp) then est_tmp :c(glob_prec)*c(abs(array_y[1])), if c(est_tmp) >= c(array_max_est_error[1]) then array_max_est_error[1]:c(est_tmp)) (%i245) reached_interval():=block(mode_declare([[ret],boolean]), if glob_check_sign*array_x[1] >= glob_check_sign*glob_next_display -glob_h/glob__10 then ret:true else ret:false, return(ret)) (%i246) display_alot(iter):=( block(mode_declare( [[abserr,est_rel_err],convfloat, [closed_form_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, " "), closed_form_val_y :exact_soln_y(ind_var), omniout_float(always, "y[1] (closed_form) ", 33, closed_form_val_y, 20," "), term_no:1, numeric_val:array_y[term_no], abserr :abs( numeric_val -closed_form_val_y), omniout_float(always, "y[1] (numeric) ", 33,numeric_val, 20," "), if c(abs(closed_form_val_y)) > c(glob_prec) then ( relerr :abserr*glob__100 /abs(closed_form_val_y), if c(relerr) > c(glob_prec) then glob_good_digits :3 -floor(log10(c(relerr))) else glob_good_digits:16) else (relerr:glob__m1, glob_good_digits:-16), if glob_good_digits < glob_min_good_digits then glob_min_good_digits :glob_good_digits, if glob_apfp_est_good_digits < glob_min_apfp_est_good_digits then glob_min_apfp_est_good_digits :glob_apfp_est_good_digits, if c(abs(numeric_val)) > c(glob_prec) then ( est_rel_err :c(array_max_est_error[1]) *glob__100 *c(sqrt(glob_iter))*c(21) *c(ats_max_terms) /c(abs(numeric_val)), if est_rel_err > glob_prec then glob_est_digits :3 -floor( log10(est_rel_err)) else glob_est_digits:16) else (relerr:glob__m1, glob_est_digits:-16), array_est_digits[1] :glob_est_digits, if glob_iter = 1 then array_1st_rel_error[1] :relerr else array_last_rel_error[ 1] :relerr, array_est_rel_error[1] :est_rel_err, omniout_float(always, "absolute error ", 4,abserr,20," "), omniout_float(always, "relative error ", 4,relerr,20,"%"), omniout_int(info, "Desired digits ", 32, glob_desired_digits_correct, 4," "), omniout_int(info, "Estimated correct digits ", 32,glob_est_digits, 4," "), omniout_int(info, "Correct digits ", 32, glob_good_digits,4, " "), omniout_float(always, "h ", 4,glob_h,20, " ")))),0) (%i247) 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 :c(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 c(percent_done) < glob__100 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) (%i248) 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:-10-2+ats_max_terms,cnt:0, while last_no < ats_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), if abs(prev_tmp_rad) > glob__0 then tmp_ratio:tmp_rad/prev_tmp_rad else tmp_ratio:glob_large_float, 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:-10-2+ats_max_terms,cnt:0, while last_no < ats_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), if abs(prev_tmp_rad) > glob__0 then tmp_ratio:tmp_rad/prev_tmp_rad else tmp_ratio:glob_large_float, 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:-10-2+ats_max_terms,cnt:0, while last_no < ats_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), if abs(prev_tmp_rad) > glob__0 then tmp_ratio:tmp_rad/prev_tmp_rad else tmp_ratio:glob_large_float, 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:c(1.0), while term <= ats_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) (%i249) atomall():=( block(mode_declare([[kkk,order_d],fixnum, [adj2,adj3,temporary,term,temp,temp2], convfloat]), array_tmp1[1]:array_y_higher[2,1], array_tmp2[1]:array_tmp1[1]+array_const_0D0[1], if not array_y_set_initial[1,3] then (if 1 <= ats_max_terms then ( temporary :c(array_tmp2[1])*expt(glob_h,c(2)) *c(factorial_3(0,2)), if 3 <= ats_max_terms then (array_y[3]:temporary, array_y_higher[1,3]:temporary), temporary:c(temporary)*c(2)/c(glob_h), array_y_higher[2,2]:c(temporary), temporary:c(temporary)*c(1)/c(glob_h), array_y_higher[3,1]:c(temporary),0)), kkk:2,array_tmp1[2]:array_y_higher[2,2], array_tmp2[2]:array_tmp1[2], if not array_y_set_initial[1,4] then (if 2 <= ats_max_terms then ( temporary :c(array_tmp2[2])*expt(glob_h,c(2)) *c(factorial_3(1,3)), if 4 <= ats_max_terms then (array_y[4]:temporary, array_y_higher[1,4]:temporary), temporary:c(temporary)*c(3)/c(glob_h), array_y_higher[2,3]:c(temporary), temporary:c(temporary)*c(2)/c(glob_h), array_y_higher[3,2]:c(temporary),0)), kkk:3,array_tmp1[3]:array_y_higher[2,3], array_tmp2[3]:array_tmp1[3], if not array_y_set_initial[1,5] then (if 3 <= ats_max_terms then ( temporary :c(array_tmp2[3])*expt(glob_h,c(2)) *c(factorial_3(2,4)), if 5 <= ats_max_terms then (array_y[5]:temporary, array_y_higher[1,5]:temporary), temporary:c(temporary)*c(4)/c(glob_h), array_y_higher[2,4]:c(temporary), temporary:c(temporary)*c(3)/c(glob_h), array_y_higher[3,3]:c(temporary),0)), kkk:4,array_tmp1[4]:array_y_higher[2,4], array_tmp2[4]:array_tmp1[4], if not array_y_set_initial[1,6] then (if 4 <= ats_max_terms then ( temporary :c(array_tmp2[4])*expt(glob_h,c(2)) *c(factorial_3(3,5)), if 6 <= ats_max_terms then (array_y[6]:temporary, array_y_higher[1,6]:temporary), temporary:c(temporary)*c(5)/c(glob_h), array_y_higher[2,5]:c(temporary), temporary:c(temporary)*c(4)/c(glob_h), array_y_higher[3,4]:c(temporary),0)), kkk:5,array_tmp1[5]:array_y_higher[2,5], array_tmp2[5]:array_tmp1[5], if not array_y_set_initial[1,7] then (if 5 <= ats_max_terms then ( temporary :c(array_tmp2[5])*expt(glob_h,c(2)) *c(factorial_3(4,6)), if 7 <= ats_max_terms then (array_y[7]:temporary, array_y_higher[1,7]:temporary), temporary:c(temporary)*c(6)/c(glob_h), array_y_higher[2,6]:c(temporary), temporary:c(temporary)*c(5)/c(glob_h), array_y_higher[3,5]:c(temporary),0)), kkk:6, while kkk <= ats_max_terms do (if kkk <= ats_max_terms then array_tmp1[kkk]:array_y_higher[2,kkk], array_tmp2[kkk]:array_tmp1[kkk],order_d:2, if order_d+kkk <= ats_max_terms then (if not array_y_set_initial[1,order_d+kkk] then ( temporary :c(array_tmp2[kkk])*expt(glob_h,c(order_d)) *c( factorial_3( kkk-1, -1+order_d+kkk)), array_y[order_d+kkk]:c(temporary), array_y_higher[1,order_d+kkk]:c(temporary), term:-1+order_d+kkk,adj2:-1+order_d+kkk, adj3:2, while term >= 1 and term <= ats_max_terms and adj3 < 1+order_d do ( if adj3 <= 1+order_d then ( if adj2 > 0 then temporary :c(temporary)*c(adj2) /c(glob_h) else temporary:c(temporary), array_y_higher[adj3,term] :c(temporary)),term:term-1, adj2:adj2-1,adj3:1+adj3))), kkk:1+kkk)),0) (%i250) exact_soln_y(x):=block(exp(c(x))+c(1.0)) (%o250) exact_soln_y(x) := block(exp(c(x)) + c(1.0)) (%i251) exact_soln_yp(x):=block(exp(c(x))) (%o251) exact_soln_yp(x) := block(exp(c(x))) (%i252) exact_soln_ypp(x):=block(exp(c(x))) (%o252) exact_soln_ypp(x) := block(exp(c(x))) (%i253) main_prog():=block( mode_declare([[d1,d2,d3,d4,est_err_2,display_max],convfloat, [niii,done_once,term,ord,order_diff,term_no, html_log_file,iiif,jjjf,rows,r_order, sub_iter,calc_term,iii],fixnum,[temp_sum], convfloat,[current_iter],fixnum, [x_start,x_end],convfloat,[it,opt_iter], fixnum,[tmp],convfloat,[subiter],fixnum, [est_needed_step_err,estimated_step_error, min_value,est_answer,last_min_pole_est], convfloat,[repeat_it],fixnum],[found_h], boolean),Digits:32,max_terms:30, glob_html_log:true,term:1, while term <= 30 do (array_y_init[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_norms[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_fact_1[term]:c(0.0),term:1+term), term:1, while term <= 2 do (array_1st_rel_error[term]:c(0.0),term:1+term),term:1, while term <= 2 do (array_last_rel_error[term]:c(0.0),term:1+term), term:1, while term <= 2 do (array_est_rel_error[term]:c(0.0),term:1+term),term:1, while term <= 2 do (array_max_est_error[term]:c(0.0),term:1+term),term:1, while term <= 2 do (array_type_pole[term]:0,term:1+term), term:1, while term <= 2 do (array_type_real_pole[term]:0,term:1+term),term:1, while term <= 2 do (array_type_complex_pole[term]:0,term:1+term),term:1, while term <= 2 do (array_est_digits[term]:0,term:1+term), term:1, while term <= 30 do (array_y[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_x[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_tmp0[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_tmp1[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_tmp2[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_m1[term]:c(0.0),term:1+term), ord:1, while ord <= 3 do (term:1, while term <= 30 do (array_y_higher[ord,term]:c(0.0),term:1+term), ord:1+ord),ord:1, while ord <= 3 do (term:1, while term <= 30 do (array_y_higher_work[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 3 do (term:1, while term <= 30 do (array_y_higher_work2[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 30 do (array_y_set_initial[ord,term]:c(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]:c(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]:c(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]:c(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]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 30 do (term:1, while term <= 30 do (array_fact_2[ord,term]:c(0.0),term:1+term), ord:1+ord),zero_ats_ar(array_y),zero_ats_ar(array_x), zero_ats_ar(array_tmp0),zero_ats_ar(array_tmp1), zero_ats_ar(array_tmp2),zero_ats_ar(array_m1), zero_ats_ar(array_const_2),array_const_2[1]:c(2), zero_ats_ar(array_const_0D0),array_const_0D0[1]:c(0.0), zero_ats_ar(array_const_1),array_const_1[1]:c(1), zero_ats_ar(array_m1),array_m1[1]:glob__m1,iiif:0, while iiif <= ats_max_terms do (jjjf:0, while jjjf <= ats_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]:true, 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,glob_log_10:log(10.0), glob_orig_start_sec:elapsed_time_seconds(), 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/diff_Bpostode.ode#################"), omniout_str(always, "diff ( y , x , 2 ) = diff ( y , x , 1 ) ; "), omniout_str(always,"!"), omniout_str(always,"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(always,"Digits:32,"), omniout_str(always,"max_terms:30,"),omniout_str(always,"!"), omniout_str(always,"/* END FIRST INPUT BLOCK */"), omniout_str(always,"/* BEGIN SECOND INPUT BLOCK */"), omniout_str(always,"x_start:c(1.0),"), omniout_str(always,"x_end:c(5.0),"), omniout_str(always, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(always, "array_y_init[1 + 1] : exact_soln_yp(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:3,"), omniout_str(always,"/* END SECOND INPUT BLOCK */"), omniout_str(always,"/* BEGIN OVERRIDE BLOCK */"), omniout_str(always,"glob_desired_digits_correct:8,"), omniout_str(always,"glob_max_minutes:(3.0),"), omniout_str(always,"glob_subiter_method:3,"), omniout_str(always,"glob_max_iter:100000,"), omniout_str(always,"glob_upper_ratio_limit:c(1.000001),"), omniout_str(always,"glob_lower_ratio_limit:c(0.999999),"), omniout_str(always,"glob_look_poles:false,"), omniout_str(always,"glob_h:c(0.001),"), omniout_str(always,"glob_display_interval:c(0.01),"), 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," (c(1.0) + exp(c(x))) "), omniout_str(always,"));"), omniout_str(always,"exact_soln_yp (x) := (block("), omniout_str(always," (exp(c(x))) "), omniout_str(always,"));"), omniout_str(always,"exact_soln_ypp (x) := (block("), omniout_str(always," (exp(c(x))) "), 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:glob__0,glob_smallish_float:glob__0, glob_large_float:c(1.0E+100),glob_larger_float:c(1.1E+100), glob_almost_1:c(0.99),x_start:c(1.0),x_end:c(5.0), array_y_init[1+0]:exact_soln_y(x_start), array_y_init[1+1]:exact_soln_yp(x_start), glob_look_poles:true,glob_type_given_pole:3, glob_desired_digits_correct:8,glob_max_minutes:3.0, glob_subiter_method:3,glob_max_iter:100000, glob_upper_ratio_limit:c(1.000001), glob_lower_ratio_limit:c(0.999999),glob_look_poles:false, glob_h:c(0.001),glob_display_interval:c(0.01), glob_last_good_h:glob_h, glob_max_sec:3600.0*glob_max_hours+60.0*glob_max_minutes, glob_check_sign:c(my_check_sign(x_start,x_end)), glob__pi:3.141592654,glob_prec:1.0E-16, if glob_optimize then (omniout_str(always,"START of Optimize"), 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 :c(abs(c(glob_display_interval)) *glob_check_sign), display_max:c(x_end)-c(x_start)/glob__10, if glob_display_interval > display_max then glob_display_interval:c(display_max), 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:glob_small_float, while opt_iter <= 100 and not found_h do (omniout_int(always,"opt_iter",32,opt_iter, 4,""),array_x[1]:c(x_start), array_x[2]:c(glob_h), glob_next_display:c(x_start),order_diff:2, term_no:1, while term_no <= order_diff do ( array_y[term_no] :array_y_init[term_no] *expt(glob_h,c(term_no-1)) /c(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 < ats_max_terms then array_y_higher[ r_order,term_no] :array_y_init[it] *expt(glob_h, c(term_no-1)) /c( factorial_1( term_no-1)), term_no:1+term_no), r_order:1+r_order),atomall(), if glob_check_sign*glob_min_h >= glob_check_sign*glob_h then ( omniout_str(always, "SETTING H FOR MIN H"), glob_h:glob_check_sign*abs(glob_min_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 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*glob__2) else ( omniout_str(always, "Found H for OPTIMAL"), found_h:true,glob_h_reason:3, glob_h:glob_h/glob__2)), 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_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)) else (found_h:true,glob_h:glob_h*glob_check_sign), if glob_html_log then html_log_file:openw("entry.html"), if found_h then (omniout_str(always,"START of Soultion"), array_x[1]:c(x_start),array_x[2]:c(glob_h), glob_next_display:c(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:2, term_no:1, while term_no <= order_diff do (array_y[term_no] :array_y_init[term_no] *expt(glob_h,c(term_no-1)) /c(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 < ats_max_terms then array_y_higher[ r_order,term_no] :array_y_init[it] *expt(glob_h,c(term_no-1)) /c(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_iter:0, omniout_str(debugl," "), glob_reached_optimal_h:true, glob_optimal_clock_start_sec :elapsed_time_seconds(), while glob_iter < glob_max_iter and glob_check_sign*array_x[1] < glob_check_sign*x_end and glob_clock_sec-glob_orig_start_sec < glob_max_sec do (if reached_interval() then (omniout_str(info," "), omniout_str(info, "TOP MAIN SOLVE Loop")), glob_iter:1+glob_iter, glob_clock_sec:elapsed_time_seconds(), track_estimated_error(),atomall(), track_estimated_error(), display_alot(current_iter), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display :glob_display_interval +glob_next_display, array_x[1]:glob_h+array_x[1], array_x[2]:glob_h,order_diff:3,ord:3, calc_term:1,iii:ats_max_terms, while iii >= calc_term do ( array_y_higher_work[3,iii] :array_y_higher[3,iii] /expt(glob_h,c(calc_term-1)) /c( factorial_3(iii-calc_term,iii-1)), iii:iii-1),temp_sum:glob__0,ord:3, calc_term:1,iii:ats_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,c(calc_term-1)) /c(factorial_1(calc_term-1)),ord:2, calc_term:2,iii:ats_max_terms, while iii >= calc_term do ( array_y_higher_work[2,iii] :array_y_higher[2,iii] /expt(glob_h,c(calc_term-1)) /c( factorial_3(iii-calc_term,iii-1)), iii:iii-1),temp_sum:glob__0,ord:2, calc_term:2,iii:ats_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,c(calc_term-1)) /c(factorial_1(calc_term-1)),ord:2, calc_term:1,iii:ats_max_terms, while iii >= calc_term do ( array_y_higher_work[2,iii] :array_y_higher[2,iii] /expt(glob_h,c(calc_term-1)) /c( factorial_3(iii-calc_term,iii-1)), iii:iii-1),temp_sum:glob__0,ord:2, calc_term:1,iii:ats_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,c(calc_term-1)) /c(factorial_1(calc_term-1)),ord:1, calc_term:3,iii:ats_max_terms, while iii >= calc_term do ( array_y_higher_work[1,iii] :array_y_higher[1,iii] /expt(glob_h,c(calc_term-1)) /c( factorial_3(iii-calc_term,iii-1)), iii:iii-1),temp_sum:glob__0,ord:1, calc_term:3,iii:ats_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,c(calc_term-1)) /c(factorial_1(calc_term-1)),ord:1, calc_term:2,iii:ats_max_terms, while iii >= calc_term do ( array_y_higher_work[1,iii] :array_y_higher[1,iii] /expt(glob_h,c(calc_term-1)) /c( factorial_3(iii-calc_term,iii-1)), iii:iii-1),temp_sum:glob__0,ord:1, calc_term:2,iii:ats_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,c(calc_term-1)) /c(factorial_1(calc_term-1)),ord:1, calc_term:1,iii:ats_max_terms, while iii >= calc_term do ( array_y_higher_work[1,iii] :array_y_higher[1,iii] /expt(glob_h,c(calc_term-1)) /c( factorial_3(iii-calc_term,iii-1)), iii:iii-1),temp_sum:glob__0,ord:1, calc_term:1,iii:ats_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,c(calc_term-1)) /c(factorial_1(calc_term-1)), term_no:ats_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 , 2 ) = diff ( y , x , 1 ) ; "), 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, "2015-04-24T20:36:56-05:00"), logitem_str(html_log_file,"Maxima"), logitem_str(html_log_file, "diff_B"), logitem_str(html_log_file, "diff ( y , x , 2 ) = diff ( y , x , 1 ) ; "), logitem_float(html_log_file,x_start), logitem_float(html_log_file,x_end), logitem_float(html_log_file,array_x[1]), logitem_float(html_log_file,glob_h), logitem_h_reason(html_log_file), logitem_str(html_log_file,"16"), logitem_float(html_log_file, glob_desired_digits_correct), if array_est_digits[1] # -16 then ( logitem_integer(html_log_file, array_est_digits[ 1]),0) else ( logitem_str(html_log_file, "Unknown"),0), if glob_min_good_digits # -16 then ( logitem_integer(html_log_file, glob_min_good_digits), 0) else ( logitem_str(html_log_file, "Unknown"),0), if glob_good_digits # -16 then ( logitem_integer(html_log_file, glob_good_digits),0) else ( logitem_str(html_log_file, "Unknown"),0), logitem_str(html_log_file,"NA"), logitem_str(html_log_file,"NA"), logitem_integer(html_log_file, ats_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 c(glob_percent_done) < glob__100 then ( logitem_time(html_log_file, glob_total_exp_sec),0) else ( logitem_str(html_log_file,"Done"), 0), log_revs(html_log_file, " 308.maple.seems.ok "), logitem_str(html_log_file, "diff_B diffeq.max"), logitem_str(html_log_file, "diff_B maxima results"), logitem_str(html_log_file,"OK"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%i254) main():=(glob_iolevel:2,compile(all),main_prog()) (%i255) 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 ats_max_terms in translation. warning: encountered undefined variable glob__0 in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob__0 in translation. 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 ats_max_terms in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable iii_att in translation. warning: encountered undefined variable ats_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 glob_min_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 glob__0 in translation. 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__100 in translation. warning: encountered undefined variable glob_small_float in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable ret in translation. warning: encountered undefined variable glob__1 in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable glob__m2 in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable temp in translation. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable glob__4 in translation. warning: encountered undefined variable glob__3 in translation. warning: encountered undefined variable glob__2 in translation. warning: encountered undefined variable rm0 in translation. warning: encountered undefined variable glob__2 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 glob__m1 in translation. warning: encountered undefined variable glob__1 in translation. warning: encountered undefined variable rm4 in translation. warning: encountered undefined variable glob__3 in translation. warning: encountered undefined variable glob__8 in translation. warning: encountered undefined variable glob__5 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 glob__0 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. modedeclare: false 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. 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 ats_max_terms in translation. warning: encountered undefined variable glob_log_10 in translation. warning: encountered undefined variable always in translation. warning: encountered undefined variable glob_desired_digits_correct in translation. warning: encountered undefined variable glob__10 in translation. warning: encountered undefined variable ats_max_terms in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable array_x in translation. warning: encountered undefined variable array_given_rad_poles in translation. warning: encountered undefined variable always in translation. warning: encountered undefined variable rad_given in translation. warning: encountered undefined variable array_given_ord_poles in translation. warning: variable glob_least_given_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_given_sing in translation. warning: encountered undefined variable glob_type_given_pole in translation. warning: encountered undefined variable array_rad_test_poles in translation. warning: variable glob_least_ratio_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_ratio_sing in translation. warning: encountered undefined variable array_ord_test_poles in translation. warning: encountered undefined variable glob_large_float in translation. warning: variable glob_least_3_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_3_sing in translation. warning: encountered undefined variable glob__small 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__1 in translation. warning: encountered undefined variable glob__m1 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 glob__1 in translation. warning: encountered undefined variable glob__small in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable glob__0_5 in translation. warning: encountered undefined variable glob__0_25 in translation. warning: encountered undefined variable glob__0_125 in translation. warning: encountered undefined variable always in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable glob__0_5 in translation. warning: encountered undefined variable glob__0_25 in translation. warning: encountered undefined variable glob__0_125 in translation. warning: encountered undefined variable glob_prec in translation. warning: encountered undefined variable array_max_est_error in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob_check_sign in translation. warning: encountered undefined variable glob_next_display in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob__10 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 closed_form_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 glob__100 in translation. warning: encountered undefined variable relerr in translation. warning: variable glob_good_digits (declared type fixnum) assigned type any. warning: encountered undefined variable glob_prec in translation. warning: encountered undefined variable glob__m1 in translation. warning: encountered undefined variable glob_good_digits in translation. warning: encountered undefined variable glob_min_good_digits in translation. warning: encountered undefined variable glob_apfp_est_good_digits in translation. warning: encountered undefined variable glob_min_apfp_est_good_digits in translation. warning: encountered undefined variable glob_iter in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable est_rel_err in translation. warning: variable glob_est_digits (declared type fixnum) assigned type any. warning: encountered undefined variable glob_est_digits in translation. warning: encountered undefined variable array_est_digits in translation. warning: encountered undefined variable array_1st_rel_error in translation. warning: encountered undefined variable array_last_rel_error in translation. warning: encountered undefined variable array_est_rel_error in translation. warning: encountered undefined variable info in translation. warning: encountered undefined variable glob_desired_digits_correct in translation. warning: encountered undefined variable glob_h in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable clock_sec1 in translation. warning: encountered undefined variable glob_orig_start_sec in translation. warning: encountered undefined variable glob_clock_start_sec in translation. warning: variable glob_clock_sec (declared type convfloat) assigned type any. warning: encountered undefined variable glob_max_sec in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob_optimal_clock_start_sec in translation. warning: encountered undefined variable opt_clock_sec in translation. warning: variable glob_optimal_expect_sec (declared type convfloat) assigned type any. warning: encountered undefined variable glob_optimal_expect_sec in translation. warning: encountered undefined variable total_clock_sec in translation. warning: variable glob_total_exp_sec (declared type convfloat) assigned type any. warning: encountered undefined variable percent_done in translation. warning: variable glob_percent_done (declared type convfloat) assigned type any. warning: encountered undefined variable info in translation. warning: encountered undefined variable glob_clock_sec in translation. warning: encountered undefined variable expect_sec in translation. warning: encountered undefined variable glob_total_exp_sec in translation. warning: encountered undefined variable glob__100 in translation. warning: encountered undefined variable left_sec in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable ats_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 glob__0 in translation. warning: encountered undefined variable glob_large_float 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: variable ratio (declared type convfloat) assigned type any. 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_tmp1 in translation. warning: encountered undefined variable array_const_0D0 in translation. warning: encountered undefined variable array_tmp2 in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable temporary in translation. warning: encountered undefined variable ats_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 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_fact_1 in translation. warning: encountered undefined variable array_type_pole in translation. warning: encountered undefined variable array_type_real_pole in translation. warning: encountered undefined variable array_type_complex_pole in translation. warning: encountered undefined variable array_tmp0 in translation. warning: encountered undefined variable array_m1 in translation. warning: 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_2 in translation. warning: encountered undefined variable array_const_1 in translation. warning: encountered undefined variable glob__m1 in translation. warning: variable iiif (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable iiif in translation. warning: encountered undefined variable ats_max_terms 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: 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: encountered undefined variable glob__0 in translation. warning: variable glob_large_float (declared type convfloat) assigned type any. warning: variable glob_larger_float (declared type convfloat) assigned type any. warning: variable glob_almost_1 (declared type convfloat) assigned type any. warning: variable x_start (declared type [found_h]) assigned type any. warning: variable x_end (declared type [found_h]) assigned type any. warning: encountered undefined variable x_start in translation. warning: variable glob_upper_ratio_limit (declared type convfloat) assigned type any. warning: variable glob_lower_ratio_limit (declared type convfloat) assigned type any. warning: variable glob_h (declared type convfloat) assigned type any. warning: variable glob_display_interval (declared type convfloat) assigned type any. 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: encountered undefined variable glob__10 in translation. warning: variable display_max (declared type [found_h]) assigned type any. warning: encountered undefined variable display_max 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: encountered undefined variable glob_small_float 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 any. 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_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: encountered undefined variable glob__2 in translation. warning: variable opt_iter (declared type [found_h]) assigned type any. warning: encountered undefined variable glob_optimize in translation. 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_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 info in translation. warning: encountered undefined variable current_iter in translation. warning: encountered undefined variable glob_next_display in translation. warning: variable calc_term (declared type [found_h]) assigned type fixnum. warning: variable iii (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable calc_term in translation. warning: variable iii (declared type [found_h]) assigned type any. warning: variable temp_sum (declared type [found_h]) assigned type convfloat. warning: encountered undefined variable temp_sum in translation. warning: variable temp_sum (declared type [found_h]) assigned type any. warning: encountered undefined variable html_log_file in translation. warning: encountered undefined variable glob_desired_digits_correct in translation. warning: encountered undefined variable glob_min_good_digits in translation. warning: encountered undefined variable glob_good_digits 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: encountered undefined variable glob__100 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 : $GLOB_DISPLAY_FLAG is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_NO_EQS is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_UNCHANGED_H_CNT is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_WARNED is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_WARNED2 is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_SMALLISH_FLOAT is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_ALMOST_1 is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_SUBITER_METHOD is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_LAST_GOOD_H is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB__PI is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $LAST_MIN_POLE_EST 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. "##############ECHO OF PROBLEM#################" "##############temp/diff_Bpostode.ode#################" "diff ( y , x , 2 ) = diff ( y , x , 1 ) ; " "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:c(1.0)," "x_end:c(5.0)," "array_y_init[0 + 1] : exact_soln_y(x_start)," "array_y_init[1 + 1] : exact_soln_yp(x_start)," "glob_look_poles:true," "" "" "" "" "" "" "" "glob_type_given_pole:3," "/* END SECOND INPUT BLOCK */" "/* BEGIN OVERRIDE BLOCK */" "glob_desired_digits_correct:8," "glob_max_minutes:(3.0)," "glob_subiter_method:3," "glob_max_iter:100000," "glob_upper_ratio_limit:c(1.000001)," "glob_lower_ratio_limit:c(0.999999)," "glob_look_poles:false," "glob_h:c(0.001)," "glob_display_interval:c(0.01)," "/* END OVERRIDE BLOCK */" "!" "/* BEGIN USER DEF BLOCK */" "exact_soln_y (x) := (block(" " (c(1.0) + exp(c(x))) " "));" "exact_soln_yp (x) := (block(" " (exp(c(x))) " "));" "exact_soln_ypp (x) := (block(" " (exp(c(x))) " "));" "" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Soultion" " " "TOP MAIN SOLVE Loop" x[1] = 1. " " y[1] (closed_form) = 3.718281828459045 " " y[1] (numeric) = 3.718281828459045 " " absolute error = 0.0 " " relative error = 0.0 "%" Desired digits = 8 Estimated correct digits = 15 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.009999999999999 " " y[1] (closed_form) = 3.7456010150169137 " " y[1] (numeric) = 3.7456010150169163 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 7.11377225822420700000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0199999999999978 " " y[1] (closed_form) = 3.773194763964292 " " y[1] (numeric) = 3.773194763964298 " " absolute error = 6.217248937900877000000000000000E-15 " " relative error = 1.64774132448141870000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0299999999999967 " " y[1] (closed_form) = 3.80106583469907 " " y[1] (numeric) = 3.801065834699079 " " absolute error = 9.325873406851315000000000000000E-15 " " relative error = 2.45348905081241330000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0399999999999956 " " y[1] (closed_form) = 3.829217014351547 " " y[1] (numeric) = 3.8292170143515594 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 3.24726904461105750000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0499999999999945 " " y[1] (closed_form) = 3.857651118063148 " " y[1] (numeric) = 3.857651118063164 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 4.14428652703801860000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0599999999999934 " " y[1] (closed_form) = 3.886370989267939 " " y[1] (numeric) = 3.8863709892679577 " " absolute error = 1.86517468137026300000000000000E-14 " " relative error = 4.7992708017862170000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0699999999999923 " " y[1] (closed_form) = 3.915379499976974 " " y[1] (numeric) = 3.9153794999769955 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 5.4442441844854030000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0799999999999912 " " y[1] (closed_form) = 3.944679551065498 " " y[1] (numeric) = 3.944679551065523 " " absolute error = 2.486899575160350700000000000000E-14 " " relative error = 6.3044400513816490000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.08999999999999 " " y[1] (closed_form) = 3.974274072563036 " " y[1] (numeric) = 3.974274072563064 " " absolute error = 2.797762022055394500000000000000E-14 " " relative error = 7.0396806334272240000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.099999999999989 " " y[1] (closed_form) = 4.0041660239464 " " y[1] (numeric) = 4.004166023946432 " " absolute error = 3.19744231092045100000000000000E-14 " " relative error = 7.9852890509498310000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1099999999999879 " " y[1] (closed_form) = 4.034358394435639 " " y[1] (numeric) = 4.034358394435674 " " absolute error = 3.463895836830488400000000000000E-14 " " relative error = 8.5859893895595470000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1199999999999868 " " y[1] (closed_form) = 4.0648542032929615 " " y[1] (numeric) = 4.064854203293000 " " absolute error = 3.90798504668055100000000000000E-14 " " relative error = 9.6140841743220950000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1299999999999857 " " y[1] (closed_form) = 4.095656500124667 " " y[1] (numeric) = 4.09565650012471 " " absolute error = 4.26325641456060100000000000000E-14 " " relative error = 1.040921379620296000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1399999999999846 " " y[1] (closed_form) = 4.126768365186107 " " y[1] (numeric) = 4.1267683651861535 " " absolute error = 4.61852778244065100000000000000E-14 " " relative error = 1.1191633195124502000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1499999999999835 " " y[1] (closed_form) = 4.158192909689715 " " y[1] (numeric) = 4.158192909689767 " " absolute error = 5.151434834260726000000000000000E-14 " " relative error = 1.2388638396877857000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1599999999999824 " " y[1] (closed_form) = 4.189933276116129 " " y[1] (numeric) = 4.189933276116184 " " absolute error = 5.506706202140776000000000000000E-14 " " relative error = 1.314270619422664000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1699999999999813 " " y[1] (closed_form) = 4.221992638528440 " " y[1] (numeric) = 4.2219926385285 " " absolute error = 6.03961325396085200000000000000E-14 " " relative error = 1.4305125022827936000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1799999999999802 " " y[1] (closed_form) = 4.254374202889606 " " y[1] (numeric) = 4.254374202889670 " " absolute error = 6.48370246381091400000000000000E-14 " " relative error = 1.5240085038610685000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.189999999999979 " " y[1] (closed_form) = 4.28708120738305 " " y[1] (numeric) = 4.2870812073831175 " " absolute error = 6.75015598972095200000000000000E-14 " " relative error = 1.5745342024536618000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.199999999999978 " " y[1] (closed_form) = 4.320116922736474 " " y[1] (numeric) = 4.320116922736548 " " absolute error = 7.3718808835110390000000000000E-14 " " relative error = 1.7064077235301997000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2099999999999769 " " y[1] (closed_form) = 4.353484652548946 " " y[1] (numeric) = 4.353484652549024 " " absolute error = 7.7271522513910900000000000000E-14 " " relative error = 1.7749349930214814000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2199999999999758 " " y[1] (closed_form) = 4.387187733621253 " " y[1] (numeric) = 4.387187733621335 " " absolute error = 8.26005930321116500000000000000E-14 " " relative error = 1.8827685990982618000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2299999999999747 " " y[1] (closed_form) = 4.421229536289587 " " y[1] (numeric) = 4.421229536289673 " " absolute error = 8.61533067109121500000000000000E-14 " " relative error = 1.9486277743275526000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2399999999999736 " " y[1] (closed_form) = 4.4556134647625845 " " y[1] (numeric) = 4.455613464762675 " " absolute error = 9.05941988094127700000000000000E-14 " " relative error = 2.0332598311294503000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2499999999999725 " " y[1] (closed_form) = 4.4903429574617455 " " y[1] (numeric) = 4.4903429574618405 " " absolute error = 9.5035090907913400000000000000E-14 " " relative error = 2.1164327938468613000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2599999999999714 " " y[1] (closed_form) = 4.525421487365281 " " y[1] (numeric) = 4.5254214873653815 " " absolute error = 1.00364161426114150000000000000E-13 " " relative error = 2.2177859389744176000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2699999999999703 " " y[1] (closed_form) = 4.560852562355414 " " y[1] (numeric) = 4.560852562355520 " " absolute error = 1.04805053524614780000000000000E-13 " " relative error = 2.2979268040729883000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2799999999999692 " " y[1] (closed_form) = 4.596639725569170 " " y[1] (numeric) = 4.596639725569280 " " absolute error = 1.10134124042815530000000000000E-13 " " relative error = 2.3959703308959754000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.289999999999968 " " y[1] (closed_form) = 4.632786555752693 " " y[1] (numeric) = 4.632786555752810 " " absolute error = 1.1635137298071640000000000000E-13 " " relative error = 2.511477090094704000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.299999999999967 " " y[1] (closed_form) = 4.669296667619123 " " y[1] (numeric) = 4.6692966676192444 " " absolute error = 1.21680443498917160000000000000E-13 " " relative error = 2.605969424533526000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3099999999999659 " " y[1] (closed_form) = 4.706173712210072 " " y[1] (numeric) = 4.706173712210197 " " absolute error = 1.25233157177717660000000000000E-13 " " relative error = 2.6610398348195860000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3199999999999648 " " y[1] (closed_form) = 4.743421377260730 " " y[1] (numeric) = 4.74342137726086 " " absolute error = 1.29674049276218280000000000000E-13 " " relative error = 2.733766177676239000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3299999999999637 " " y[1] (closed_form) = 4.781043387568643 " " y[1] (numeric) = 4.781043387568778 " " absolute error = 1.35003119794419040000000000000E-13 " " relative error = 2.823716683798464000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3399999999999626 " " y[1] (closed_form) = 4.819043505366192 " " y[1] (numeric) = 4.8190435053663325 " " absolute error = 1.40332190312619800000000000000E-13 " " relative error = 2.912034102957453000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3499999999999615 " " y[1] (closed_form) = 4.857425530696826 " " y[1] (numeric) = 4.85742553069697 " " absolute error = 1.4388490399142030000000000000E-13 " " relative error = 2.9621638681258206000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3599999999999604 " " y[1] (closed_form) = 4.89619330179506 " " y[1] (numeric) = 4.89619330179521 " " absolute error = 1.50102152929321160000000000000E-13 " " relative error = 3.065690908777849000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3699999999999593 " " y[1] (closed_form) = 4.935350695470312 " " y[1] (numeric) = 4.935350695470470 " " absolute error = 1.57207580286922170000000000000E-13 " " relative error = 3.1853375775546816000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3799999999999581 " " y[1] (closed_form) = 4.974901627494582 " " y[1] (numeric) = 4.974901627494743 " " absolute error = 1.6164847238542280000000000000E-13 " " relative error = 3.2492797745395990000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.389999999999957 " " y[1] (closed_form) = 5.01485005299403 " " y[1] (numeric) = 5.0148500529941975 " " absolute error = 1.67865721323323670000000000000E-13 " " relative error = 3.3473726940868814000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.399999999999956 " " y[1] (closed_form) = 5.055199966844496 " " y[1] (numeric) = 5.055199966844671 " " absolute error = 1.74971148680924670000000000000E-13 " " relative error = 3.4612112246499980000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4099999999999548 " " y[1] (closed_form) = 5.095955404070992 " " y[1] (numeric) = 5.095955404071173 " " absolute error = 1.81188397618825550000000000000E-13 " " relative error = 3.5555334231159100000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4199999999999537 " " y[1] (closed_form) = 5.137120440251201 " " y[1] (numeric) = 5.137120440251388 " " absolute error = 1.8651746813702630000000000000E-13 " " relative error = 3.6307785715046564000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4299999999999526 " " y[1] (closed_form) = 5.178699191923048 " " y[1] (numeric) = 5.178699191923242 " " absolute error = 1.9362289549462730000000000000E-13 " " relative error = 3.738832635743953000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4399999999999515 " " y[1] (closed_form) = 5.220695816996348 " " y[1] (numeric) = 5.220695816996547 " " absolute error = 1.98951966012828050000000000000E-13 " " relative error = 3.810832367691788000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4499999999999504 " " y[1] (closed_form) = 5.263114515168606 " " y[1] (numeric) = 5.263114515168812 " " absolute error = 2.06057393370429050000000000000E-13 " " relative error = 3.915122742941646000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4599999999999493 " " y[1] (closed_form) = 5.305959528344988 " " y[1] (numeric) = 5.3059595283452 " " absolute error = 2.12274642308329930000000000000E-13 " " relative error = 4.0006834046572853000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4699999999999482 " " y[1] (closed_form) = 5.349235141062516 " " y[1] (numeric) = 5.349235141062734 " " absolute error = 2.1849189124623080000000000000E-13 " " relative error = 4.084544528039421000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4799999999999471 " " y[1] (closed_form) = 5.392945680918524 " " y[1] (numeric) = 5.39294568091875 " " absolute error = 2.2559731860383180000000000000E-13 " " relative error = 4.183192858812703000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.489999999999946 " " y[1] (closed_form) = 5.437095519003425 " " y[1] (numeric) = 5.437095519003657 " " absolute error = 2.3181456754173269000000000000E-13 " " relative error = 4.2635735703282696000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.499999999999945 " " y[1] (closed_form) = 5.481689070337818 " " y[1] (numeric) = 5.481689070338060 " " absolute error = 2.41584530158434060000000000000E-13 " " relative error = 4.407118445766680700000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5099999999999438 " " y[1] (closed_form) = 5.526730794313998 " " y[1] (numeric) = 5.526730794314247 " " absolute error = 2.48689957516035070000000000000E-13 " " relative error = 4.4997660782010923000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5199999999999427 " " y[1] (closed_form) = 5.572225195141898 " " y[1] (numeric) = 5.572225195142154 " " absolute error = 2.5668356329333620000000000000E-13 " " relative error = 4.606482227551102000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5299999999999416 " " y[1] (closed_form) = 5.618176822299511 " " y[1] (numeric) = 5.618176822299775 " " absolute error = 2.6378899065093720000000000000E-13 " " relative error = 4.695277471579628000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5399999999999405 " " y[1] (closed_form) = 5.664590270987849 " " y[1] (numeric) = 5.664590270988121 " " absolute error = 2.72670774847938450000000000000E-13 " " relative error = 4.813601016201783400000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5499999999999394 " " y[1] (closed_form) = 5.711470182590456 " " y[1] (numeric) = 5.7114701825907375 " " absolute error = 2.8155255904493970000000000000E-13 " " relative error = 4.929598685521643400000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5599999999999383 " " y[1] (closed_form) = 5.75882124513756 " " y[1] (numeric) = 5.758821245137850 " " absolute error = 2.90434343241940950000000000000E-13 " " relative error = 5.043294988313244000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5699999999999372 " " y[1] (closed_form) = 5.806648193774876 " " y[1] (numeric) = 5.8066481937751755 " " absolute error = 2.9931612743894220000000000000E-13 " " relative error = 5.154714345529484000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5799999999999361 " " y[1] (closed_form) = 5.854955811237123 " " y[1] (numeric) = 5.854955811237431 " " absolute error = 3.08197911635943460000000000000E-13 " " relative error = 5.263881087615292000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.589999999999935 " " y[1] (closed_form) = 5.903748928326303 " " y[1] (numeric) = 5.903748928326620 " " absolute error = 3.1619151741324460000000000000E-13 " " relative error = 5.35577513969389000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.599999999999934 " " y[1] (closed_form) = 5.953032424394787 " " y[1] (numeric) = 5.953032424395112 " " absolute error = 3.25073301610245840000000000000E-13 " " relative error = 5.460633815433893000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6099999999999328 " " y[1] (closed_form) = 6.002811227833251 " " y[1] (numeric) = 6.002811227833585 " " absolute error = 3.3395508580724710000000000000E-13 " " relative error = 5.5633114741106060000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6199999999999317 " " y[1] (closed_form) = 6.053090316563522 " " y[1] (numeric) = 6.053090316563867 " " absolute error = 3.4461322684364860000000000000E-13 " " relative error = 5.6931783406677040000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6299999999999306 " " y[1] (closed_form) = 6.103874718536372 " " y[1] (numeric) = 6.103874718536726 " " absolute error = 3.54383189460349970000000000000E-13 " " relative error = 5.805872594077853000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6399999999999295 " " y[1] (closed_form) = 6.155169512234318 " " y[1] (numeric) = 6.155169512234684 " " absolute error = 3.6592950891645160000000000000E-13 " " relative error = 5.9450760566238200000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6499999999999284 " " y[1] (closed_form) = 6.206979827179476 " " y[1] (numeric) = 6.206979827179852 " " absolute error = 3.7658764995285310000000000000E-13 " " relative error = 6.067164070742258000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6599999999999273 " " y[1] (closed_form) = 6.259310844446516 " " y[1] (numeric) = 6.259310844446902 " " absolute error = 3.85469434149854350000000000000E-13 " " relative error = 6.158336656053064000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6699999999999262 " " y[1] (closed_form) = 6.312167797180775 " " y[1] (numeric) = 6.312167797181173 " " absolute error = 3.9790393202565610000000000000E-13 " " relative error = 6.30376036903476000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.679999999999925 " " y[1] (closed_form) = 6.365555971121573 " " y[1] (numeric) = 6.365555971121980 " " absolute error = 4.0767389464235750000000000000E-13 " " relative error = 6.404372163120384000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.689999999999924 " " y[1] (closed_form) = 6.419480705130795 " " y[1] (numeric) = 6.419480705131212 " " absolute error = 4.17443857259058860000000000000E-13 " " relative error = 6.5027667569031760000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.699999999999923 " " y[1] (closed_form) = 6.473947391726778 " " y[1] (numeric) = 6.473947391727207 " " absolute error = 4.2899017671516050000000000000E-13 " " relative error = 6.626408136454398000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7099999999999218 " " y[1] (closed_form) = 6.528961477623572 " " y[1] (numeric) = 6.52896147762401 " " absolute error = 4.38760139331861860000000000000E-13 " " relative error = 6.720213326967935000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7199999999999207 " " y[1] (closed_form) = 6.5845284642756114 " " y[1] (numeric) = 6.584528464276060 " " absolute error = 4.49418280368263370000000000000E-13 " " relative error = 6.8253677208107510000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7299999999999196 " " y[1] (closed_form) = 6.6406539084278675 " " y[1] (numeric) = 6.640653908428330 " " absolute error = 4.6185277824406510000000000000E-13 " " relative error = 6.9549292074672480000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7399999999999185 " " y[1] (closed_form) = 6.697343422671526 " " y[1] (numeric) = 6.697343422672 " " absolute error = 4.7339909770016675000000000000E-13 " " relative error = 7.068460848187041000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7499999999999174 " " y[1] (closed_form) = 6.7546026760052555 " " y[1] (numeric) = 6.7546026760057405 " " absolute error = 4.8494541715626840000000000000E-13 " " relative error = 7.1794810208299380000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7599999999999163 " " y[1] (closed_form) = 6.812437394402102 " " y[1] (numeric) = 6.8124373944025995 " " absolute error = 4.9737991503207013000000000000E-13 " " relative error = 7.301056673794547000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7699999999999152 " " y[1] (closed_form) = 6.870853361382103 " " y[1] (numeric) = 6.870853361382612 " " absolute error = 5.0892623448817180000000000000E-13 " " relative error = 7.407030942453398000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.779999999999914 " " y[1] (closed_form) = 6.929856418590637 " " y[1] (numeric) = 6.929856418591157 " " absolute error = 5.2047255394427340000000000000E-13 " " relative error = 7.510582074226075000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.789999999999913 " " y[1] (closed_form) = 6.989452466382592 " " y[1] (numeric) = 6.989452466383125 " " absolute error = 5.3290705182007510000000000000E-13 " " relative error = 7.62444632656444000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.799999999999912 " " y[1] (closed_form) = 7.049647464412413 " " y[1] (numeric) = 7.049647464412958 " " absolute error = 5.4534154969587690000000000000E-13 " " relative error = 7.735727955884826000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8099999999999108 " " y[1] (closed_form) = 7.110447432230065 " " y[1] (numeric) = 7.110447432230624 " " absolute error = 5.5955240441107890000000000000E-13 " " relative error = 7.869440140640843000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8199999999999097 " " y[1] (closed_form) = 7.171858449882996 " " y[1] (numeric) = 7.17185844988357 " " absolute error = 5.7376325912628090000000000000E-13 " " relative error = 8.000203338308237000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8299999999999086 " " y[1] (closed_form) = 7.233886658524147 " " y[1] (numeric) = 7.233886658524736 " " absolute error = 5.888622922611830000000000000E-13 " " relative error = 8.140330641858887000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8399999999999075 " " y[1] (closed_form) = 7.2965382610260745 " " y[1] (numeric) = 7.296538261026676 " " absolute error = 6.0129679013698480000000000000E-13 " " relative error = 8.240850230975525000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8499999999999064 " " y[1] (closed_form) = 7.359819522601236 " " y[1] (numeric) = 7.359819522601850 " " absolute error = 6.1461946643248670000000000000E-13 " " relative error = 8.35101274623725000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8599999999999053 " " y[1] (closed_form) = 7.423736771428525 " " y[1] (numeric) = 7.423736771429154 " " absolute error = 6.2883032114768870000000000000E-13 " " relative error = 8.470536341857455000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8699999999999042 " " y[1] (closed_form) = 7.48829639928609 " " y[1] (numeric) = 7.488296399286730 " " absolute error = 6.4126481902349040000000000000E-13 " " relative error = 8.563560853235277000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.879999999999903 " " y[1] (closed_form) = 7.553504862190513 " " y[1] (numeric) = 7.5535048621911685 " " absolute error = 6.5547567373869240000000000000E-13 " " relative error = 8.677768608049915000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.889999999999902 " " y[1] (closed_form) = 7.619368681042428 " " y[1] (numeric) = 7.619368681043098 " " absolute error = 6.6968652845389440000000000000E-13 " " relative error = 8.789265311706543000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8999999999999009 " " y[1] (closed_form) = 7.685894442278607 " " y[1] (numeric) = 7.68589444227929 " " absolute error = 6.8300920474939630000000000000E-13 " " relative error = 8.886528560583603000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9099999999998998 " " y[1] (closed_form) = 7.75308879853061 " " y[1] (numeric) = 7.753088798531308 " " absolute error = 6.9810823788429840000000000000E-13 " " relative error = 9.00425954126317000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9199999999998987 " " y[1] (closed_form) = 7.8209584692900584 " " y[1] (numeric) = 7.820958469290772 " " absolute error = 7.1320727101920060000000000000E-13 " " relative error = 9.119179878268057000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9299999999998976 " " y[1] (closed_form) = 7.889510241580587 " " y[1] (numeric) = 7.889510241581315 " " absolute error = 7.2830630415410270000000000000E-13 " " relative error = 9.231324655815308000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9399999999998965 " " y[1] (closed_form) = 7.958750970636552 " " y[1] (numeric) = 7.958750970637295 " " absolute error = 7.4340533728900480000000000000E-13 " " relative error = 9.340728715243948000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9499999999998954 " " y[1] (closed_form) = 8.028687580588558 " " y[1] (numeric) = 8.028687580589317 " " absolute error = 7.5850437042390700000000000000E-13 " " relative error = 9.447426653613832000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9599999999998943 " " y[1] (closed_form) = 8.099327065155883 " " y[1] (numeric) = 8.099327065156656 " " absolute error = 7.727152251391090000000000000E-13 " " relative error = 9.540486745663197000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9699999999998932 " " y[1] (closed_form) = 8.170676488345848 " " y[1] (numeric) = 8.17067648834664 " " absolute error = 7.9225515037251170000000000000E-13 " " relative error = 9.696322593392798000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.979999999999892 " " y[1] (closed_form) = 8.24274298516023 " " y[1] (numeric) = 8.242742985161039 " " absolute error = 8.082423619271140000000000000E-13 " " relative error = 9.805502408387936000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.989999999999891 " " y[1] (closed_form) = 8.31553376230877 " " y[1] (numeric) = 8.315533762309595 " " absolute error = 8.2600593032111650000000000000E-13 " " relative error = 9.933288156018258000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9999999999998899 " " y[1] (closed_form) = 8.389056098929837 " " y[1] (numeric) = 8.38905609893068 " " absolute error = 8.437694987151190000000000000E-13 " " relative error = 1.00579789759989300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0099999999998888 " " y[1] (closed_form) = 8.463317347318364 " " y[1] (numeric) = 8.463317347319224 " " absolute error = 8.5975671026972120000000000000E-13 " " relative error = 1.015862545367199900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0199999999998877 " " y[1] (closed_form) = 8.538324933661075 " " y[1] (numeric) = 8.53832493366195 " " absolute error = 8.7574392182432350000000000000E-13 " " relative error = 1.025662443896733600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0299999999998866 " " y[1] (closed_form) = 8.614086358779112 " " y[1] (numeric) = 8.614086358780005 " " absolute error = 8.935074902183260000000000000E-13 " " relative error = 1.03726321400028810000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0399999999998855 " " y[1] (closed_form) = 8.690609198878118 " " y[1] (numeric) = 8.690609198879029 " " absolute error = 9.1127105861232850000000000000E-13 " " relative error = 1.048569827222199200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0499999999998844 " " y[1] (closed_form) = 8.767901106305874 " " y[1] (numeric) = 8.767901106306802 " " absolute error = 9.2725827016693070000000000000E-13 " " relative error = 1.057560137739289200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0599999999998833 " " y[1] (closed_form) = 8.845969810317532 " " y[1] (numeric) = 8.84596981031848 " " absolute error = 9.4679819540033350000000000000E-13 " " relative error = 1.07031587909788200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.069999999999882 " " y[1] (closed_form) = 8.924823117848554 " " y[1] (numeric) = 8.92482311784952 " " absolute error = 9.6633812063373630000000000000E-13 " " relative error = 1.082753246617491300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.079999999999881 " " y[1] (closed_form) = 9.004468914295401 " " y[1] (numeric) = 9.004468914296387 " " absolute error = 9.858780458671390000000000000E-13 " " relative error = 1.09487639443340100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.08999999999988 " " y[1] (closed_form) = 9.084915164304089 " " y[1] (numeric) = 9.084915164305094 " " absolute error = 1.0054179711005418000000000000E-12 " " relative error = 1.106689443893731200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.099999999999879 " " y[1] (closed_form) = 9.16616991256666 " " y[1] (numeric) = 9.166169912567685 " " absolute error = 1.0249578963339445000000000000E-12 " " relative error = 1.118196483493880100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1099999999998778 " " y[1] (closed_form) = 9.248241284625653 " " y[1] (numeric) = 9.2482412846267 " " absolute error = 1.0462741784067475000000000000E-12 " " relative error = 1.13132231978644610000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1199999999998766 " " y[1] (closed_form) = 9.331137487686664 " " y[1] (numeric) = 9.33113748768773 " " absolute error = 1.0658141036401503000000000000E-12 " " relative error = 1.142212409844560600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1299999999998755 " " y[1] (closed_form) = 9.414866811439081 " " y[1] (numeric) = 9.414866811440172 " " absolute error = 1.0906830993917538000000000000E-12 " " relative error = 1.158468963221627000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1399999999998744 " " y[1] (closed_form) = 9.499437628885056 " " y[1] (numeric) = 9.499437628886167 " " absolute error = 1.1102230246251565000000000000E-12 " " relative error = 1.168725000361377000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1499999999998733 " " y[1] (closed_form) = 9.584858397176806 " " y[1] (numeric) = 9.584858397177937 " " absolute error = 1.1315393066979595000000000000E-12 " " relative error = 1.180548798750382700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1599999999998722 " " y[1] (closed_form) = 9.671137658462348 " " y[1] (numeric) = 9.6711376584635 " " absolute error = 1.1528555887707626000000000000E-12 " " relative error = 1.192057883450766300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.169999999999871 " " y[1] (closed_form) = 9.758284040739706 " " y[1] (numeric) = 9.758284040740879 " " absolute error = 1.1723955140041653000000000000E-12 " " relative error = 1.201436142983284500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.17999999999987 " " y[1] (closed_form) = 9.846306258719732 " " y[1] (numeric) = 9.846306258720928 " " absolute error = 1.1954881529163686000000000000E-12 " " relative error = 1.214148861008323100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.189999999999869 " " y[1] (closed_form) = 9.935213114697579 " " y[1] (numeric) = 9.935213114698797 " " absolute error = 1.2185807918285718000000000000E-12 " " relative error = 1.226527078745672800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.199999999999868 " " y[1] (closed_form) = 10.025013499432928 " " y[1] (numeric) = 10.02501349943417 " " absolute error = 1.241673430740775100000000000E-12 " " relative error = 1.238575320433245400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2099999999998667 " " y[1] (closed_form) = 10.115716393039092 " " y[1] (numeric) = 10.115716393040357 " " absolute error = 1.2647660696529783000000000000E-12 " " relative error = 1.250298071348954800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2199999999998656 " " y[1] (closed_form) = 10.207330865881014 " " y[1] (numeric) = 10.207330865882303 " " absolute error = 1.2896350654045818000000000000E-12 " " relative error = 1.263440053378999700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2299999999998645 " " y[1] (closed_form) = 10.299866079482326 " " y[1] (numeric) = 10.299866079483639 " " absolute error = 1.312727704316785000000000000E-12 " " relative error = 1.274509487974588600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2399999999998634 " " y[1] (closed_form) = 10.3933312874415 " " y[1] (numeric) = 10.393331287442837 " " absolute error = 1.3375967000683886000000000000E-12 " " relative error = 1.286975910875310400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2499999999998623 " " y[1] (closed_form) = 10.487735836357219 " " y[1] (numeric) = 10.487735836358581 " " absolute error = 1.3624656958199920000000000000E-12 " " relative error = 1.29910375039845320000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2599999999998612 " " y[1] (closed_form) = 10.583089166763049 " " y[1] (numeric) = 10.583089166764438 " " absolute error = 1.3891110484109960000000000000E-12 " " relative error = 1.312576154771140600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.26999999999986 " " y[1] (closed_form) = 10.679400814071487 " " y[1] (numeric) = 10.679400814072903 " " absolute error = 1.4157564010019996000000000000E-12 " " relative error = 1.325688983539749000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.279999999999859 " " y[1] (closed_form) = 10.776680409527527 " " y[1] (numeric) = 10.77668040952897 " " absolute error = 1.4424017535930034000000000000E-12 " " relative error = 1.338447182972777300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.289999999999858 " " y[1] (closed_form) = 10.87493768117178 " " y[1] (numeric) = 10.874937681173249 " " absolute error = 1.4690471061840070000000000000E-12 " " relative error = 1.350855654766121600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.299999999999857 " " y[1] (closed_form) = 10.974182454813294 " " y[1] (numeric) = 10.974182454814786 " " absolute error = 1.4921397450962104000000000000E-12 " " relative error = 1.359681918211370400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3099999999998557 " " y[1] (closed_form) = 11.074424655012132 " " y[1] (numeric) = 11.074424655013653 " " absolute error = 1.5205614545266144000000000000E-12 " " relative error = 1.373038782505445200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3199999999998546 " " y[1] (closed_form) = 11.175674306071855 " " y[1] (numeric) = 11.175674306073406 " " absolute error = 1.5507595207964187000000000000E-12 " " relative error = 1.38762053932967200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3299999999998535 " " y[1] (closed_form) = 11.277941533041941 " " y[1] (numeric) = 11.277941533043519 " " absolute error = 1.5774048733874224000000000000E-12 " " relative error = 1.398663815347832600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3399999999998524 " " y[1] (closed_form) = 11.381236562730313 " " y[1] (numeric) = 11.381236562731916 " " absolute error = 1.602273869139026000000000000E-12 " " relative error = 1.407820547712653000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3499999999998513 " " y[1] (closed_form) = 11.485569724726016 " " y[1] (numeric) = 11.485569724727647 " " absolute error = 1.63069557856943000000000000E-12 " " relative error = 1.419777701631017300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.35999999999985 " " y[1] (closed_form) = 11.590951452432193 " " y[1] (numeric) = 11.590951452433853 " " absolute error = 1.659117287999834000000000000E-12 " " relative error = 1.43139007596455120000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.369999999999849 " " y[1] (closed_form) = 11.697392284109439 " " y[1] (numeric) = 11.697392284111128 " " absolute error = 1.6893153542696382000000000000E-12 " " relative error = 1.444181158705366300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.379999999999848 " " y[1] (closed_form) = 11.804902863929616 " " y[1] (numeric) = 11.80490286393134 " " absolute error = 1.723066134218243000000000000E-12 " " relative error = 1.459619070211195800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.389999999999847 " " y[1] (closed_form) = 11.913493943040303 " " y[1] (numeric) = 11.913493943042054 " " absolute error = 1.751487843648647000000000000E-12 " " relative error = 1.470171430835235000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.399999999999846 " " y[1] (closed_form) = 12.023176380639901 " " y[1] (numeric) = 12.023176380641685 " " absolute error = 1.7834622667578515000000000000E-12 " " relative error = 1.483353658214345600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4099999999998447 " " y[1] (closed_form) = 12.133961145063576 " " y[1] (numeric) = 12.133961145065385 " " absolute error = 1.808331262509455000000000000E-12 " " relative error = 1.490305796178631500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4199999999998436 " " y[1] (closed_form) = 12.245859314880088 " " y[1] (numeric) = 12.245859314881926 " " absolute error = 1.8385293287792592000000000000E-12 " " relative error = 1.501347746617700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4299999999998425 " " y[1] (closed_form) = 12.358882079999667 " " y[1] (numeric) = 12.35888208000154 " " absolute error = 1.8740564655672642000000000000E-12 " " relative error = 1.516364063866296500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4399999999998414 " " y[1] (closed_form) = 12.473040742793014 " " y[1] (numeric) = 12.473040742794922 " " absolute error = 1.907807245515869000000000000E-12 " " relative error = 1.529544627374210800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4499999999998403 " " y[1] (closed_form) = 12.588346719221539 " " y[1] (numeric) = 12.58834671922348 " " absolute error = 1.9415580254644738000000000000E-12 " " relative error = 1.54234552699430200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.459999999999839 " " y[1] (closed_form) = 12.704811539978973 " " y[1] (numeric) = 12.704811539980945 " " absolute error = 1.971756091734278000000000000E-12 " " relative error = 1.55197586798484800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.469999999999838 " " y[1] (closed_form) = 12.822446851644447 " " y[1] (numeric) = 12.822446851646452 " " absolute error = 2.0055068716828828000000000000E-12 " " relative error = 1.5640594146238798000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.479999999999837 " " y[1] (closed_form) = 12.941264417847156 " " y[1] (numeric) = 12.9412644178492 " " absolute error = 2.042810365310288000000000000E-12 " " relative error = 1.578524554751443400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.489999999999836 " " y[1] (closed_form) = 13.061276120442738 " " y[1] (numeric) = 13.061276120444816 " " absolute error = 2.078337502098293000000000000E-12 " " relative error = 1.591220859993459400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.499999999999835 " " y[1] (closed_form) = 13.18249396070146 " " y[1] (numeric) = 13.182493960703573 " " absolute error = 2.112088282046897800000000000E-12 " " relative error = 1.602191731202970400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5099999999998337 " " y[1] (closed_form) = 13.304930060508365 " " y[1] (numeric) = 13.304930060510515 " " absolute error = 2.149391775674303000000000000E-12 " " relative error = 1.6154852117968800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5199999999998326 " " y[1] (closed_form) = 13.428596663575464 " " y[1] (numeric) = 13.428596663577649 " " absolute error = 2.184918912462308000000000000E-12 " " relative error = 1.627064217654860500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5299999999998315 " " y[1] (closed_form) = 13.553506136666115 " " y[1] (numeric) = 13.55350613666834 " " absolute error = 2.2239987629291136000000000000E-12 " " relative error = 1.640902907707814400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5399999999998304 " " y[1] (closed_form) = 13.679670970831726 " " y[1] (numeric) = 13.679670970833987 " " absolute error = 2.261302256556518800000000000E-12 " " relative error = 1.653038484169792600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5499999999998293 " " y[1] (closed_form) = 13.807103782660846 " " y[1] (numeric) = 13.807103782663146 " " absolute error = 2.3003821070233244000000000000E-12 " " relative error = 1.666085910002484700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.559999999999828 " " y[1] (closed_form) = 13.935817315540854 " " y[1] (numeric) = 13.935817315543193 " " absolute error = 2.33946195749013000000000000E-12 " " relative error = 1.67874040289063200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.569999999999827 " " y[1] (closed_form) = 14.0658244409323 " " y[1] (numeric) = 14.065824440934684 " " absolute error = 2.383870878475136000000000000E-12 " " relative error = 1.694796411320153300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.579999999999826 " " y[1] (closed_form) = 14.197138159656062 " " y[1] (numeric) = 14.197138159658484 " " absolute error = 2.4229507289419416000000000000E-12 " " relative error = 1.706647284610661200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.589999999999825 " " y[1] (closed_form) = 14.32977160319344 " " y[1] (numeric) = 14.329771603195905 " " absolute error = 2.4655832930875476000000000000E-12 " " relative error = 1.720601947722658600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.599999999999824 " " y[1] (closed_form) = 14.463738034999318 " " y[1] (numeric) = 14.463738035001825 " " absolute error = 2.5064395003937534000000000000E-12 " " relative error = 1.73291267743419900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6099999999998227 " " y[1] (closed_form) = 14.599050851828515 " " y[1] (numeric) = 14.599050851831064 " " absolute error = 2.5490720645393594000000000000E-12 " " relative error = 1.746053281415956600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6199999999998216 " " y[1] (closed_form) = 14.735723585075474 " " y[1] (numeric) = 14.735723585078064 " " absolute error = 2.589928271845565000000000000E-12 " " relative error = 1.7575847272737100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6299999999998205 " " y[1] (closed_form) = 14.873769902127416 " " y[1] (numeric) = 14.873769902130045 " " absolute error = 2.6290081223123707000000000000E-12 " " relative error = 1.767546586784524700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6399999999998194 " " y[1] (closed_form) = 15.013203607731082 " " y[1] (numeric) = 15.013203607733754 " " absolute error = 2.6716406864579767000000000000E-12 " " relative error = 1.779527378874825300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6499999999998183 " " y[1] (closed_form) = 15.15403864537323 " " y[1] (numeric) = 15.154038645375946 " " absolute error = 2.716049607442983000000000000E-12 " " relative error = 1.792294233242064700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.659999999999817 " " y[1] (closed_form) = 15.296289098674988 " " y[1] (numeric) = 15.296289098677748 " " absolute error = 2.7604585284279890000000000000E-12 " " relative error = 1.804658967034761800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.669999999999816 " " y[1] (closed_form) = 15.439969192800225 " " y[1] (numeric) = 15.43996919280303 " " absolute error = 2.8048674494129955000000000000E-12 " " relative error = 1.816627620423573200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.679999999999815 " " y[1] (closed_form) = 15.58509329587809 " " y[1] (numeric) = 15.58509329588094 " " absolute error = 2.8492763703980020000000000000E-12 " " relative error = 1.828206168744316900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.689999999999814 " " y[1] (closed_form) = 15.731675920439828 " " y[1] (numeric) = 15.731675920442724 " " absolute error = 2.8954616482224080000000000000E-12 " " relative error = 1.840529682193870500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6999999999998128 " " y[1] (closed_form) = 15.879731724870048 " " y[1] (numeric) = 15.879731724872991 " " absolute error = 2.943423282886215000000000000E-12 " " relative error = 1.853572424196796300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7099999999998117 " " y[1] (closed_form) = 16.029275514872573 " " y[1] (numeric) = 16.02927551487556 " " absolute error = 2.9878322038712213000000000000E-12 " " relative error = 1.863984558191040500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7199999999998106 " " y[1] (closed_form) = 16.18032224495102 " " y[1] (numeric) = 16.18032224495406 " " absolute error = 3.0375701953744283000000000000E-12 " " relative error = 1.8773236709313900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7299999999998095 " " y[1] (closed_form) = 16.332887019904277 " " y[1] (numeric) = 16.33288701990736 " " absolute error = 3.083755473198835000000000000E-12 " " relative error = 1.888065146988880400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7399999999998084 " " y[1] (closed_form) = 16.486985096336966 " " y[1] (numeric) = 16.4869850963401 " " absolute error = 3.133493464702042000000000000E-12 " " relative error = 1.90058609648299700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7499999999998073 " " y[1] (closed_form) = 16.642631884185157 " " y[1] (numeric) = 16.642631884188336 " " absolute error = 3.1796787425264483000000000000E-12 " " relative error = 1.910562442679497600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.759999999999806 " " y[1] (closed_form) = 16.799842948257336 " " y[1] (numeric) = 16.799842948260565 " " absolute error = 3.2294167340296553000000000000E-12 " " relative error = 1.92228983567054500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.769999999999805 " " y[1] (closed_form) = 16.95863400979092 " " y[1] (numeric) = 16.9586340097942 " " absolute error = 3.2791547255328624000000000000E-12 " " relative error = 1.933619608536672800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.779999999999804 " " y[1] (closed_form) = 17.119020948024385 " " y[1] (numeric) = 17.119020948027714 " " absolute error = 3.3288927170360694000000000000E-12 " " relative error = 1.944557885140177400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.789999999999803 " " y[1] (closed_form) = 17.281019801785217 " " y[1] (numeric) = 17.281019801788595 " " absolute error = 3.3786307085392764000000000000E-12 " " relative error = 1.955110721064185500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7999999999998018 " " y[1] (closed_form) = 17.44464677109379 " " y[1] (numeric) = 17.444646771097215 " " absolute error = 3.424815986363683000000000000E-12 " " relative error = 1.96324754023606100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8099999999998007 " " y[1] (closed_form) = 17.60991821878339 " " y[1] (numeric) = 17.609918218786863 " " absolute error = 3.47455397786689000000000000E-12 " " relative error = 1.973066504170815600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8199999999997996 " " y[1] (closed_form) = 17.77685067213651 " " y[1] (numeric) = 17.77685067214004 " " absolute error = 3.5278446830488974000000000000E-12 " " relative error = 1.984516126120388400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8299999999997985 " " y[1] (closed_form) = 17.9454608245376 " " y[1] (numeric) = 17.94546082454119 " " absolute error = 3.588240815588506000000000000E-12 " " relative error = 1.999525590717709500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8399999999997974 " " y[1] (closed_form) = 18.11576553714241 " " y[1] (numeric) = 18.115765537146057 " " absolute error = 3.6486369481281145000000000000E-12 " " relative error = 2.014067217113946200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8499999999997963 " " y[1] (closed_form) = 18.28778184056412 " " y[1] (numeric) = 18.28778184056782 " " absolute error = 3.701927653310122000000000000E-12 " " relative error = 2.02426280321152920000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.859999999999795 " " y[1] (closed_form) = 18.461526936576412 " " y[1] (numeric) = 18.46152693658018 " " absolute error = 3.7694292132073315000000000000E-12 " " relative error = 2.041775431770624600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.869999999999794 " " y[1] (closed_form) = 18.637018199833687 " " y[1] (numeric) = 18.637018199837513 " " absolute error = 3.8262726320681395000000000000E-12 " " relative error = 2.053049791034857700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.879999999999793 " " y[1] (closed_form) = 18.81427317960851 " " y[1] (numeric) = 18.8142731796124 " " absolute error = 3.8902214782865485000000000000E-12 " " relative error = 2.067696924111259700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.889999999999792 " " y[1] (closed_form) = 18.99330960154657 " " y[1] (numeric) = 18.993309601550525 " " absolute error = 3.9541703245049575000000000000E-12 " " relative error = 2.08187535898587200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8999999999997907 " " y[1] (closed_form) = 19.17414536943926 " " y[1] (numeric) = 19.174145369443277 " " absolute error = 4.0181191707233666000000000000E-12 " " relative error = 2.095592316269622200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9099999999997896 " " y[1] (closed_form) = 19.35679856701406 " " y[1] (numeric) = 19.35679856701814 " " absolute error = 4.078515303262975000000000000E-12 " " relative error = 2.10701955137001700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9199999999997885 " " y[1] (closed_form) = 19.54128745974295 " " y[1] (numeric) = 19.54128745974709 " " absolute error = 4.1389114358025836000000000000E-12 " " relative error = 2.118034159381342600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9299999999997874 " " y[1] (closed_form) = 19.727630496668937 " " y[1] (numeric) = 19.72763049667314 " " absolute error = 4.202860282020992600000000000E-12 " " relative error = 2.130443533363348700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9399999999997863 " " y[1] (closed_form) = 19.915846312251 " " y[1] (numeric) = 19.915846312255265 " " absolute error = 4.266809128239401600000000000E-12 " " relative error = 2.142419187887950600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9499999999997852 " " y[1] (closed_form) = 20.105953728227544 " " y[1] (numeric) = 20.105953728231874 " " absolute error = 4.330757974457810600000000000E-12 " " relative error = 2.153967940539765800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.959999999999784 " " y[1] (closed_form) = 20.297971755498594 " " y[1] (numeric) = 20.29797175550299 " " absolute error = 4.39470682067621960000000000E-12 " " relative error = 2.165096529649924700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.969999999999783 " " y[1] (closed_form) = 20.49191959602689 " " y[1] (numeric) = 20.49191959603135 " " absolute error = 4.462208380573429000000000000E-12 " " relative error = 2.177545329349521700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.979999999999782 " " y[1] (closed_form) = 20.687816644758108 " " y[1] (numeric) = 20.687816644762634 " " absolute error = 4.526157226791838000000000000E-12 " " relative error = 2.187837075566250700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.989999999999781 " " y[1] (closed_form) = 20.88568249156037 " " y[1] (numeric) = 20.88568249156497 " " absolute error = 4.600764214046648700000000000E-12 " " relative error = 2.202831636412052600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9999999999997797 " " y[1] (closed_form) = 21.085536923183245 " " y[1] (numeric) = 21.08553692318792 " " absolute error = 4.675371201301459000000000000E-12 " " relative error = 2.21733561651017600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0099999999997786 " " y[1] (closed_form) = 21.28739992523644 " " y[1] (numeric) = 21.287399925241193 " " absolute error = 4.75353090223507000000000000E-12 " " relative error = 2.233025601496643500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0199999999997775 " " y[1] (closed_form) = 21.491291684188383 " " y[1] (numeric) = 21.491291684193207 " " absolute error = 4.82458517581108000000000000E-12 " " relative error = 2.244902375672763200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0299999999997764 " " y[1] (closed_form) = 21.697232589384875 " " y[1] (numeric) = 21.69723258938977 " " absolute error = 4.89563944938709030000000000E-12 " " relative error = 2.256342798197327000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0399999999997753 " " y[1] (closed_form) = 21.905243235088058 " " y[1] (numeric) = 21.90524323509303 " " absolute error = 4.973799150320701300000000000E-12 " " relative error = 2.27059754458860120000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0499999999997742 " " y[1] (closed_form) = 22.115344422535845 " " y[1] (numeric) = 22.115344422540893 " " absolute error = 5.048406137575512000000000000E-12 " " relative error = 2.282761706587357300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.059999999999773 " " y[1] (closed_form) = 22.327557162022064 " " y[1] (numeric) = 22.327557162027183 " " absolute error = 5.119460411151522000000000000E-12 " " relative error = 2.292888726698431600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.069999999999772 " " y[1] (closed_form) = 22.541902674997505 " " y[1] (numeric) = 22.541902675002707 " " absolute error = 5.201172825763933000000000000E-12 " " relative error = 2.307335321579951400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.079999999999771 " " y[1] (closed_form) = 22.758402396192093 " " y[1] (numeric) = 22.75840239619738 " " absolute error = 5.286437954055145000000000000E-12 " " relative error = 2.3228510780438902000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.08999999999977 " " y[1] (closed_form) = 22.977077975758363 " " y[1] (numeric) = 22.977077975763727 " " absolute error = 5.364597654988756000000000000E-12 " " relative error = 2.334760608223812600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0999999999997687 " " y[1] (closed_form) = 23.1979512814365 " " y[1] (numeric) = 23.197951281441945 " " absolute error = 5.446310069601168000000000000E-12 " " relative error = 2.347754766585540300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.1099999999997676 " " y[1] (closed_form) = 23.421044400741135 " " y[1] (numeric) = 23.42104440074666 " " absolute error = 5.524469770534779000000000000E-12 " " relative error = 2.358763202874062700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.1199999999997665 " " y[1] (closed_form) = 23.646379643170107 " " y[1] (numeric) = 23.646379643175713 " " absolute error = 5.6061821851471900000000000000E-12 " " relative error = 2.370841655148021600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.1299999999997654 " " y[1] (closed_form) = 23.873979542435446 " " y[1] (numeric) = 23.873979542441134 " " absolute error = 5.687894599759602000000000000E-12 " " relative error = 2.382466060863251000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.1399999999997643 " " y[1] (closed_form) = 24.10386685871674 " " y[1] (numeric) = 24.103866858722512 " " absolute error = 5.773159728050814000000000000E-12 " " relative error = 2.39511766385444200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.149999999999763 " " y[1] (closed_form) = 24.336064580937187 " " y[1] (numeric) = 24.336064580943052 " " absolute error = 5.865530283699627000000000000E-12 " " relative error = 2.410221366808085500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.159999999999762 " " y[1] (closed_form) = 24.570595929062517 " " y[1] (numeric) = 24.570595929068467 " " absolute error = 5.950795411990839000000000000E-12 " " relative error = 2.421917412655074400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.169999999999761 " " y[1] (closed_form) = 24.80748435642298 " " y[1] (numeric) = 24.80748435642902 " " absolute error = 6.0396132539608520000000000000E-12 " " relative error = 2.43459319259718400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.17999999999976 " " y[1] (closed_form) = 25.04675355205872 " " y[1] (numeric) = 25.04675355206485 " " absolute error = 6.128431095930864000000000000E-12 " " relative error = 2.446796581119047600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.189999999999759 " " y[1] (closed_form) = 25.288427443088697 " " y[1] (numeric) = 25.288427443094914 " " absolute error = 6.217248937900877000000000000E-12 " " relative error = 2.45853521413805620000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.1999999999997577 " " y[1] (closed_form) = 25.532530197103405 " " y[1] (numeric) = 25.532530197109715 " " absolute error = 6.30961949354969000000000000E-12 " " relative error = 2.471208080374853700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.2099999999997566 " " y[1] (closed_form) = 25.779086224581665 " " y[1] (numeric) = 25.779086224588067 " " absolute error = 6.401990049198503000000000000E-12 " " relative error = 2.483404568116103800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.2199999999997555 " " y[1] (closed_form) = 26.02812018133169 " " y[1] (numeric) = 26.028120181338185 " " absolute error = 6.494360604847316000000000000E-12 " " relative error = 2.495132402802299200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.2299999999997544 " " y[1] (closed_form) = 26.279656970956683 " " y[1] (numeric) = 26.279656970963273 " " absolute error = 6.590283874174929000000000000E-12 " " relative error = 2.50775110248138700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.2399999999997533 " " y[1] (closed_form) = 26.533721747345226 " " y[1] (numeric) = 26.5337217473519 " " absolute error = 6.675549002466141000000000000E-12 " " relative error = 2.515873598898371000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.249999999999752 " " y[1] (closed_form) = 26.79033991718667 " " y[1] (numeric) = 26.790339917193446 " " absolute error = 6.775024985472555000000000000E-12 " " relative error = 2.528905943864568000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.259999999999751 " " y[1] (closed_form) = 27.04953714251186 " " y[1] (numeric) = 27.049537142518734 " " absolute error = 6.874500968478969000000000000E-12 " " relative error = 2.541448651139689400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.26999999999975 " " y[1] (closed_form) = 27.311339343259313 " " y[1] (numeric) = 27.311339343266297 " " absolute error = 6.984635092521785000000000000E-12 " " relative error = 2.55741214472722500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.279999999999749 " " y[1] (closed_form) = 27.575772699867287 " " y[1] (numeric) = 27.57577269987437 " " absolute error = 7.084111075528199000000000000E-12 " " relative error = 2.56896194809521800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.289999999999748 " " y[1] (closed_form) = 27.842863655891794 " " y[1] (numeric) = 27.842863655898984 " " absolute error = 7.190692485892214000000000000E-12 " " relative error = 2.582598031137002000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.2999999999997467 " " y[1] (closed_form) = 28.11263892065102 " " y[1] (numeric) = 28.11263892065831 " " absolute error = 7.290168468898628000000000000E-12 " " relative error = 2.59319962436660700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3099999999997456 " " y[1] (closed_form) = 28.38512547189625 " " y[1] (numeric) = 28.38512547190365 " " absolute error = 7.400302592941443000000000000E-12 " " relative error = 2.607105823882437400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3199999999997445 " " y[1] (closed_form) = 28.660350558509684 " " y[1] (numeric) = 28.66035055851719 " " absolute error = 7.506884003305458000000000000E-12 " " relative error = 2.61925756559755400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3299999999997434 " " y[1] (closed_form) = 28.938341703229337 " " y[1] (numeric) = 28.93834170323695 " " absolute error = 7.613465413669473000000000000E-12 " " relative error = 2.630926641114289500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3399999999997423 " " y[1] (closed_form) = 29.21912670540134 " " y[1] (numeric) = 29.21912670540906 " " absolute error = 7.720046824033489000000000000E-12 " " relative error = 2.642120998984678300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.349999999999741 " " y[1] (closed_form) = 29.5027336437599 " " y[1] (numeric) = 29.50273364376773 " " absolute error = 7.830180948076304000000000000E-12 " " relative error = 2.65405268631181900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.35999999999974 " " y[1] (closed_form) = 29.789190879235196 " " y[1] (numeric) = 29.78919087924314 " " absolute error = 7.94386778579792000000000000E-12 " " relative error = 2.666694714200935000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.369999999999739 " " y[1] (closed_form) = 30.078527057789483 " " y[1] (numeric) = 30.07852705779754 " " absolute error = 8.057554623519536000000000000E-12 " " relative error = 2.678839495045306500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.379999999999738 " " y[1] (closed_form) = 30.370771113281737 " " y[1] (numeric) = 30.370771113289905 " " absolute error = 8.167688747562352000000000000E-12 " " relative error = 2.689325442906011500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.389999999999737 " " y[1] (closed_form) = 30.665952270361043 " " y[1] (numeric) = 30.665952270369324 " " absolute error = 8.281375585283968000000000000E-12 " " relative error = 2.700511470269260600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3999999999997357 " " y[1] (closed_form) = 30.964100047389092 " " y[1] (numeric) = 30.96410004739749 " " absolute error = 8.398615136684384000000000000E-12 " " relative error = 2.712371786627320600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4099999999997346 " " y[1] (closed_form) = 31.26524425939205 " " y[1] (numeric) = 31.265244259400564 " " absolute error = 8.5158546880848010000000000E-12 " " relative error = 2.72374481306879500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4199999999997335 " " y[1] (closed_form) = 31.56941502104206 " " y[1] (numeric) = 31.5694150210507 " " absolute error = 8.636646953164018000000000000E-12 " " relative error = 2.735764013177756000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4299999999997324 " " y[1] (closed_form) = 31.87664274966878 " " y[1] (numeric) = 31.876642749677536 " " absolute error = 8.757439218243235000000000000E-12 " " relative error = 2.747290323832559700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4399999999997313 " " y[1] (closed_form) = 32.18695816830108 " " y[1] (numeric) = 32.18695816830997 " " absolute error = 8.888889624358853000000000000E-12 " " relative error = 2.76164326491496860000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.44999999999973 " " y[1] (closed_form) = 32.500392308739436 " " y[1] (numeric) = 32.50039230874845 " " absolute error = 9.016787316795671000000000000E-12 " " relative error = 2.774362608038745000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.459999999999729 " " y[1] (closed_form) = 32.816976514659075 " " y[1] (numeric) = 32.816976514668205 " " absolute error = 9.130474154517287000000000000E-12 " " relative error = 2.78224112158497570000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.469999999999728 " " y[1] (closed_form) = 33.136742444744414 " " y[1] (numeric) = 33.13674244475367 " " absolute error = 9.258371846954105000000000000E-12 " " relative error = 2.793989741868097000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.479999999999727 " " y[1] (closed_form) = 33.459722075854934 " " y[1] (numeric) = 33.45972207586432 " " absolute error = 9.386269539390923000000000000E-12 " " relative error = 2.8052443227447500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4899999999997258 " " y[1] (closed_form) = 33.7859477062229 " " y[1] (numeric) = 33.78594770623242 " " absolute error = 9.521272659185342000000000000E-12 " " relative error = 2.818116200846323400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4999999999997247 " " y[1] (closed_form) = 34.115451958683195 " " y[1] (numeric) = 34.11545195869286 " " absolute error = 9.663381206337363000000000000E-12 " " relative error = 2.832552597585565000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5099999999997236 " " y[1] (closed_form) = 34.44826778393566 " " y[1] (numeric) = 34.448267783945475 " " absolute error = 9.812595180846984000000000000E-12 " " relative error = 2.848501771523883000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5199999999997225 " " y[1] (closed_form) = 34.78442846384018 " " y[1] (numeric) = 34.784428463850126 " " absolute error = 9.947598300641403000000000000E-12 " " relative error = 2.859784892249224000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5299999999997214 " " y[1] (closed_form) = 35.123967614744856 " " y[1] (numeric) = 35.12396761475493 " " absolute error = 1.00754959930782200000000000E-11 " " relative error = 2.86855292192234600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5399999999997203 " " y[1] (closed_form) = 35.46691919084775 " " y[1] (numeric) = 35.46691919085796 " " absolute error = 1.02104991128726400000000000E-11 " " relative error = 2.878879628064075500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.549999999999719 " " y[1] (closed_form) = 35.81331748759224 " " y[1] (numeric) = 35.813317487602596 " " absolute error = 1.03526076600246600000000000E-11 " " relative error = 2.890714512446770400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.559999999999718 " " y[1] (closed_form) = 36.163197145096696 " " y[1] (numeric) = 36.1631971451072 " " absolute error = 1.05018216345342810000000000E-11 " " relative error = 2.904008069971823500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.569999999999717 " " y[1] (closed_form) = 36.51659315161842 " " y[1] (numeric) = 36.51659315162907 " " absolute error = 1.0643930181686301000000000E-11 " " relative error = 2.91482015791896500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.579999999999716 " " y[1] (closed_form) = 36.87354084705257 " " y[1] (numeric) = 36.87354084706336 " " absolute error = 1.079314415619592200000000000E-11 " " relative error = 2.92707017233975700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5899999999997148 " " y[1] (closed_form) = 37.23407592646613 " " y[1] (numeric) = 37.23407592647708 " " absolute error = 1.094946355806314400000000000E-11 " " relative error = 2.9407104340892803000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5999999999997137 " " y[1] (closed_form) = 37.59823444366751 " " y[1] (numeric) = 37.598234443678614 " " absolute error = 1.110578295993036600000000000E-11 " " relative error = 2.953804380514165600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6099999999997125 " " y[1] (closed_form) = 37.96605281481188 " " y[1] (numeric) = 37.96605281482313 " " absolute error = 1.124789150708238600000000000E-11 " " relative error = 2.96261809515636300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6199999999997114 " " y[1] (closed_form) = 38.33756782204288 " " y[1] (numeric) = 38.33756782205429 " " absolute error = 1.141131633630720900000000000E-11 " " relative error = 2.976536328354681400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6299999999997103 " " y[1] (closed_form) = 38.71281661717082 " " y[1] (numeric) = 38.71281661718239 " " absolute error = 1.156763573817443100000000000E-11 " " relative error = 2.98806357919296440000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6399999999997092 " " y[1] (closed_form) = 39.09183672538794 " " y[1] (numeric) = 39.09183672539966 " " absolute error = 1.171684971268405200000000000E-11 " " relative error = 2.997262521838637300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.649999999999708 " " y[1] (closed_form) = 39.4746660490209 " " y[1] (numeric) = 39.47466604903278 " " absolute error = 1.188027454190887500000000000E-11 " " relative error = 3.00959469224022600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.659999999999707 " " y[1] (closed_form) = 39.86134287132108 " " y[1] (numeric) = 39.861342871333115 " " absolute error = 1.203659394377609700000000000E-11 " " relative error = 3.019615767244015500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.669999999999706 " " y[1] (closed_form) = 40.25190586029296 " " y[1] (numeric) = 40.25190586030516 " " absolute error = 1.22000187730009200000000000E-11 " " relative error = 3.0309170490820897000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.679999999999705 " " y[1] (closed_form) = 40.646394072560895 " " y[1] (numeric) = 40.646394072573266 " " absolute error = 1.237054902958334400000000000E-11 " " relative error = 3.04345546802989700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6899999999997037 " " y[1] (closed_form) = 41.044846957274856 " " y[1] (numeric) = 41.0448469572874 " " absolute error = 1.254107928616576800000000000E-11 " " relative error = 3.05545768003965430000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6999999999997026 " " y[1] (closed_form) = 41.44730436005536 " " y[1] (numeric) = 41.44730436006808 " " absolute error = 1.271871497010579300000000000E-11 " " relative error = 3.06864708489061440000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7099999999997015 " " y[1] (closed_form) = 41.853806526978076 " " y[1] (numeric) = 41.85380652699097 " " absolute error = 1.289635065404581800000000000E-11 " " relative error = 3.08128500707172350000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7199999999997004 " " y[1] (closed_form) = 42.26439410859843 " " y[1] (numeric) = 42.264394108611505 " " absolute error = 1.307398633798584300000000000E-11 " " relative error = 3.093380755534366000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7299999999996993 " " y[1] (closed_form) = 42.67910816401676 " " y[1] (numeric) = 42.67910816403001 " " absolute error = 1.325162202192586800000000000E-11 " " relative error = 3.10494351732927330000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7399999999996982 " " y[1] (closed_form) = 43.097990164984196 " " y[1] (numeric) = 43.09799016499764 " " absolute error = 1.344346856058109600000000000E-11 " " relative error = 3.1192796947416596000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.749999999999697 " " y[1] (closed_form) = 43.5210820000499 " " y[1] (numeric) = 43.52108200006353 " " absolute error = 1.362820967187872200000000000E-11 " " relative error = 3.131404148422388700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.759999999999696 " " y[1] (closed_form) = 43.94842597874997 " " y[1] (numeric) = 43.94842597876378 " " absolute error = 1.381295078317634800000000000E-11 " " relative error = 3.14299101174982100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.769999999999695 " " y[1] (closed_form) = 44.38006483583838 " " y[1] (numeric) = 44.38006483585237 " " absolute error = 1.399058646711637300000000000E-11 " " relative error = 3.15244840647878170000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.779999999999694 " " y[1] (closed_form) = 44.81604173556055 " " y[1] (numeric) = 44.816041735574736 " " absolute error = 1.4182433005771600000000000E-11 " " relative error = 3.16458849477510850000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7899999999996927 " " y[1] (closed_form) = 45.25640027596977 " " y[1] (numeric) = 45.25640027598414 " " absolute error = 1.437427954442682700000000000E-11 " " relative error = 3.17618711536349900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7999999999996916 " " y[1] (closed_form) = 45.70118449328704 " " y[1] (numeric) = 45.7011844933016 " " absolute error = 1.455902065572445300000000000E-11 " " relative error = 3.18569875532722800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.8099999999996905 " " y[1] (closed_form) = 46.15043886630475 " " y[1] (numeric) = 46.15043886631951 " " absolute error = 1.476507804909488200000000000E-11 " " relative error = 3.19933643358592800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.8199999999996894 " " y[1] (closed_form) = 46.60420832083457 " " y[1] (numeric) = 46.604208320849544 " " absolute error = 1.49711354424653100000000000E-11 " " relative error = 3.21239990590558200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.8299999999996883 " " y[1] (closed_form) = 47.06253823420012 " " y[1] (numeric) = 47.06253823421528 " " absolute error = 1.516298198112053800000000000E-11 " " relative error = 3.221879343962300600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.839999999999687 " " y[1] (closed_form) = 47.525474439774655 " " y[1] (numeric) = 47.52547443979003 " " absolute error = 1.537614480184856800000000000E-11 " " relative error = 3.235347986127642400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.849999999999686 " " y[1] (closed_form) = 47.993063231564534 " " y[1] (numeric) = 47.99306323158011 " " absolute error = 1.557509676786139600000000000E-11 " " relative error = 3.24528082167045700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.859999999999685 " " y[1] (closed_form) = 48.465351368838576 " " y[1] (numeric) = 48.46535136885437 " " absolute error = 1.579536501594702700000000000E-11 " " relative error = 3.25910461181611500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.869999999999684 " " y[1] (closed_form) = 48.9423860808041 " " y[1] (numeric) = 48.942386080820114 " " absolute error = 1.601563326403265800000000000E-11 " " relative error = 3.27234418803994900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.879999999999683 " " y[1] (closed_form) = 49.42421507132982 " " y[1] (numeric) = 49.42421507134606 " " absolute error = 1.62430069394758900000000000E-11 " " relative error = 3.286447122333399600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.8899999999996817 " " y[1] (closed_form) = 49.910886523716314 " " y[1] (numeric) = 49.91088652373277 " " absolute error = 1.64561697602039200000000000E-11 " " relative error = 3.29711029123563870000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.8999999999996806 " " y[1] (closed_form) = 50.40244910551439 " " y[1] (numeric) = 50.402449105531076 " " absolute error = 1.668354343564715200000000000E-11 " " relative error = 3.3100660249110503000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.9099999999996795 " " y[1] (closed_form) = 50.89895197339187 " " y[1] (numeric) = 50.89895197340877 " " absolute error = 1.690381168373278300000000000E-11 " " relative error = 3.32105299389454700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.9199999999996784 " " y[1] (closed_form) = 51.40044477804928 " " y[1] (numeric) = 51.4004447780664 " " absolute error = 1.712407993181841400000000000E-11 " " relative error = 3.33150423226129530000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.9299999999996773 " " y[1] (closed_form) = 51.906977669185004 " " y[1] (numeric) = 51.90697766920235 " " absolute error = 1.734434817990404600000000000E-11 " " relative error = 3.34142902529280860000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.939999999999676 " " y[1] (closed_form) = 52.41860130051027 " " y[1] (numeric) = 52.41860130052784 " " absolute error = 1.757172185534727800000000000E-11 " " relative error = 3.352192050034007000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.949999999999675 " " y[1] (closed_form) = 52.93536683481456 " " y[1] (numeric) = 52.935366834832365 " " absolute error = 1.78062009581481100000000000E-11 " " relative error = 3.36376264543751500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.959999999999674 " " y[1] (closed_form) = 53.45732594908195 " " y[1] (numeric) = 53.4573259491 " " absolute error = 1.805489091566414600000000000E-11 " " relative error = 3.37743996638765900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.969999999999673 " " y[1] (closed_form) = 53.98453083965883 " " y[1] (numeric) = 53.98453083967712 " " absolute error = 1.82893700184649800000000000E-11 " " relative error = 3.38789088911170100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.979999999999672 " " y[1] (closed_form) = 54.517034227473594 " " y[1] (numeric) = 54.51703422749213 " " absolute error = 1.853805997598101400000000000E-11 " " relative error = 3.40041607887738850000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.9899999999996707 " " y[1] (closed_form) = 55.05488936330879 " " y[1] (numeric) = 55.05488936332759 " " absolute error = 1.88009607882122500000000000E-11 " " relative error = 3.41494842794872800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.9999999999996696 " " y[1] (closed_form) = 55.5981500331262 " " y[1] (numeric) = 55.59815003314525 " " absolute error = 1.904965074572828600000000000E-11 " " relative error = 3.426310180172942000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.009999999999673 " " y[1] (closed_form) = 56.14687056344578 " " y[1] (numeric) = 56.14687056346485 " " absolute error = 1.90709670278010900000000000E-11 " " relative error = 3.39662154567474230000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.019999999999676 " " y[1] (closed_form) = 56.701105826777585 " " y[1] (numeric) = 56.70110582679667 " " absolute error = 1.90851778825162900000000000E-11 " " relative error = 3.36592692580312100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.02999999999968 " " y[1] (closed_form) = 57.26091124710981 " " y[1] (numeric) = 57.26091124712891 " " absolute error = 1.909938873723149300000000000E-11 " " relative error = 3.335502059128602000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.039999999999683 " " y[1] (closed_form) = 57.826342805451006 " " y[1] (numeric) = 57.826342805470105 " " absolute error = 1.909938873723149300000000000E-11 " " relative error = 3.30288719822535400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.049999999999686 " " y[1] (closed_form) = 58.39745704542819 " " y[1] (numeric) = 58.39745704544728 " " absolute error = 1.909228330987389200000000000E-11 " " relative error = 3.26936895471693900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.05999999999969 " " y[1] (closed_form) = 58.9743110789413 " " y[1] (numeric) = 58.97431107896038 " " absolute error = 1.90851778825162900000000000E-11 " " relative error = 3.23618496483484600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.069999999999693 " " y[1] (closed_form) = 59.55696259187439 " " y[1] (numeric) = 59.556962591893466 " " absolute error = 1.90780724551586900000000000E-11 " " relative error = 3.203332007694024700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.079999999999696 " " y[1] (closed_form) = 60.145469849864305 " " y[1] (numeric) = 60.145469849883376 " " absolute error = 1.90709670278010900000000000E-11 " " relative error = 3.17080689125984300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.0899999999997 " " y[1] (closed_form) = 60.73989170412726 " " y[1] (numeric) = 60.73989170414633 " " absolute error = 1.90709670278010900000000000E-11 " " relative error = 3.13977626445211770000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.099999999999703 " " y[1] (closed_form) = 61.34028759734405 " " y[1] (numeric) = 61.34028759736311 " " absolute error = 1.905675617308588700000000000E-11 " " relative error = 3.10672755533526700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.109999999999706 " " y[1] (closed_form) = 61.94671756960431 " " y[1] (numeric) = 61.94671756962336 " " absolute error = 1.904965074572828600000000000E-11 " " relative error = 3.07516709409563100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.11999999999971 " " y[1] (closed_form) = 62.55924226441064 " " y[1] (numeric) = 62.55924226442967 " " absolute error = 1.902833446365548300000000000E-11 " " relative error = 3.04165040606326540000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.129999999999713 " " y[1] (closed_form) = 63.17792293474296 " " y[1] (numeric) = 63.177922934761966 " " absolute error = 1.90070181815826800000000000E-11 " " relative error = 3.008490513563606400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.139999999999716 " " y[1] (closed_form) = 63.80282144918386 " " y[1] (numeric) = 63.80282144920285 " " absolute error = 1.899280732686747800000000000E-11 " " relative error = 2.97679740417034930000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.14999999999972 " " y[1] (closed_form) = 64.43400029810554 " " y[1] (numeric) = 64.43400029812452 " " absolute error = 1.897149104479467500000000000E-11 " " relative error = 2.944329229447587600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.159999999999723 " " y[1] (closed_form) = 65.07152259991888 " " y[1] (numeric) = 65.07152259993784 " " absolute error = 1.895728019007947300000000000E-11 " " relative error = 2.913299002796517000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.169999999999726 " " y[1] (closed_form) = 65.71545210738533 " " y[1] (numeric) = 65.71545210740426 " " absolute error = 1.89288584806490700000000000E-11 " " relative error = 2.88042733841616200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.17999999999973 " " y[1] (closed_form) = 66.36585321399225 " " y[1] (numeric) = 66.36585321401117 " " absolute error = 1.891464762593386700000000000E-11 " " relative error = 2.8500571769860100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.189999999999733 " " y[1] (closed_form) = 67.0227909603923 " " y[1] (numeric) = 67.02279096041119 " " absolute error = 1.888622591650346300000000000E-11 " " relative error = 2.817881148468502400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.199999999999736 " " y[1] (closed_form) = 67.68633104090756 " " y[1] (numeric) = 67.6863310409264 " " absolute error = 1.884359335235785700000000000E-11 " " relative error = 2.78395845402956800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.20999999999974 " " y[1] (closed_form) = 68.35653981009905 " " y[1] (numeric) = 68.35653981011788 " " absolute error = 1.882938249764265500000000000E-11 " " relative error = 2.75458391398284100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.219999999999743 " " y[1] (closed_form) = 69.0334842894022 " " y[1] (numeric) = 69.03348428942097 " " absolute error = 1.877253907878184700000000000E-11 " " relative error = 2.719338198269640000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.229999999999746 " " y[1] (closed_form) = 69.71723217382903 " " y[1] (numeric) = 69.71723217384776 " " absolute error = 1.87299065146362400000000000E-11 " " relative error = 2.68655337147294400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.23999999999975 " " y[1] (closed_form) = 70.40785183873781 " " y[1] (numeric) = 70.4078518387565 " " absolute error = 1.868727395049063500000000000E-11 " " relative error = 2.654146300797811000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.249999999999753 " " y[1] (closed_form) = 71.10541234667055 " " y[1] (numeric) = 71.10541234668918 " " absolute error = 1.863043053162982700000000000E-11 " " relative error = 2.620114266519991700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.259999999999756 " " y[1] (closed_form) = 71.80998345425932 " " y[1] (numeric) = 71.8099834542779 " " absolute error = 1.85735871127690200000000000E-11 " " relative error = 2.586490933339346000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.26999999999976 " " y[1] (closed_form) = 72.52163561920204 " " y[1] (numeric) = 72.52163561922058 " " absolute error = 1.853095454862341300000000000E-11 " " relative error = 2.555231192788604000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.279999999999763 " " y[1] (closed_form) = 73.24044000730825 " " y[1] (numeric) = 73.24044000732671 " " absolute error = 1.845990027504740300000000000E-11 " " relative error = 2.520451853266500500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.2899999999997664 " " y[1] (closed_form) = 73.96646849961576 " " y[1] (numeric) = 73.96646849963417 " " absolute error = 1.841726771090179700000000000E-11 " " relative error = 2.489948227148017800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.29999999999977 " " y[1] (closed_form) = 74.69979369957883 " " y[1] (numeric) = 74.6997936995972 " " absolute error = 1.83604242920409900000000000E-11 " " relative error = 2.45789491278668780000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.309999999999773 " " y[1] (closed_form) = 75.44048894032856 " " y[1] (numeric) = 75.44048894034687 " " absolute error = 1.83035808731801800000000000E-11 " " relative error = 2.426227763138946400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.3199999999997765 " " y[1] (closed_form) = 76.18862829200629 " " y[1] (numeric) = 76.18862829202452 " " absolute error = 1.82325265996041700000000000E-11 " " relative error = 2.3930771570955198000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.32999999999978 " " y[1] (closed_form) = 76.9442865691706 " " y[1] (numeric) = 76.94428656918878 " " absolute error = 1.817568318074336300000000000E-11 " " relative error = 2.36218749840561200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.339999999999783 " " y[1] (closed_form) = 77.70753933827896 " " y[1] (numeric) = 77.70753933829707 " " absolute error = 1.810462890716735300000000000E-11 " " relative error = 2.32984200263422310000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.3499999999997865 " " y[1] (closed_form) = 78.47846292524432 " " y[1] (numeric) = 78.47846292526233 " " absolute error = 1.80193637788761400000000000E-11 " " relative error = 2.296090303914428100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.35999999999979 " " y[1] (closed_form) = 79.25713442306781 " " y[1] (numeric) = 79.25713442308574 " " absolute error = 1.79340986505849300000000000E-11 " " relative error = 2.262774043135882500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.369999999999793 " " y[1] (closed_form) = 80.0436316995481 " " y[1] (numeric) = 80.04363169956594 " " absolute error = 1.783462266757851500000000000E-11 " " relative error = 2.22811262918736400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.3799999999997965 " " y[1] (closed_form) = 80.83803340506827 " " y[1] (numeric) = 80.83803340508602 " " absolute error = 1.774935753928730300000000000E-11 " " relative error = 2.195669141324568300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.3899999999998 " " y[1] (closed_form) = 81.64041898046086 " " y[1] (numeric) = 81.64041898047853 " " absolute error = 1.76640924109960900000000000E-11 " " relative error = 2.163645487319665300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.399999999999803 " " y[1] (closed_form) = 82.45086866495208 " " y[1] (numeric) = 82.45086866496965 " " absolute error = 1.756461642798967700000000000E-11 " " relative error = 2.130313083706294700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.4099999999998065 " " y[1] (closed_form) = 83.26946350418575 " " y[1] (numeric) = 83.26946350420323 " " absolute error = 1.747935129969846500000000000E-11 " " relative error = 2.099131009631138300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.41999999999981 " " y[1] (closed_form) = 84.09628535832798 " " y[1] (numeric) = 84.09628535834533 " " absolute error = 1.735145360726164700000000000E-11 " " relative error = 2.063284190654605400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.429999999999813 " " y[1] (closed_form) = 84.93141691025315 " " y[1] (numeric) = 84.9314169102704 " " absolute error = 1.725197762425523300000000000E-11 " " relative error = 2.031283387451943700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.4399999999998165 " " y[1] (closed_form) = 85.77494167381245 " " y[1] (numeric) = 85.77494167382959 " " absolute error = 1.713829078653361600000000000E-11 " " relative error = 1.998053330273033300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.44999999999982 " " y[1] (closed_form) = 86.62694400218516 " " y[1] (numeric) = 86.62694400220217 " " absolute error = 1.7010393094096798000000000E-11 " " relative error = 1.963637675325094200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.459999999999823 " " y[1] (closed_form) = 87.4875090963141 " " y[1] (numeric) = 87.48750909633101 " " absolute error = 1.691091711109038400000000000E-11 " " relative error = 1.932952176347063600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.469999999999827 " " y[1] (closed_form) = 88.35672301342585 " " y[1] (numeric) = 88.35672301344263 " " absolute error = 1.678301941865356600000000000E-11 " " relative error = 1.89946150629685280000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.47999999999983 " " y[1] (closed_form) = 89.23467267563647 " " y[1] (numeric) = 89.23467267565314 " " absolute error = 1.66693325809319500000000000E-11 " " relative error = 1.868033140158885400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.489999999999833 " " y[1] (closed_form) = 90.1214458786438 " " y[1] (numeric) = 90.12144587866034 " " absolute error = 1.654143488849513200000000000E-11 " " relative error = 1.83546044198731380000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.499999999999837 " " y[1] (closed_form) = 91.0171313005071 " " y[1] (numeric) = 91.01713130052352 " " absolute error = 1.641353719605831400000000000E-11 " " relative error = 1.80334591538229100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.50999999999984 " " y[1] (closed_form) = 91.921818510515 " " y[1] (numeric) = 91.92181851053127 " " absolute error = 1.627142864890629400000000000E-11 " " relative error = 1.770137809778534200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.519999999999843 " " y[1] (closed_form) = 92.83559797814239 " " y[1] (numeric) = 92.8355979781585 " " absolute error = 1.611510924703907200000000000E-11 " " relative error = 1.735876064570972300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.529999999999847 " " y[1] (closed_form) = 93.75856108209751 " " y[1] (numeric) = 93.75856108211347 " " absolute error = 1.59587898451718500000000000E-11 " " relative error = 1.702115482680872600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.53999999999985 " " y[1] (closed_form) = 94.69080011945991 " " y[1] (numeric) = 94.69080011947571 " " absolute error = 1.580247044330462800000000000E-11 " " relative error = 1.668849605597224600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.549999999999853 " " y[1] (closed_form) = 95.6324083149102 " " y[1] (numeric) = 95.63240831492584 " " absolute error = 1.564615104143740600000000000E-11 " " relative error = 1.636072051005536800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.559999999999857 " " y[1] (closed_form) = 96.58347983005257 " " y[1] (numeric) = 96.58347983006807 " " absolute error = 1.550404249428538600000000000E-11 " " relative error = 1.60524786656746700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.56999999999986 " " y[1] (closed_form) = 97.54410977283113 " " y[1] (numeric) = 97.54410977284648 " " absolute error = 1.534772309241816400000000000E-11 " " relative error = 1.573413620582649600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.579999999999863 " " y[1] (closed_form) = 98.51439420704067 " " y[1] (numeric) = 98.51439420705584 " " absolute error = 1.51771928358357400000000000E-11 " " relative error = 1.540606624849046600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.589999999999867 " " y[1] (closed_form) = 99.4944301619332 " " y[1] (numeric) = 99.49443016194819 " " absolute error = 1.499245172453811400000000000E-11 " " relative error = 1.506863419403176300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.59999999999987 " " y[1] (closed_form) = 100.48431564192087 " " y[1] (numeric) = 100.4843156419357 " " absolute error = 1.48219214679556900000000000E-11 " " relative error = 1.475048257359296600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.609999999999873 " " y[1] (closed_form) = 101.48414963637663 " " y[1] (numeric) = 101.48414963639128 " " absolute error = 1.465139121137326600000000000E-11 " " relative error = 1.443712270721094800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.619999999999877 " " y[1] (closed_form) = 102.4940321295331 " " y[1] (numeric) = 102.49403212954755 " " absolute error = 1.445243924536043800000000000E-11 " " relative error = 1.410076171761423500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.62999999999988 " " y[1] (closed_form) = 103.51406411048117 " " y[1] (numeric) = 103.51406411049541 " " absolute error = 1.423927642463240800000000000E-11 " " relative error = 1.375588577938041700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.639999999999883 " " y[1] (closed_form) = 104.54434758326896 " " y[1] (numeric) = 104.54434758328301 " " absolute error = 1.405453531333478200000000000E-11 " " relative error = 1.34436109060228510000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.649999999999887 " " y[1] (closed_form) = 105.58498557710234 " " y[1] (numeric) = 105.58498557711617 " " absolute error = 1.38271616378915500000000000E-11 " " relative error = 1.309576504870989300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.65999999999989 " " y[1] (closed_form) = 106.63608215664787 " " y[1] (numeric) = 106.63608215666152 " " absolute error = 1.364242052659392400000000000E-11 " " relative error = 1.279343750322079200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.669999999999893 " " y[1] (closed_form) = 107.69774243243945 " " y[1] (numeric) = 107.69774243245287 " " absolute error = 1.341504685115069200000000000E-11 " " relative error = 1.245620061123023900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.679999999999897 " " y[1] (closed_form) = 108.77007257138935 " " y[1] (numeric) = 108.77007257140254 " " absolute error = 1.31876731757074600000000000E-11 " " relative error = 1.212435816575552900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.6899999999999 " " y[1] (closed_form) = 109.8531798074051 " " y[1] (numeric) = 109.85317980741807 " " absolute error = 1.29745103549794300000000000E-11 " " relative error = 1.181077359592719900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.699999999999903 " " y[1] (closed_form) = 110.94717245211288 " " y[1] (numeric) = 110.94717245212561 " " absolute error = 1.273292582482099500000000000E-11 " " relative error = 1.147656631836813400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.709999999999907 " " y[1] (closed_form) = 112.05215990568882 " " y[1] (numeric) = 112.0521599057013 " " absolute error = 1.24771304399473590000000000E-11 " " relative error = 1.113510926558578700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.71999999999991 " " y[1] (closed_form) = 113.16825266779911 " " y[1] (numeric) = 113.16825266781136 " " absolute error = 1.224975676450412700000000000E-11 " " relative error = 1.082437563162064500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.729999999999913 " " y[1] (closed_form) = 114.29556234865005 " " y[1] (numeric) = 114.29556234866205 " " absolute error = 1.199396137963049100000000000E-11 " " relative error = 1.049381194962216600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.739999999999917 " " y[1] (closed_form) = 115.43420168014914 " " y[1] (numeric) = 115.43420168016087 " " absolute error = 1.172395514004165300000000000E-11 " " relative error = 1.015639643138605700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.74999999999992 " " y[1] (closed_form) = 116.58428452717843 " " y[1] (numeric) = 116.58428452718988 " " absolute error = 1.145394890045281500000000000E-11 " " relative error = 9.824607962304422000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.759999999999923 " " y[1] (closed_form) = 117.74592589898097 " " y[1] (numeric) = 117.74592589899216 " " absolute error = 1.118394266086397700000000000E-11 " " relative error = 9.498369115937937000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.769999999999927 " " y[1] (closed_form) = 118.91924196066203 " " y[1] (numeric) = 118.91924196067292 " " absolute error = 1.088551471184473500000000000E-11 " " relative error = 9.153703414495036000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.77999999999993 " " y[1] (closed_form) = 120.10435004480551 " " y[1] (numeric) = 120.10435004481616 " " absolute error = 1.0643930181686301000000000E-11 " " relative error = 8.862235362595552000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.789999999999933 " " y[1] (closed_form) = 121.30136866320746 " " y[1] (numeric) = 121.3013686632178 " " absolute error = 1.034550223266705900000000000E-11 " " relative error = 8.52875968892921900000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.799999999999937 " " y[1] (closed_form) = 122.5104175187272 " " y[1] (numeric) = 122.51041751873726 " " absolute error = 1.006128513836301900000000000E-11 " " relative error = 8.212595583412349000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.80999999999994 " " y[1] (closed_form) = 123.73161751725783 " " y[1] (numeric) = 123.73161751726757 " " absolute error = 9.734435479913373000000000000E-12 " " relative error = 7.867379151133811000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.819999999999943 " " y[1] (closed_form) = 124.9650907798169 " " y[1] (numeric) = 124.96509077982628 " " absolute error = 9.379164112033322000000000000E-12 " " relative error = 7.505427358556482000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.829999999999947 " " y[1] (closed_form) = 126.21096065475854 " " y[1] (numeric) = 126.2109606547676 " " absolute error = 9.066525308298878000000000000E-12 " " relative error = 7.1836275243160050000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.83999999999995 " " y[1] (closed_form) = 127.46935173010847 " " y[1] (numeric) = 127.46935173011724 " " absolute error = 8.768097359279636000000000000E-12 " " relative error = 6.878592571682937000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.8499999999999535 " " y[1] (closed_form) = 128.7403898460229 " " y[1] (numeric) = 128.74038984603135 " " absolute error = 8.44124770082999000000000000E-12 " " relative error = 6.556798306208298000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.859999999999957 " " y[1] (closed_form) = 130.02420210737264 " " y[1] (numeric) = 130.02420210738075 " " absolute error = 8.100187187665142000000000000E-12 " " relative error = 6.229753427731932000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.86999999999996 " " y[1] (closed_form) = 131.32091689645364 " " y[1] (numeric) = 131.32091689646143 " " absolute error = 7.787548383930698000000000000E-12 " " relative error = 5.9301660146579460000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.8799999999999635 " " y[1] (closed_form) = 132.6306638858254 " " y[1] (numeric) = 132.63066388583283 " " absolute error = 7.418066161335446000000000000E-12 " " relative error = 5.5930249792923150000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.889999999999967 " " y[1] (closed_form) = 133.95357405127837 " " y[1] (numeric) = 133.95357405128544 " " absolute error = 7.077005648170598000000000000E-12 " " relative error = 5.283177920629031000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.89999999999997 " " y[1] (closed_form) = 135.2897796849315 " " y[1] (numeric) = 135.28977968493817 " " absolute error = 6.679101716144942000000000000E-12 " " relative error = 4.936885647755147000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.9099999999999735 " " y[1] (closed_form) = 136.63941440846162 " " y[1] (numeric) = 136.63941440846793 " " absolute error = 6.30961949354969000000000000E-12 " " relative error = 4.617715555109227000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.919999999999977 " " y[1] (closed_form) = 138.00261318646582 " " y[1] (numeric) = 138.0026131864717 " " absolute error = 5.8832938520936300000000000000E-12 " " relative error = 4.263175686495344600000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.92999999999998 " " y[1] (closed_form) = 139.3795123399579 " " y[1] (numeric) = 139.37951233996338 " " absolute error = 5.4853899200679730000000000000E-12 " " relative error = 3.935578355797848000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.9399999999999835 " " y[1] (closed_form) = 140.77024956000065 " " y[1] (numeric) = 140.7702495600057 " " absolute error = 5.059064278611913000000000000E-12 " " relative error = 3.5938447892397773000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.949999999999987 " " y[1] (closed_form) = 142.17496392147498 " " y[1] (numeric) = 142.1749639214796 " " absolute error = 4.604316927725449000000000000E-12 " " relative error = 3.238486440037693000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.95999999999999 " " y[1] (closed_form) = 143.5937958969877 " " y[1] (numeric) = 143.59379589699185 " " absolute error = 4.149569576838985000000000000E-12 " " relative error = 2.8897972582435466000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.9699999999999935 " " y[1] (closed_form) = 145.02688737091864 " " y[1] (numeric) = 145.0268873709224 " " absolute error = 3.751665644813329000000000000E-12 " " relative error = 2.5868759323353085000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.979999999999997 " " y[1] (closed_form) = 146.47438165360953 " " y[1] (numeric) = 146.47438165361282 " " absolute error = 3.296918293926865000000000000E-12 " " relative error = 2.250849777760860800000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.99 " " y[1] (closed_form) = 147.9364234956948 " " y[1] (numeric) = 147.93642349569768 " " absolute error = 2.8705926524708050000000000000E-12 " " relative error = 1.9404231795250504000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " "Finished!" "diff ( y , x , 2 ) = diff ( y , x , 1 ) ; " Iterations = 4000 "Total Elapsed Time "= 1 Minutes 22 Seconds "Elapsed Time(since restart) "= 1 Minutes 22 Seconds "Time to Timeout "= 1 Minutes 37 Seconds Percent Done = 100.02500000000009 "%" (%o255) temp/diffeq.diff_B.max