(%i1) batch("temp/diffeq.h2sin.max") read and interpret file: /home/dennis/src/mine/omni/testtar/omnisode0060dir/temp/diffeq.h2sin.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([40],convfloat)),fixnum) (%i24) mode_declare(ats([mmm_ats],fixnum,[arr_a], completearray([40],convfloat),[arr_b], completearray([40],convfloat),[jjj_ats],fixnum), convfloat) (%i25) mode_declare(att([mmm_att],fixnum,[arr_a], completearray([40],convfloat),[arr_b], completearray([40],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,40,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,[40],convfloat) (%i173) completearray(array_norms,[40],convfloat) (%i174) completearray(array_fact_1,[40],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,[40],convfloat) (%i184) completearray(array_x,[40],convfloat) (%i185) completearray(array_tmp0,[40],convfloat) (%i186) completearray(array_tmp1_g,[40],convfloat) (%i187) completearray(array_tmp1,[40],convfloat) (%i188) completearray(array_tmp2,[40],convfloat) (%i189) completearray(array_m1,[40],convfloat) (%i190) completearray(array_y_higher,[3,40],convfloat) (%i191) completearray(array_y_higher_work,[3,40],convfloat) (%i192) completearray(array_y_higher_work2,[3,40],convfloat) (%i193) completearray(array_y_set_initial,[2,40],convfloat) (%i194) completearray(array_given_rad_poles,[2,3],convfloat) (%i195) completearray(array_given_ord_poles,[2,3],convfloat) (%i196) completearray(array_rad_test_poles,[2,4],convfloat) (%i197) completearray(array_ord_test_poles,[2,4],convfloat) (%i198) completearray(array_fact_2,[40,40],convfloat) (%i199) omniout_str(iolevel,str):=if glob_iolevel >= iolevel then printf(true,"~a~%",string(str)) (%i200) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel then printf(true,"~a",string(str)) (%i201) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel then printf(true,"~a = ~a~%",string(label), string(str)) (%i202) 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)) (%i203) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if glob_iolevel >= iolevel then (printf(true,"~a = ~d ~a~%",prelabel,value, postlabel),newline()) (%i204) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen, postlabel):=if glob_iolevel >= iolevel then (sprint(prelabel,"[",elemnt,"]=",value, postlabel),newline()) (%i205) 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) (%i206) 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) (%i207) 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) (%i208) 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) (%i209) 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) (%i210) logditto(file):=(printf(file,""),printf(file,"ditto"), printf(file,""),0) (%i211) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n), printf(file,""),0) (%i212) logitem_str(file,str):=(printf(file,""),printf(file,str), printf(file,""),0) (%i213) logitem_good_digits(file,rel_error):=( block(mode_declare([[good_digits],fixnum]), printf(file,""), printf(file,"~d",glob_min_good_digits), printf(file,"")),0) (%i214) log_revs(file,revs):=printf(file,revs) (%i215) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x), printf(file,""),0) (%i216) 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) (%i217) logstart(file):=(printf(file,""),0) (%i218) logend(file):=(printf(file,"~%"),0) (%i219) 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) (%i220) 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) (%i221) 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) (%i222) 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) (%i223) 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) (%i224) c(in_val):=(ret:in_val,ret) (%i225) 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) (%i226) 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) (%i227) 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) (%i228) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save (%i229) factorial_2(nnn):=block(mode_declare([[ret],convfloat]),ret:nnn!,ret) (%i230) 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) (%i231) factorial_1(in):=block(mode_declare([[ret],convfloat]),ret:in!,ret) (%i232) neg(in):=block(mode_declare([[ret],convfloat]),ret:-in,ret) (%i233) 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) (%i234) log10(x):=log(x)/glob_log_10 (%i235) c(x):=x (%i236) 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 (%i237) 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) (%i238) exact_soln_y(x):=block(c(2.0)-sin(c(x))) (%o238) exact_soln_y(x) := block(c(2.0) - sin(c(x))) (%i239) exact_soln_yp(x):=block(neg(cos(c(x)))) (%o239) exact_soln_yp(x) := block(neg(cos(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(17) *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]:sin(array_x[1]), array_tmp1_g[1]:cos(array_x[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_tmp1_g[1]*array_x[2]/c(1), array_tmp1_g[2]:neg(array_tmp1[1])*array_x[2]/c(1), 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_tmp1_g[2]*array_x[2]/c(2), array_tmp1_g[3]:neg(array_tmp1[2])*array_x[2]/c(2), 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_tmp1_g[3]*array_x[2]/c(3), array_tmp1_g[4]:neg(array_tmp1[3])*array_x[2]/c(3), 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_tmp1_g[4]*array_x[2]/c(4), array_tmp1_g[5]:neg(array_tmp1[4])*array_x[2]/c(4), 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 (array_tmp1[kkk] :array_tmp1_g[kkk-1]*array_x[2]/c(kkk-1), array_tmp1_g[kkk] :neg(array_tmp1[kkk-1])*array_x[2]/c(kkk-1), 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(c(2.0)-sin(c(x))) (%o250) exact_soln_y(x) := block(c(2.0) - sin(c(x))) (%i251) exact_soln_yp(x):=block(neg(cos(c(x)))) (%o251) exact_soln_yp(x) := block(neg(cos(c(x)))) (%i252) 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:40, glob_html_log:true,term:1, while term <= 40 do (array_y_init[term]:c(0.0),term:1+term), term:1, while term <= 40 do (array_norms[term]:c(0.0),term:1+term), term:1, while term <= 40 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 <= 40 do (array_y[term]:c(0.0),term:1+term), term:1, while term <= 40 do (array_x[term]:c(0.0),term:1+term), term:1, while term <= 40 do (array_tmp0[term]:c(0.0),term:1+term), term:1, while term <= 40 do (array_tmp1_g[term]:c(0.0),term:1+term), term:1, while term <= 40 do (array_tmp1[term]:c(0.0),term:1+term), term:1, while term <= 40 do (array_tmp2[term]:c(0.0),term:1+term), term:1, while term <= 40 do (array_m1[term]:c(0.0),term:1+term), ord:1, while ord <= 3 do (term:1, while term <= 40 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 <= 40 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 <= 40 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 <= 40 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 <= 40 do (term:1, while term <= 40 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_g), 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_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, array_y_set_initial[1,31]:false, array_y_set_initial[1,32]:false, array_y_set_initial[1,33]:false, array_y_set_initial[1,34]:false, array_y_set_initial[1,35]:false, array_y_set_initial[1,36]:false, array_y_set_initial[1,37]:false, array_y_set_initial[1,38]:false, array_y_set_initial[1,39]:false, array_y_set_initial[1,40]: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/h2sinpostode.ode#################"), omniout_str(always, "diff ( y , x , 2 ) = sin ( x ) ; "), omniout_str(always,"!"), omniout_str(always,"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(always,"Digits:32,"), omniout_str(always,"max_terms:40,"),omniout_str(always,"!"), omniout_str(always,"/* END FIRST INPUT BLOCK */"), omniout_str(always,"/* BEGIN SECOND INPUT BLOCK */"), omniout_str(always,"x_start:c(0.1),"), 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(2.0) - sin(c(x))) "), omniout_str(always,"));"), omniout_str(always,"exact_soln_yp (x) := (block("), omniout_str(always," (neg( cos(c(x)))) "), omniout_str(always,"));"), omniout_str(always,"/* END USER DEF BLOCK */"), omniout_str(always, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt:0,glob_warned:false,glob_warned2:false, glob_small_float: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(0.1),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 ) = sin ( x ) ; "), omniout_int(info, "Iterations ",32, glob_iter,4," "), prog_report(x_start,x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2015-04-24T21:18:47-05:00"), logitem_str(html_log_file,"Maxima"), logitem_str(html_log_file, "h2sin"), logitem_str(html_log_file, "diff ( y , x , 2 ) = sin ( x ) ; "), logitem_float(html_log_file,x_start), logitem_float(html_log_file,x_end), logitem_float(html_log_file,array_x[1]), logitem_float(html_log_file,glob_h), logitem_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, "h2sin diffeq.max"), logitem_str(html_log_file, "h2sin maxima results"), logitem_str(html_log_file,"OK"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%i253) main():=(glob_iolevel:2,compile(all),main_prog()) (%i254) 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_tmp1_g 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 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/h2sinpostode.ode#################" "diff ( y , x , 2 ) = sin ( x ) ; " "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:40," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:c(0.1)," "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(2.0) - sin(c(x))) " "));" "exact_soln_yp (x) := (block(" " (neg( cos(c(x)))) " "));" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Soultion" " " "TOP MAIN SOLVE Loop" x[1] = 0.1 " " y[1] (closed_form) = 1.9001665833531718 " " y[1] (numeric) = 1.9001665833531718 " " 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] = 0.11000000000000001 " " y[1] (closed_form) = 1.8902216991628251 " " y[1] (numeric) = 1.8902216991628251 " " absolute error = 0.0 " " relative error = 0.0 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.12000000000000002 " " y[1] (closed_form) = 1.8802877927110806 " " y[1] (numeric) = 1.8802877927110808 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.180907549289982600000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.13000000000000003 " " y[1] (closed_form) = 1.870365857380305 " " y[1] (numeric) = 1.8703658573803057 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.561516118071693700000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.14000000000000004 " " y[1] (closed_form) = 1.8604568853557635 " " y[1] (numeric) = 1.8604568853557641 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.580485094916421000000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.15000000000000005 " " y[1] (closed_form) = 1.8505618675264008 " " y[1] (numeric) = 1.8505618675264015 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.5996300716252100000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.16000000000000006 " " y[1] (closed_form) = 1.840681793385754 " " y[1] (numeric) = 1.8406817933857549 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.82526867431229300000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.17000000000000007 " " y[1] (closed_form) = 1.8308176509330039 " " y[1] (numeric) = 1.830817650933005 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 6.06408302901916700000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.18000000000000008 " " y[1] (closed_form) = 1.8209704265741757 " " y[1] (numeric) = 1.8209704265741766 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.87750051696924650000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.19000000000000009 " " y[1] (closed_form) = 1.8111411050234993 " " y[1] (numeric) = 1.8111411050235005 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 6.1299642614579800000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2000000000000001 " " y[1] (closed_form) = 1.8013306692049387 " " y[1] (numeric) = 1.8013306692049396 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.930679496464381000000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2100000000000001 " " y[1] (closed_form) = 1.7915401001539004 " " y[1] (numeric) = 1.7915401001539013 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.95762511608770100000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2200000000000001 " " y[1] (closed_form) = 1.7817703769191306 " " y[1] (numeric) = 1.7817703769191315 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.984808543264029300000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.23000000000000012 " " y[1] (closed_form) = 1.7720224764648114 " " y[1] (numeric) = 1.7720224764648125 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 6.26528748574371200000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.24000000000000013 " " y[1] (closed_form) = 1.7622973735728653 " " y[1] (numeric) = 1.762297373572866 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.77991719652047300000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2500000000000001 " " y[1] (closed_form) = 1.752596040745477 " " y[1] (numeric) = 1.7525960407454777 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.80084057756829130000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2600000000000001 " " y[1] (closed_form) = 1.7429194481078447 " " y[1] (numeric) = 1.7429194481078454 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.82194263480314500000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.27000000000000013 " " y[1] (closed_form) = 1.7332685633111686 " " y[1] (numeric) = 1.7332685633111695 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 5.12429774877693400000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.28000000000000014 " " y[1] (closed_form) = 1.7236443514358861 " " y[1] (numeric) = 1.723644351435887 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 5.15290998958239900000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.29000000000000015 " " y[1] (closed_form) = 1.7140477748951644 " " y[1] (numeric) = 1.714047774895165 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.886319999545149000000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.30000000000000016 " " y[1] (closed_form) = 1.7044797933386602 " " y[1] (numeric) = 1.704479793338661 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 5.21084745721977900000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.31000000000000016 " " y[1] (closed_form) = 1.6949413635565564 " " y[1] (numeric) = 1.6949413635565571 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.93012896550781800000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3200000000000002 " " y[1] (closed_form) = 1.6854334393838821 " " y[1] (numeric) = 1.6854334393838826 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.634866494712490600000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3300000000000002 " " y[1] (closed_form) = 1.6759569716051315 " " y[1] (numeric) = 1.675956971605132 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.649764984268901400000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3400000000000002 " " y[1] (closed_form) = 1.6665129078591854 " " y[1] (numeric) = 1.666512907859186 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.99717164885817900000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3500000000000002 " " y[1] (closed_form) = 1.6571021925445484 " " y[1] (numeric) = 1.657102192544549 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.019871663751878300000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3600000000000002 " " y[1] (closed_form) = 1.64772576672491 " " y[1] (numeric) = 1.6477257667249103 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.695164564506103000000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3700000000000002 " " y[1] (closed_form) = 1.6383845680350377 " " y[1] (numeric) = 1.6383845680350384 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.065796442248034700000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3800000000000002 " " y[1] (closed_form) = 1.6290795305870172 " " y[1] (numeric) = 1.6290795305870176 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.726013073714338400000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.39000000000000024 " " y[1] (closed_form) = 1.6198115848768384 " " y[1] (numeric) = 1.6198115848768389 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.741610283543124400000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.40000000000000024 " " y[1] (closed_form) = 1.6105816576913492 " " y[1] (numeric) = 1.61058165769135 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 5.51464382733169800000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.41000000000000025 " " y[1] (closed_form) = 1.6013906720155768 " " y[1] (numeric) = 1.6013906720155775 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.159720837743298700000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.42000000000000026 " " y[1] (closed_form) = 1.5922395469404296 " " y[1] (numeric) = 1.59223954694043 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.789085415592163500000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.43000000000000027 " " y[1] (closed_form) = 1.583129197570789 " " y[1] (numeric) = 1.5831291975707895 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.805135617051907600000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4400000000000003 " " y[1] (closed_form) = 1.5740605349340002 " " y[1] (numeric) = 1.5740605349340007 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.82129689420542600000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4500000000000003 " " y[1] (closed_form) = 1.5650344658887696 " " y[1] (numeric) = 1.56503446588877 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.83756824229342560000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4600000000000003 " " y[1] (closed_form) = 1.55605189303448 " " y[1] (numeric) = 1.5560518930344802 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.42697429256050580000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4700000000000003 " " y[1] (closed_form) = 1.5471137146209315 " " y[1] (numeric) = 1.5471137146209317 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.435218386512952200000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4800000000000003 " " y[1] (closed_form) = 1.538220824458517 " " y[1] (numeric) = 1.5382208244585167 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.443515790414521500000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4900000000000003 " " y[1] (closed_form) = 1.5293741118288418 " " y[1] (numeric) = 1.5293741118288415 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.45186585288479890000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5000000000000003 " " y[1] (closed_form) = 1.5205744613957968 " " y[1] (numeric) = 1.5205744613957968 " " absolute error = 0.0 " " relative error = 0.0 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5100000000000003 " " y[1] (closed_form) = 1.5118227531170922 " " y[1] (numeric) = 1.5118227531170922 " " absolute error = 0.0 " " relative error = 0.0 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5200000000000004 " " y[1] (closed_form) = 1.503119862156263 " " y[1] (numeric) = 1.503119862156263 " " absolute error = 0.0 " " relative error = 0.0 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5300000000000004 " " y[1] (closed_form) = 1.4944666587951527 " " y[1] (numeric) = 1.4944666587951527 " " absolute error = 0.0 " " relative error = 0.0 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5400000000000004 " " y[1] (closed_form) = 1.4858640083468866 " " y[1] (numeric) = 1.4858640083468866 " " absolute error = 0.0 " " relative error = 0.0 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5500000000000004 " " y[1] (closed_form) = 1.4773127710693406 " " y[1] (numeric) = 1.4773127710693403 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.503030429800631700000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5600000000000004 " " y[1] (closed_form) = 1.4688138020791164 " " y[1] (numeric) = 1.468813802079116 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.02345477160856700000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5700000000000004 " " y[1] (closed_form) = 1.4603679512660306 " " y[1] (numeric) = 1.4603679512660301 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.040940534644507000000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5800000000000004 " " y[1] (closed_form) = 1.451976063208126 " " y[1] (numeric) = 1.4519760632081258 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.52925802670896700000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5900000000000004 " " y[1] (closed_form) = 1.443638977087216 " " y[1] (numeric) = 1.4436389770872153 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.61426870116191200000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6000000000000004 " " y[1] (closed_form) = 1.4353575266049643 " " y[1] (numeric) = 1.4353575266049636 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.64089122346188600000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6100000000000004 " " y[1] (closed_form) = 1.4271325398995183 " " y[1] (numeric) = 1.4271325398995176 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.66763805148746100000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6200000000000004 " " y[1] (closed_form) = 1.4189648394626946 " " y[1] (numeric) = 1.4189648394626937 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.25934057701135900000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6300000000000004 " " y[1] (closed_form) = 1.41085524205773 " " y[1] (numeric) = 1.410855242057729 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 7.86914909148225600000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6400000000000005 " " y[1] (closed_form) = 1.4028045586376074 " " y[1] (numeric) = 1.402804558637606 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.10800340995808770000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6500000000000005 " " y[1] (closed_form) = 1.3948135942639601 " " y[1] (numeric) = 1.3948135942639581 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 1.43273728657615620000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6600000000000005 " " y[1] (closed_form) = 1.3868831480265658 " " y[1] (numeric) = 1.3868831480265638 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 1.44092993499045860000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6700000000000005 " " y[1] (closed_form) = 1.3790140129634398 " " y[1] (numeric) = 1.3790140129634376 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 1.6101693154507352000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6800000000000005 " " y[1] (closed_form) = 1.371206975981531 " " y[1] (numeric) = 1.3712069759815284 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 1.943204276067120000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6900000000000005 " " y[1] (closed_form) = 1.3634628177780317 " " y[1] (numeric) = 1.3634628177780286 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.27994810596772350000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7000000000000005 " " y[1] (closed_form) = 1.3557823127623085 " " y[1] (numeric) = 1.3557823127623054 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.2928640089844812000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7100000000000005 " " y[1] (closed_form) = 1.3481662289784628 " " y[1] (numeric) = 1.3481662289784597 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.305816895670140300000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7200000000000005 " " y[1] (closed_form) = 1.3406153280285265 " " y[1] (numeric) = 1.3406153280285231 " " absolute error = 3.3306690738754696000000000000000E-15 " " relative error = 2.48443308400289860000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7300000000000005 " " y[1] (closed_form) = 1.3331303649963018 " " y[1] (numeric) = 1.3331303649962982 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.66494093307248050000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7400000000000005 " " y[1] (closed_form) = 1.3257120883718545 " " y[1] (numeric) = 1.3257120883718507 " " absolute error = 3.774758283725532000000000000000E-15 " " relative error = 2.84734394204809700000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7500000000000006 " " y[1] (closed_form) = 1.3183612399766655 " " y[1] (numeric) = 1.3183612399766613 " " absolute error = 4.218847493575595000000000000000E-15 " " relative error = 3.20006942380243740000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7600000000000006 " " y[1] (closed_form) = 1.3110785548894484 " " y[1] (numeric) = 1.3110785548894441 " " absolute error = 4.218847493575595000000000000000E-15 " " relative error = 3.21784493983377900000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7700000000000006 " " y[1] (closed_form) = 1.3038647613726428 " " y[1] (numeric) = 1.3038647613726386 " " absolute error = 4.218847493575595000000000000000E-15 " " relative error = 3.2356480660879320000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7800000000000006 " " y[1] (closed_form) = 1.2967205807995894 " " y[1] (numeric) = 1.2967205807995852 " " absolute error = 4.218847493575595000000000000000E-15 " " relative error = 3.2534746159223843000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7900000000000006 " " y[1] (closed_form) = 1.2896467275823917 " " y[1] (numeric) = 1.2896467275823873 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 3.44349503125220060000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8000000000000006 " " y[1] (closed_form) = 1.2826439091004769 " " y[1] (numeric) = 1.282643909100472 " " absolute error = 4.884981308350689000000000000000E-15 " " relative error = 3.8085249332969934000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8100000000000006 " " y[1] (closed_form) = 1.275712825629857 " " y[1] (numeric) = 1.275712825629852 " " absolute error = 5.10702591327572000000000000000E-15 " " relative error = 4.00327237499884100000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8200000000000006 " " y[1] (closed_form) = 1.2688541702731038 " " y[1] (numeric) = 1.2688541702730987 " " absolute error = 5.10702591327572000000000000000E-15 " " relative error = 4.02491163517750940000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8300000000000006 " " y[1] (closed_form) = 1.262068628890037 " " y[1] (numeric) = 1.2620686288900316 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 4.22248869531568870000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8400000000000006 " " y[1] (closed_form) = 1.2553568800291401 " " y[1] (numeric) = 1.255356880029135 " " absolute error = 5.10702591327572000000000000000E-15 " " relative error = 4.0681865010029440000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8500000000000006 " " y[1] (closed_form) = 1.2487195948597067 " " y[1] (numeric) = 1.2487195948597014 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 4.2676278486680360000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8600000000000007 " " y[1] (closed_form) = 1.2421574371047226 " " y[1] (numeric) = 1.2421574371047168 " " absolute error = 5.773159728050814000000000000000E-15 " " relative error = 4.6476876083495170000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8700000000000007 " " y[1] (closed_form) = 1.2356710629744945 " " y[1] (numeric) = 1.2356710629744883 " " absolute error = 6.217248937900877000000000000000E-15 " " relative error = 5.0314757091865370000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8800000000000007 " " y[1] (closed_form) = 1.2292611211010303 " " y[1] (numeric) = 1.2292611211010238 " " absolute error = 6.439293542825908000000000000000E-15 " " relative error = 5.2383447522185780000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8900000000000007 " " y[1] (closed_form) = 1.2229282524731757 " " y[1] (numeric) = 1.222928252473169 " " absolute error = 6.661338147750939000000000000000E-15 " " relative error = 5.4470392145078450000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9000000000000007 " " y[1] (closed_form) = 1.2166730903725163 " " y[1] (numeric) = 1.2166730903725091 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 5.8400464461866990000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9100000000000007 " " y[1] (closed_form) = 1.210496260310049 " " y[1] (numeric) = 1.210496260310042 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 5.8698465997582360000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9200000000000007 " " y[1] (closed_form) = 1.2043983799636335 " " y[1] (numeric) = 1.2043983799636258 " " absolute error = 7.771561172376096000000000000000E-15 " " relative error = 6.4526499716902270000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9300000000000007 " " y[1] (closed_form) = 1.1983800591162224 " " y[1] (numeric) = 1.1983800591162144 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 6.6703427819019510000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9400000000000007 " " y[1] (closed_form) = 1.1924418995948853 " " y[1] (numeric) = 1.1924418995948776 " " absolute error = 7.771561172376096000000000000000E-15 " " relative error = 6.5173499648212370000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9500000000000007 " " y[1] (closed_form) = 1.1865844952106257 " " y[1] (numeric) = 1.186584495210618 " " absolute error = 7.771561172376096000000000000000E-15 " " relative error = 6.5495219293225280000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9600000000000007 " " y[1] (closed_form) = 1.1808084316990013 " " y[1] (numeric) = 1.1808084316989933 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 6.7696042496915110000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9700000000000008 " " y[1] (closed_form) = 1.1751142866615494 " " y[1] (numeric) = 1.1751142866615412 " " absolute error = 8.215650382226158000000000000000E-15 " " relative error = 6.991362861876590000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9800000000000008 " " y[1] (closed_form) = 1.169502629508029 " " y[1] (numeric) = 1.1695026295080204 " " absolute error = 8.659739592076221000000000000000E-15 " " relative error = 7.4046345630869470000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9900000000000008 " " y[1] (closed_form) = 1.1639740213994791 " " y[1] (numeric) = 1.16397402139947 " " absolute error = 9.103828801926284000000000000000E-15 " " relative error = 7.8213333240723790000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0000000000000007 " " y[1] (closed_form) = 1.1585290151921033 " " y[1] (numeric) = 1.1585290151920937 " " absolute error = 9.547918011776346000000000000000E-15 " " relative error = 8.2414146616717610000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0099999999999996 " " y[1] (closed_form) = 1.153168155381985 " " y[1] (numeric) = 1.1531681553819748 " " absolute error = 1.02140518265514400000000000000E-14 " " relative error = 8.8573828360427210000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0199999999999985 " " y[1] (closed_form) = 1.1478919780506378 " " y[1] (numeric) = 1.1478919780506271 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 9.28496865576260000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0299999999999974 " " y[1] (closed_form) = 1.142701010811398 " " y[1] (numeric) = 1.1427010108113866 " " absolute error = 1.132427485117659700000000000000E-14 " " relative error = 9.9100943676732770000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0399999999999963 " " y[1] (closed_form) = 1.1375957727566635 " " y[1] (numeric) = 1.1375957727566515 " " absolute error = 1.19904086659516900000000000000E-14 " " relative error = 1.0540131172337337000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0499999999999952 " " y[1] (closed_form) = 1.1325767744059854 " " y[1] (numeric) = 1.132576774405973 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 1.097894478926023000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.059999999999994 " " y[1] (closed_form) = 1.1276445176550167 " " y[1] (numeric) = 1.1276445176550034 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 1.1814606542145864000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.069999999999993 " " y[1] (closed_form) = 1.1227994957253218 " " y[1] (numeric) = 1.1227994957253078 " " absolute error = 1.398881011027697200000000000000E-14 " " relative error = 1.2458867467909115000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0799999999999919 " " y[1] (closed_form) = 1.1180421931150564 " " y[1] (numeric) = 1.1180421931150415 " " absolute error = 1.487698852997709800000000000000E-14 " " relative error = 1.3306285417124794000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0899999999999908 " " y[1] (closed_form) = 1.113373085550517 " " y[1] (numeric) = 1.1133730855505017 " " absolute error = 1.53210777398271600000000000000E-14 " " relative error = 1.3760955728736265000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0999999999999897 " " y[1] (closed_form) = 1.1087926399385695 " " y[1] (numeric) = 1.1087926399385537 " " absolute error = 1.576516694967722300000000000000E-14 " " relative error = 1.4218318540201225000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1099999999999886 " " y[1] (closed_form) = 1.1043013143199576 " " y[1] (numeric) = 1.1043013143199407 " " absolute error = 1.68753899743023800000000000000E-14 " " relative error = 1.5281508547958628000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1199999999999875 " " y[1] (closed_form) = 1.0998995578235005 " " y[1] (numeric) = 1.0998995578234831 " " absolute error = 1.731947918415244200000000000000E-14 " " relative error = 1.5746418898853380000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1299999999999863 " " y[1] (closed_form) = 1.09558781062118 " " y[1] (numeric) = 1.0955878106211625 " " absolute error = 1.754152378907747300000000000000E-14 " " relative error = 1.6011061476789998000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1399999999999852 " " y[1] (closed_form) = 1.091366503884123 " " y[1] (numeric) = 1.091366503884105 " " absolute error = 1.798561299892753600000000000000E-14 " " relative error = 1.6479901971443664000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1499999999999841 " " y[1] (closed_form) = 1.0872360597394854 " " y[1] (numeric) = 1.087236059739467 " " absolute error = 1.8429702208777599000000000000E-14 " " relative error = 1.6950966667895080000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.159999999999983 " " y[1] (closed_form) = 1.0831968912282397 " " y[1] (numeric) = 1.0831968912282208 " " absolute error = 1.88737914186276600000000000000E-14 " " relative error = 1.7424155821963835000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.169999999999982 " " y[1] (closed_form) = 1.0792494022638714 " " y[1] (numeric) = 1.0792494022638521 " " absolute error = 1.931788062847772400000000000000E-14 " " relative error = 1.7899366530067898000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1799999999999808 " " y[1] (closed_form) = 1.075393987591987 " " y[1] (numeric) = 1.0753939875919671 " " absolute error = 1.976196983832778600000000000000E-14 " " relative error = 1.837649277041117000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1899999999999797 " " y[1] (closed_form) = 1.0716310327508407 " " y[1] (numeric) = 1.0716310327508205 " " absolute error = 2.02060590481778500000000000000E-14 " " relative error = 1.8855425450221966000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1999999999999786 " " y[1] (closed_form) = 1.0679609140327813 " " y[1] (numeric) = 1.0679609140327606 " " absolute error = 2.065014825802791200000000000000E-14 " " relative error = 1.933605245912029000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2099999999999775 " " y[1] (closed_form) = 1.0643839984466221 " " y[1] (numeric) = 1.064383998446601 " " absolute error = 2.109423746787797400000000000000E-14 " " relative error = 1.9818258728676136000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2199999999999764 " " y[1] (closed_form) = 1.0609006436809405 " " y[1] (numeric) = 1.0609006436809194 " " absolute error = 2.109423746787797400000000000000E-14 " " relative error = 1.9883329879684697000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2299999999999753 " " y[1] (closed_form) = 1.0575111980683107 " " y[1] (numeric) = 1.0575111980682892 " " absolute error = 2.153832667772803700000000000000E-14 " " relative error = 2.0366996318403763000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2399999999999742 " " y[1] (closed_form) = 1.0542160005504693 " " y[1] (numeric) = 1.0542160005504473 " " absolute error = 2.1982415887578100000000000000E-14 " " relative error = 2.0851908789185294000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2499999999999731 " " y[1] (closed_form) = 1.0510153806444222 " " y[1] (numeric) = 1.0510153806443998 " " absolute error = 2.242650509742816200000000000000E-14 " " relative error = 2.133794187072459200000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.259999999999972 " " y[1] (closed_form) = 1.047909658409493 " " y[1] (numeric) = 1.04790965840947 " " absolute error = 2.287059430727822500000000000000E-14 " " relative error = 2.1824967566374937000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.269999999999971 " " y[1] (closed_form) = 1.0448991444153164 " " y[1] (numeric) = 1.044899144415293 " " absolute error = 2.331468351712828700000000000000E-14 " " relative error = 2.231285540019678000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2799999999999698 " " y[1] (closed_form) = 1.0419841397107836 " " y[1] (numeric) = 1.0419841397107599 " " absolute error = 2.37587727269783500000000000000E-14 " " relative error = 2.280147251912386000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2899999999999687 " " y[1] (closed_form) = 1.039164935793936 " " y[1] (numeric) = 1.0391649357939117 " " absolute error = 2.442490654175344400000000000000E-14 " " relative error = 2.3504359799334917000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2999999999999676 " " y[1] (closed_form) = 1.0364418145828158 " " y[1] (numeric) = 1.0364418145827914 " " absolute error = 2.442490654175344400000000000000E-14 " " relative error = 2.3566114564361587000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3099999999999665 " " y[1] (closed_form) = 1.0338150483872746 " " y[1] (numeric) = 1.03381504838725 " " absolute error = 2.464695114667847500000000000000E-14 " " relative error = 2.3840774213073315000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3199999999999654 " " y[1] (closed_form) = 1.0312848998817432 " " y[1] (numeric) = 1.0312848998817186 " " absolute error = 2.464695114667847500000000000000E-14 " " relative error = 2.389926503287765000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3299999999999643 " " y[1] (closed_form) = 1.0288516220789639 " " y[1] (numeric) = 1.0288516220789392 " " absolute error = 2.464695114667847500000000000000E-14 " " relative error = 2.395578781017544000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3399999999999632 " " y[1] (closed_form) = 1.0265154583046892 " " y[1] (numeric) = 1.026515458304664 " " absolute error = 2.509104035652854000000000000000E-14 " " relative error = 2.4442924997902024000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3499999999999621 " " y[1] (closed_form) = 1.0242766421733491 " " y[1] (numeric) = 1.0242766421733243 " " absolute error = 2.486899575160350700000000000000E-14 " " relative error = 2.4279569334740977000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.359999999999961 " " y[1] (closed_form) = 1.0221353975646918 " " y[1] (numeric) = 1.0221353975646672 " " absolute error = 2.464695114667847500000000000000E-14 " " relative error = 2.411319596738508200000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.36999999999996 " " y[1] (closed_form) = 1.0200919386013938 " " y[1] (numeric) = 1.020091938601369 " " absolute error = 2.486899575160350700000000000000E-14 " " relative error = 2.437917094580746000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3799999999999588 " " y[1] (closed_form) = 1.018146469627648 " " y[1] (numeric) = 1.0181464696276232 " " absolute error = 2.486899575160350700000000000000E-14 " " relative error = 2.442575453873398200000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3899999999999577 " " y[1] (closed_form) = 1.016299185188731 " " y[1] (numeric) = 1.0162991851887064 " " absolute error = 2.464695114667847500000000000000E-14 " " relative error = 2.4251668707282717000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3999999999999566 " " y[1] (closed_form) = 1.0145502700115472 " " y[1] (numeric) = 1.0145502700115225 " " absolute error = 2.464695114667847500000000000000E-14 " " relative error = 2.4293474532708914000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4099999999999555 " " y[1] (closed_form) = 1.0128998989861566 " " y[1] (numeric) = 1.0128998989861322 " " absolute error = 2.442490654175344400000000000000E-14 " " relative error = 2.4113840435961245000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4199999999999544 " " y[1] (closed_form) = 1.0113482371482871 " " y[1] (numeric) = 1.0113482371482623 " " absolute error = 2.486899575160350700000000000000E-14 " " relative error = 2.4589943244205345000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4299999999999533 " " y[1] (closed_form) = 1.0098954396628288 " " y[1] (numeric) = 1.0098954396628042 " " absolute error = 2.464695114667847500000000000000E-14 " " relative error = 2.440544850356715000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4399999999999522 " " y[1] (closed_form) = 1.00854165180832 " " y[1] (numeric) = 1.0085416518082955 " " absolute error = 2.442490654175344400000000000000E-14 " " relative error = 2.4218044438679823000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.449999999999951 " " y[1] (closed_form) = 1.0072870089624173 " " y[1] (numeric) = 1.0072870089623933 " " absolute error = 2.39808173319033800000000000000E-14 " " relative error = 2.3807333082360962000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.45999999999995 " " y[1] (closed_form) = 1.0061316365883606 " " y[1] (numeric) = 1.0061316365883366 " " absolute error = 2.39808173319033800000000000000E-14 " " relative error = 2.3834671786306896000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.469999999999949 " " y[1] (closed_form) = 1.0050756502224243 " " y[1] (numeric) = 1.0050756502224008 " " absolute error = 2.35367281220533200000000000000E-14 " " relative error = 2.341786721909402000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4799999999999478 " " y[1] (closed_form) = 1.0041191554623645 " " y[1] (numeric) = 1.0041191554623414 " " absolute error = 2.309263891220325600000000000000E-14 " " relative error = 2.299790695813371000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4899999999999467 " " y[1] (closed_form) = 1.003262247956861 " " y[1] (numeric) = 1.003262247956838 " " absolute error = 2.287059430727822500000000000000E-14 " " relative error = 2.2796227361145190000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4999999999999456 " " y[1] (closed_form) = 1.0025050133959494 " " y[1] (numeric) = 1.002505013395927 " " absolute error = 2.242650509742816200000000000000E-14 " " relative error = 2.237046677847444300000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5099999999999445 " " y[1] (closed_form) = 1.0018475275024552 " " y[1] (numeric) = 1.0018475275024334 " " absolute error = 2.176037128265306800000000000000E-14 " " relative error = 2.1720242537205586000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5199999999999434 " " y[1] (closed_form) = 1.0012898560244199 " " y[1] (numeric) = 1.0012898560243984 " " absolute error = 2.153832667772803700000000000000E-14 " " relative error = 2.1510581125075084000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5299999999999423 " " y[1] (closed_form) = 1.0008320547285263 " " y[1] (numeric) = 1.0008320547285054 " " absolute error = 2.087219286295294300000000000000E-14 " " relative error = 2.085484049430699000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5399999999999412 " " y[1] (closed_form) = 1.0004741693945227 " " y[1] (numeric) = 1.000474169394502 " " absolute error = 2.065014825802791200000000000000E-14 " " relative error = 2.0640361230440543000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.54999999999994 " " y[1] (closed_form) = 1.0002162358106443 " " y[1] (numeric) = 1.000216235810624 " " absolute error = 2.04281036531028800000000000000E-14 " " relative error = 2.0423687320518782000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.559999999999939 " " y[1] (closed_form) = 1.0000582797700344 " " y[1] (numeric) = 1.0000582797700144 " " absolute error = 1.998401444325281800000000000000E-14 " " relative error = 1.9982849847359085000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.569999999999938 " " y[1] (closed_form) = 1.0000003170681655 " " y[1] (numeric) = 1.0000003170681462 " " absolute error = 1.931788062847772400000000000000E-14 " " relative error = 1.9317874503394694000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5799999999999368 " " y[1] (closed_form) = 1.0000423535012595 " " y[1] (numeric) = 1.0000423535012406 " " absolute error = 1.88737914186276600000000000000E-14 " " relative error = 1.887299208133377300000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5899999999999357 " " y[1] (closed_form) = 1.000184384865708 " " y[1] (numeric) = 1.0001843848656893 " " absolute error = 1.86517468137026300000000000000E-14 " " relative error = 1.8648308347872228000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5999999999999346 " " y[1] (closed_form) = 1.0004263969584928 " " y[1] (numeric) = 1.0004263969584746 " " absolute error = 1.820765760385256700000000000000E-14 " " relative error = 1.819989722303178800000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6099999999999335 " " y[1] (closed_form) = 1.0007683655786068 " " y[1] (numeric) = 1.0007683655785893 " " absolute error = 1.754152378907747300000000000000E-14 " " relative error = 1.7528055834314488000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6199999999999324 " " y[1] (closed_form) = 1.0012102565294727 " " y[1] (numeric) = 1.0012102565294558 " " absolute error = 1.68753899743023800000000000000E-14 " " relative error = 1.6854991111255777000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6299999999999313 " " y[1] (closed_form) = 1.0017520256223635 " " y[1] (numeric) = 1.0017520256223473 " " absolute error = 1.620925615952728500000000000000E-14 " " relative error = 1.6180906796227218000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6399999999999302 " " y[1] (closed_form) = 1.0023936186808216 " " y[1] (numeric) = 1.002393618680806 " " absolute error = 1.55431223447521920000000000000E-14 " " relative error = 1.5506006877026393000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.649999999999929 " " y[1] (closed_form) = 1.0031349715460756 " " y[1] (numeric) = 1.0031349715460605 " " absolute error = 1.50990331349021300000000000000E-14 " " relative error = 1.5051846025895038000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.659999999999928 " " y[1] (closed_form) = 1.003976010083457 " " y[1] (numeric) = 1.0039760100834423 " " absolute error = 1.465494392505206600000000000000E-14 " " relative error = 1.4596906477709415000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6699999999999269 " " y[1] (closed_form) = 1.0049166501898126 " " y[1] (numeric) = 1.0049166501897986 " " absolute error = 1.398881011027697200000000000000E-14 " " relative error = 1.3920368527712930000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6799999999999258 " " y[1] (closed_form) = 1.005956797801916 " " y[1] (numeric) = 1.0059567978019026 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 1.3243785741706635000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6899999999999247 " " y[1] (closed_form) = 1.0070963489058724 " " y[1] (numeric) = 1.0070963489058595 " " absolute error = 1.287858708565181600000000000000E-14 " " relative error = 1.2787840110475374000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6999999999999236 " " y[1] (closed_form) = 1.0083351895475214 " " y[1] (numeric) = 1.008335189547509 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 1.2331710729426777000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7099999999999225 " " y[1] (closed_form) = 1.0096731958438312 " " y[1] (numeric) = 1.0096731958438196 " " absolute error = 1.154631945610162800000000000000E-14 " " relative error = 1.143569969335654900000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7199999999999214 " " y[1] (closed_form) = 1.0111102339952869 " " y[1] (numeric) = 1.011110233995276 " " absolute error = 1.088018564132653400000000000000E-14 " " relative error = 1.0760632496354745000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7299999999999203 " " y[1] (closed_form) = 1.012646160299271 " " y[1] (numeric) = 1.0126461602992605 " " absolute error = 1.043609643147647100000000000000E-14 " " relative error = 1.0305768036875047000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7399999999999192 " " y[1] (closed_form) = 1.0142808211644327 " " y[1] (numeric) = 1.0142808211644234 " " absolute error = 9.325873406851315000000000000000E-15 " " relative error = 9.1945674336470850000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.749999999999918 " " y[1] (closed_form) = 1.0160140531260486 " " y[1] (numeric) = 1.0160140531260398 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 8.7417926648494510000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.759999999999917 " " y[1] (closed_form) = 1.0178456828623659 " " y[1] (numeric) = 1.0178456828623579 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 7.8534555010555850000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7699999999999159 " " y[1] (closed_form) = 1.0197755272119378 " " y[1] (numeric) = 1.0197755272119307 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 6.9676386302652430000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7799999999999148 " " y[1] (closed_form) = 1.0218033931919375 " " y[1] (numeric) = 1.021803393191931 " " absolute error = 6.439293542825908000000000000000E-15 " " relative error = 6.3018909368764830000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7899999999999137 " " y[1] (closed_form) = 1.023929078017457 " " y[1] (numeric) = 1.023929078017451 " " absolute error = 5.995204332975845000000000000000E-15 " " relative error = 5.855097253985430000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7999999999999126 " " y[1] (closed_form) = 1.0261523691217849 " " y[1] (numeric) = 1.02615236912178 " " absolute error = 4.884981308350689000000000000000E-15 " " relative error = 4.7604833895490750000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8099999999999115 " " y[1] (closed_form) = 1.0284730441776637 " " y[1] (numeric) = 1.0284730441776597 " " absolute error = 3.9968028886505635000000000000000E-15 " " relative error = 3.8861523024614486000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8199999999999104 " " y[1] (closed_form) = 1.0308908711195215 " " y[1] (numeric) = 1.0308908711195182 " " absolute error = 3.3306690738754696000000000000000E-15 " " relative error = 3.23086484436363950000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8299999999999093 " " y[1] (closed_form) = 1.0334056081666791 " " y[1] (numeric) = 1.0334056081666765 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 2.57840216662595270000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8399999999999082 " " y[1] (closed_form) = 1.0360170038475274 " " y[1] (numeric) = 1.036017003847526 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.28595150909922740000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.849999999999907 " " y[1] (closed_form) = 1.0387247970246745 " " y[1] (numeric) = 1.038724797024674 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.27533078176349200000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.859999999999906 " " y[1] (closed_form) = 1.041528716921059 " " y[1] (numeric) = 1.0415287169210594 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.26382107987255500000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8699999999999048 " " y[1] (closed_form) = 1.044428483147028 " " y[1] (numeric) = 1.0444284831470294 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.27559488375485030000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8799999999999037 " " y[1] (closed_form) = 1.0474238057283753 " " y[1] (numeric) = 1.0474238057283776 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 2.11991176552095000000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8899999999999026 " " y[1] (closed_form) = 1.050514385135339 " " y[1] (numeric) = 1.050514385135342 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.9591450749624440000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8999999999999015 " " y[1] (closed_form) = 1.0536999123125537 " " y[1] (numeric) = 1.0536999123125579 " " absolute error = 4.218847493575595000000000000000E-15 " " relative error = 4.0038415532525730000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9099999999999004 " " y[1] (closed_form) = 1.0569800687099562 " " y[1] (numeric) = 1.0569800687099618 " " absolute error = 5.551115123125783000000000000000E-15 " " relative error = 5.2518635757256200000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9199999999998993 " " y[1] (closed_form) = 1.0603545263146406 " " y[1] (numeric) = 1.0603545263146472 " " absolute error = 6.661338147750939000000000000000E-15 " " relative error = 6.2821801411109470000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9299999999998982 " " y[1] (closed_form) = 1.0638229476836583 " " y[1] (numeric) = 1.063822947683666 " " absolute error = 7.771561172376096000000000000000E-15 " " relative error = 7.3053144691959320000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9399999999998971 " " y[1] (closed_form) = 1.0673849859777624 " " y[1] (numeric) = 1.0673849859777715 " " absolute error = 9.103828801926284000000000000000E-15 " " relative error = 8.5290958009746180000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.949999999999896 " " y[1] (closed_form) = 1.0710402849960923 " " y[1] (numeric) = 1.0710402849961027 " " absolute error = 1.043609643147647100000000000000E-14 " " relative error = 9.7438878608702830000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.959999999999895 " " y[1] (closed_form) = 1.0747884792117919 " " y[1] (numeric) = 1.0747884792118032 " " absolute error = 1.132427485117659700000000000000E-14 " " relative error = 1.0536282319923433000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9699999999998938 " " y[1] (closed_form) = 1.0786291938085633 " " y[1] (numeric) = 1.0786291938085757 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 1.1528056117131805000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9799999999998927 " " y[1] (closed_form) = 1.0825620447181474 " " y[1] (numeric) = 1.082562044718161 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 1.2511727125952743000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9899999999998916 " " y[1] (closed_form) = 1.0865866386587308 " " y[1] (numeric) = 1.0865866386587453 " " absolute error = 1.443289932012703500000000000000E-14 " " relative error = 1.3282787406573330000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9999999999998905 " " y[1] (closed_form) = 1.0907025731742728 " " y[1] (numeric) = 1.0907025731742888 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 1.4657718747352597000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0099999999998897 " " y[1] (closed_form) = 1.0949094366747523 " " y[1] (numeric) = 1.0949094366747694 " " absolute error = 1.70974345792274100000000000000E-14 " " relative error = 1.5615386995980637000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0199999999998886 " " y[1] (closed_form) = 1.0992068084773243 " " y[1] (numeric) = 1.0992068084773432 " " absolute error = 1.88737914186276600000000000000E-14 " " relative error = 1.7170373466638703000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0299999999998875 " " y[1] (closed_form) = 1.1035942588483902 " " y[1] (numeric) = 1.1035942588484104 " " absolute error = 2.02060590481778500000000000000E-14 " " relative error = 1.8309318742979908000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0399999999998863 " " y[1] (closed_form) = 1.108071349046569 " " y[1] (numeric) = 1.1080713490465908 " " absolute error = 2.176037128265306800000000000000E-14 " " relative error = 1.9638059680341524000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0499999999998852 " " y[1] (closed_form) = 1.1126376313665718 " " y[1] (numeric) = 1.1126376313665953 " " absolute error = 2.35367281220533200000000000000E-14 " " relative error = 2.115399251160045000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.059999999999884 " " y[1] (closed_form) = 1.1172926491839714 " " y[1] (numeric) = 1.1172926491839967 " " absolute error = 2.53130849614535700000000000000E-14 " " relative error = 2.265573391173861000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.069999999999883 " " y[1] (closed_form) = 1.122035937000866 " " y[1] (numeric) = 1.1220359370008925 " " absolute error = 2.664535259100375700000000000000E-14 " " relative error = 2.3747325475354353000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.079999999999882 " " y[1] (closed_form) = 1.1268670204924258 " " y[1] (numeric) = 1.126867020492454 " " absolute error = 2.819966482547897600000000000000E-14 " " relative error = 2.5024838168709646000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.089999999999881 " " y[1] (closed_form) = 1.1317854165543282 " " y[1] (numeric) = 1.1317854165543575 " " absolute error = 2.93098878501041300000000000000E-14 " " relative error = 2.589703615314007000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0999999999998797 " " y[1] (closed_form) = 1.1367906333510656 " " y[1] (numeric) = 1.136790633351096 " " absolute error = 3.04201108747292900000000000000E-14 " " relative error = 2.675964243746095000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1099999999998786 " " y[1] (closed_form) = 1.141882170365129 " " y[1] (numeric) = 1.141882170365161 " " absolute error = 3.19744231092045100000000000000E-14 " " relative error = 2.8001508333368885000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1199999999998775 " " y[1] (closed_form) = 1.1470595184470598 " " y[1] (numeric) = 1.1470595184470935 " " absolute error = 3.37507799486047600000000000000E-14 " " relative error = 2.9423739052615216000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1299999999998764 " " y[1] (closed_form) = 1.1523221598663647 " " y[1] (numeric) = 1.1523221598664 " " absolute error = 3.53050921830799800000000000000E-14 " " relative error = 3.0638213351007954000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1399999999998753 " " y[1] (closed_form) = 1.157669568363287 " " y[1] (numeric) = 1.1576695683633238 " " absolute error = 3.6859404417555197000000000000E-14 " " relative error = 3.1839313587267404000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1499999999998742 " " y[1] (closed_form) = 1.1631012092014335 " " y[1] (numeric) = 1.163101209201472 " " absolute error = 3.86357612569554500000000000000E-14 " " relative error = 3.3217884180072466000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.159999999999873 " " y[1] (closed_form) = 1.1686165392212464 " " y[1] (numeric) = 1.1686165392212868 " " absolute error = 4.0412118096355700000000000000E-14 " " relative error = 3.458116220337417000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.169999999999872 " " y[1] (closed_form) = 1.1742150068943198 " " y[1] (numeric) = 1.174215006894362 " " absolute error = 4.21884749357559500000000000000E-14 " " relative error = 3.5929088529825737000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.179999999999871 " " y[1] (closed_form) = 1.179896052378552 " " y[1] (numeric) = 1.179896052378596 " " absolute error = 4.3964831775156200000000000000E-14 " " relative error = 3.7261614433345647000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.18999999999987 " " y[1] (closed_form) = 1.1856591075741285 " " y[1] (numeric) = 1.185659107574174 " " absolute error = 4.55191440096314200000000000000E-14 " " relative error = 3.8391426101186943000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1999999999998687 " " y[1] (closed_form) = 1.1915035961803326 " " y[1] (numeric) = 1.19150359618038 " " absolute error = 4.72955008490316700000000000000E-14 " " relative error = 3.969396399696099000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2099999999998676 " " y[1] (closed_form) = 1.1974289337531738 " " y[1] (numeric) = 1.1974289337532231 " " absolute error = 4.92939022933569500000000000000E-14 " " relative error = 4.1166453309969790000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2199999999998665 " " y[1] (closed_form) = 1.2034345277638328 " " y[1] (numeric) = 1.2034345277638836 " " absolute error = 5.08482145278321700000000000000E-14 " " relative error = 4.225258072187442000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2299999999998654 " " y[1] (closed_form) = 1.209519777657913 " " y[1] (numeric) = 1.2095197776579656 " " absolute error = 5.26245713672324200000000000000E-14 " " relative error = 4.3508648919436000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2399999999998643 " " y[1] (closed_form) = 1.2156840749154958 " " y[1] (numeric) = 1.2156840749155502 " " absolute error = 5.44009282066326700000000000000E-14 " " relative error = 4.474923158832542000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.249999999999863 " " y[1] (closed_form) = 1.2219268031119928 " " y[1] (numeric) = 1.2219268031120492 " " absolute error = 5.63993296509579500000000000000E-14 " " relative error = 4.615606230039362400000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.259999999999862 " " y[1] (closed_form) = 1.2282473379797865 " " y[1] (numeric) = 1.2282473379798446 " " absolute error = 5.8175686490358200000000000000E-14 " " relative error = 4.73647975382916030000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.269999999999861 " " y[1] (closed_form) = 1.2346450474706572 " " y[1] (numeric) = 1.2346450474707171 " " absolute error = 5.99520433297584500000000000000E-14 " " relative error = 4.855812077534234500000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.27999999999986 " " y[1] (closed_form) = 1.2411192918189868 " " y[1] (numeric) = 1.241119291819049 " " absolute error = 6.21724893790087700000000000000E-14 " " relative error = 5.00938868558627000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.289999999999859 " " y[1] (closed_form) = 1.2476694236057364 " " y[1] (numeric) = 1.2476694236058001 " " absolute error = 6.37268016134839900000000000000E-14 " " relative error = 5.10766717591868000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2999999999998577 " " y[1] (closed_form) = 1.2542947878231852 " " y[1] (numeric) = 1.2542947878232507 " " absolute error = 6.55031584528842400000000000000E-14 " " relative error = 5.222309706521563000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3099999999998566 " " y[1] (closed_form) = 1.2609947219404325 " " y[1] (numeric) = 1.2609947219405002 " " absolute error = 6.77236045021345500000000000000E-14 " " relative error = 5.370649323410389000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3199999999998555 " " y[1] (closed_form) = 1.26776855596965 " " y[1] (numeric) = 1.2677685559697198 " " absolute error = 6.97220059464598300000000000000E-14 " " relative error = 5.499584732414593000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3299999999998544 " " y[1] (closed_form) = 1.27461561253308 " " y[1] (numeric) = 1.2746156125331518 " " absolute error = 7.17204073907851100000000000000E-14 " " relative error = 5.626826369108495000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3399999999998533 " " y[1] (closed_form) = 1.281535206930772 " " y[1] (numeric) = 1.2815352069308457 " " absolute error = 7.3718808835110390000000000000E-14 " " relative error = 5.752382645160732000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.349999999999852 " " y[1] (closed_form) = 1.2885266472090517 " " y[1] (numeric) = 1.2885266472091277 " " absolute error = 7.59392548843607100000000000000E-14 " " relative error = 5.893495105347266000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.359999999999851 " " y[1] (closed_form) = 1.2955892342297182 " " y[1] (numeric) = 1.295589234229796 " " absolute error = 7.79376563286859900000000000000E-14 " " relative error = 6.015614692493426000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.36999999999985 " " y[1] (closed_form) = 1.3027222617399548 " " y[1] (numeric) = 1.3027222617400345 " " absolute error = 7.97140131680862400000000000000E-14 " " relative error = 6.119033619769253000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.379999999999849 " " y[1] (closed_form) = 1.3099250164429543 " " y[1] (numeric) = 1.309925016443036 " " absolute error = 8.17124146124115200000000000000E-14 " " relative error = 6.237945957723451000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.389999999999848 " " y[1] (closed_form) = 1.317196778069249 " " y[1] (numeric) = 1.3171967780693328 " " absolute error = 8.3710816056736800000000000000E-14 " " relative error = 6.3552247811781290000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3999999999998467 " " y[1] (closed_form) = 1.3245368194487361 " " y[1] (numeric) = 1.3245368194488218 " " absolute error = 8.57092175010620800000000000000E-14 " " relative error = 6.4708822165271120000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4099999999998456 " " y[1] (closed_form) = 1.331944406583394 " " y[1] (numeric) = 1.3319444065834818 " " absolute error = 8.77076189453873700000000000000E-14 " " relative error = 6.584930910920561000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4199999999998445 " " y[1] (closed_form) = 1.3394187987206827 " " y[1] (numeric) = 1.3394187987207722 " " absolute error = 8.94839757847876200000000000000E-14 " " relative error = 6.680806322134370000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4299999999998434 " " y[1] (closed_form) = 1.3469592484276165 " " y[1] (numeric) = 1.346959248427708 " " absolute error = 9.1482377229112900000000000000E-14 " " relative error = 6.7917702288250790000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4399999999998423 " " y[1] (closed_form) = 1.3545650016655089 " " y[1] (numeric) = 1.3545650016656026 " " absolute error = 9.37028232783632100000000000000E-14 " " relative error = 6.9175582687542260000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.449999999999841 " " y[1] (closed_form) = 1.3622352978653738 " " y[1] (numeric) = 1.36223529786547 " " absolute error = 9.61453139325385600000000000000E-14 " " relative error = 7.057907990139333000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.45999999999984 " " y[1] (closed_form) = 1.3699693700039837 " " y[1] (numeric) = 1.3699693700040818 " " absolute error = 9.81437153768638400000000000000E-14 " " relative error = 7.163935013859357000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.469999999999839 " " y[1] (closed_form) = 1.377766444680569 " " y[1] (numeric) = 1.3777664446806697 " " absolute error = 1.00586206031039180000000000000E-13 " " relative error = 7.300671780721136000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.479999999999838 " " y[1] (closed_form) = 1.3856257421941605 " " y[1] (numeric) = 1.3856257421942633 " " absolute error = 1.0280665208028950000000000000E-13 " " relative error = 7.419510835407368000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.489999999999837 " " y[1] (closed_form) = 1.3935464766215553 " " y[1] (numeric) = 1.3935464766216603 " " absolute error = 1.05027098129539810000000000000E-13 " " relative error = 7.536677096279004000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4999999999998357 " " y[1] (closed_form) = 1.401527855895912 " " y[1] (numeric) = 1.4015278558960191 " " absolute error = 1.07247544178790120000000000000E-13 " " relative error = 7.65218784112095000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5099999999998346 " " y[1] (closed_form) = 1.4095690818859536 " " y[1] (numeric) = 1.4095690818860633 " " absolute error = 1.09690034832965470000000000000E-13 " " relative error = 7.781813338740666000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5199999999998335 " " y[1] (closed_form) = 1.4176693504757827 " " y[1] (numeric) = 1.4176693504758948 " " absolute error = 1.12132525487140810000000000000E-13 " " relative error = 7.909638834295748000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5299999999998324 " " y[1] (closed_form) = 1.4258278516452902 " " y[1] (numeric) = 1.4258278516454042 " " absolute error = 1.13908882326541060000000000000E-13 " " relative error = 7.988964600116304000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5399999999998313 " " y[1] (closed_form) = 1.434043769551158 " " y[1] (numeric) = 1.4340437695512744 " " absolute error = 1.1635137298071640000000000000E-13 " " relative error = 8.113516159770582000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.54999999999983 " " y[1] (closed_form) = 1.4423162826084421 " " y[1] (numeric) = 1.4423162826085607 " " absolute error = 1.18571819029966720000000000000E-13 " " relative error = 8.220930489360385000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.559999999999829 " " y[1] (closed_form) = 1.4506445635727305 " " y[1] (numeric) = 1.450644563572851 " " absolute error = 1.205702204742920000000000000E-13 " " relative error = 8.31149293920385000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.569999999999828 " " y[1] (closed_form) = 1.459027779622867 " " y[1] (numeric) = 1.45902777962299 " " absolute error = 1.23012711128467340000000000000E-13 " " relative error = 8.431142494097266000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.579999999999827 " " y[1] (closed_form) = 1.4674650924442323 " " y[1] (numeric) = 1.4674650924443575 " " absolute error = 1.25233157177717660000000000000E-13 " " relative error = 8.533978615404568000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5899999999998258 " " y[1] (closed_form) = 1.4759556583125755 " " y[1] (numeric) = 1.4759556583127036 " " absolute error = 1.28119737041743060000000000000E-13 " " relative error = 8.680459763148932000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5999999999998247 " " y[1] (closed_form) = 1.4844986281783856 " " y[1] (numeric) = 1.4844986281785157 " " absolute error = 1.30118138486068350000000000000E-13 " " relative error = 8.765123524953007000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6099999999998236 " " y[1] (closed_form) = 1.4930931477517946 " " y[1] (numeric) = 1.4930931477519271 " " absolute error = 1.3256062914024370000000000000E-13 " " relative error = 8.878255810084261000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6199999999998225 " " y[1] (closed_form) = 1.5017383575880074 " " y[1] (numeric) = 1.5017383575881424 " " absolute error = 1.35003119794419040000000000000E-13 " " relative error = 8.989789673565514000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6299999999998214 " " y[1] (closed_form) = 1.5104333931732448 " " y[1] (numeric) = 1.5104333931733824 " " absolute error = 1.3766765505351940000000000000E-13 " " relative error = 9.11444726233810900000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6399999999998203 " " y[1] (closed_form) = 1.519177385011194 " " y[1] (numeric) = 1.5191773850113341 " " absolute error = 1.40110145707694760000000000000E-13 " " relative error = 9.222764049154296000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.649999999999819 " " y[1] (closed_form) = 1.527969458709958 " " y[1] (numeric) = 1.5279694587101005 " " absolute error = 1.4255263636187010000000000000E-13 " " relative error = 9.329547495159045000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.659999999999818 " " y[1] (closed_form) = 1.5368087350694934 " " y[1] (numeric) = 1.5368087350696384 " " absolute error = 1.44995127016045440000000000000E-13 " " relative error = 9.434819291906802000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.669999999999817 " " y[1] (closed_form) = 1.5456943301695305 " " y[1] (numeric) = 1.545694330169678 " " absolute error = 1.4743761767022080000000000000E-13 " " relative error = 9.538601183459731000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.679999999999816 " " y[1] (closed_form) = 1.5546253554579639 " " y[1] (numeric) = 1.5546253554581138 " " absolute error = 1.49880108324396130000000000000E-13 " " relative error = 9.640914950872149000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6899999999998148 " " y[1] (closed_form) = 1.563600917839707 " " y[1] (numeric) = 1.5636009178398595 " " absolute error = 1.5254464358349650000000000000E-13 " " relative error = 9.755983246303944000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6999999999998137 " " y[1] (closed_form) = 1.5726201197660017 " " y[1] (numeric) = 1.5726201197661562 " " absolute error = 1.5454304502782180000000000000E-13 " " relative error = 9.827105928850577000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7099999999998126 " " y[1] (closed_form) = 1.5816820593241707 " " y[1] (numeric) = 1.5816820593243281 " " absolute error = 1.5742962489184720000000000000E-13 " " relative error = 9.953304076744384000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7199999999998115 " " y[1] (closed_form) = 1.5907858303278104 " " y[1] (numeric) = 1.5907858303279705 " " absolute error = 1.60094160150947570000000000000E-13 " " relative error = 1.006384122229434700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7299999999998104 " " y[1] (closed_form) = 1.5999305224074067 " " y[1] (numeric) = 1.5999305224075693 " " absolute error = 1.62536650805122920000000000000E-13 " " relative error = 1.015898181381994800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7399999999998093 " " y[1] (closed_form) = 1.609115221101372 " " y[1] (numeric) = 1.6091152211015374 " " absolute error = 1.65423230669148320000000000000E-13 " " relative error = 1.028038443113620200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.749999999999808 " " y[1] (closed_form) = 1.6183390079474909 " " y[1] (numeric) = 1.618339007947659 " " absolute error = 1.6808776592824870000000000000E-13 " " relative error = 1.038643727320342400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.759999999999807 " " y[1] (closed_form) = 1.6276009605747654 " " y[1] (numeric) = 1.6276009605749355 " " absolute error = 1.70086167372573980000000000000E-13 " " relative error = 1.04501147082458300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.769999999999806 " " y[1] (closed_form) = 1.6369001527956508 " " y[1] (numeric) = 1.6369001527958236 " " absolute error = 1.72750702631674360000000000000E-13 " " relative error = 1.055352718592118100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.779999999999805 " " y[1] (closed_form) = 1.6462356546986745 " " y[1] (numeric) = 1.64623565469885 " " absolute error = 1.75415237890774730000000000000E-13 " " relative error = 1.065553630733885300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7899999999998037 " " y[1] (closed_form) = 1.6556065327414258 " " y[1] (numeric) = 1.655606532741604 " " absolute error = 1.78301817754800140000000000000E-13 " " relative error = 1.07695768426064500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7999999999998026 " " y[1] (closed_form) = 1.6650118498439093 " " y[1] (numeric) = 1.66501184984409 " " absolute error = 1.80744308408975480000000000000E-13 " " relative error = 1.085543676015998400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8099999999998015 " " y[1] (closed_form) = 1.6744506654822522 " " y[1] (numeric) = 1.6744506654824356 " " absolute error = 1.83408843668075860000000000000E-13 " " relative error = 1.095337398998572500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8199999999998004 " " y[1] (closed_form) = 1.6839220357827571 " " y[1] (numeric) = 1.6839220357829432 " " absolute error = 1.86073378927176240000000000000E-13 " " relative error = 1.10499996420963500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8299999999997993 " " y[1] (closed_form) = 1.693425013616286 " " y[1] (numeric) = 1.6934250136164748 " " absolute error = 1.8873791418627660000000000000E-13 " " relative error = 1.114533638446909100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8399999999997982 " " y[1] (closed_form) = 1.702958648692975 " " y[1] (numeric) = 1.7029586486931665 " " absolute error = 1.914024494453770000000000000E-13 " " relative error = 1.123940675789625400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.849999999999797 " " y[1] (closed_form) = 1.7125219876572613 " " y[1] (numeric) = 1.712521987657455 " " absolute error = 1.9362289549462730000000000000E-13 " " relative error = 1.130630128489646000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.859999999999796 " " y[1] (closed_form) = 1.7221140741832173 " " y[1] (numeric) = 1.7221140741834136 " " absolute error = 1.96287430753727680000000000000E-13 " " relative error = 1.139805043674734500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.869999999999795 " " y[1] (closed_form) = 1.7317339490701844 " " y[1] (numeric) = 1.731733949070383 " " absolute error = 1.985078768029780000000000000E-13 " " relative error = 1.146295462473102800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.879999999999794 " " y[1] (closed_form) = 1.7413806503386902 " " y[1] (numeric) = 1.7413806503388911 " " absolute error = 2.00950367457153330000000000000E-13 " " relative error = 1.153971519196963000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8899999999997927 " " y[1] (closed_form) = 1.7510532133266465 " " y[1] (numeric) = 1.75105321332685 " " absolute error = 2.03392858111328680000000000000E-13 " " relative error = 1.161545843172426700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8999999999997916 " " y[1] (closed_form) = 1.7607506707858154 " " y[1] (numeric) = 1.7607506707860214 " " absolute error = 2.06057393370429050000000000000E-13 " " relative error = 1.17028149862050900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9099999999997905 " " y[1] (closed_form) = 1.7704720529785318 " " y[1] (numeric) = 1.7704720529787403 " " absolute error = 2.0849988402460440000000000000E-13 " " relative error = 1.177651370852407400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9199999999997894 " " y[1] (closed_form) = 1.7802163877746777 " " y[1] (numeric) = 1.7802163877748887 " " absolute error = 2.10942374678779740000000000000E-13 " " relative error = 1.184925473820987900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9299999999997883 " " y[1] (closed_form) = 1.7899827007488938 " " y[1] (numeric) = 1.7899827007491074 " " absolute error = 2.13606909937880120000000000000E-13 " " relative error = 1.19334622534905600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9399999999997872 " " y[1] (closed_form) = 1.7997700152780212 " " y[1] (numeric) = 1.7997700152782374 " " absolute error = 2.1627144519698050000000000000E-13 " " relative error = 1.201661564316992800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.949999999999786 " " y[1] (closed_form) = 1.8095773526387628 " " y[1] (numeric) = 1.8095773526389818 " " absolute error = 2.18935980456080870000000000000E-13 " " relative error = 1.20987356598392400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.959999999999785 " " y[1] (closed_form) = 1.8194037321055556 " " y[1] (numeric) = 1.8194037321057774 " " absolute error = 2.21822560320106280000000000000E-13 " " relative error = 1.219204711993175600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.969999999999784 " " y[1] (closed_form) = 1.8292481710486417 " " y[1] (numeric) = 1.8292481710488662 " " absolute error = 2.24487095579206650000000000000E-13 " " relative error = 1.227209621592877200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.979999999999783 " " y[1] (closed_form) = 1.8391096850323299 " " y[1] (numeric) = 1.8391096850325572 " " absolute error = 2.27373675443232060000000000000E-13 " " relative error = 1.236324713494372200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9899999999997817 " " y[1] (closed_form) = 1.8489872879134401 " " y[1] (numeric) = 1.84898728791367 " " absolute error = 2.2981616609740740000000000000E-13 " " relative error = 1.242929941161208100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9999999999997806 " " y[1] (closed_form) = 1.8588799919399155 " " y[1] (numeric) = 1.858879991940148 " " absolute error = 2.3248070135650778000000000000E-13 " " relative error = 1.250649328437240200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0099999999997795 " " y[1] (closed_form) = 1.8687868078495975 " " y[1] (numeric) = 1.8687868078498322 " " absolute error = 2.3470114740575810000000000000E-13 " " relative error = 1.25590113553844800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0199999999997784 " " y[1] (closed_form) = 1.8787067449691504 " " y[1] (numeric) = 1.8787067449693877 " " absolute error = 2.37365682664858470000000000000E-13 " " relative error = 1.263452549475762900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0299999999997773 " " y[1] (closed_form) = 1.888638811313129 " " y[1] (numeric) = 1.8886388113133692 " " absolute error = 2.4025226252888388000000000000E-13 " " relative error = 1.272092160183035700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.039999999999776 " " y[1] (closed_form) = 1.8985820136831755 " " y[1] (numeric) = 1.8985820136834186 " " absolute error = 2.4313884239290928000000000000E-13 " " relative error = 1.28063386590937600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.049999999999775 " " y[1] (closed_form) = 1.908535357767339 " " y[1] (numeric) = 1.9085353577675845 " " absolute error = 2.45581333047084630000000000000E-13 " " relative error = 1.286752860237145000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.059999999999774 " " y[1] (closed_form) = 1.9184978482395056 " " y[1] (numeric) = 1.918497848239754 " " absolute error = 2.482458683061850000000000000E-13 " " relative error = 1.293959586840224300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.069999999999773 " " y[1] (closed_form) = 1.9284684888589299 " " y[1] (numeric) = 1.9284684888591812 " " absolute error = 2.51354492775135440000000000000E-13 " " relative error = 1.303389162059170000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.079999999999772 " " y[1] (closed_form) = 1.938446282569859 " " y[1] (numeric) = 1.9384462825701132 " " absolute error = 2.54241072639160850000000000000E-13 " " relative error = 1.311571411213446000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0899999999997707 " " y[1] (closed_form) = 1.9484302316012365 " " y[1] (numeric) = 1.9484302316014934 " " absolute error = 2.5690560789826120000000000000E-13 " " relative error = 1.31852608182502900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0999999999997696 " " y[1] (closed_form) = 1.9584193375664791 " " y[1] (numeric) = 1.9584193375667387 " " absolute error = 2.5957014315736160000000000000E-13 " " relative error = 1.325406352859556700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.1099999999997685 " " y[1] (closed_form) = 1.9684126015633148 " " y[1] (numeric) = 1.9684126015635772 " " absolute error = 2.624567230213870000000000000E-13 " " relative error = 1.333342017892710500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.1199999999997674 " " y[1] (closed_form) = 1.9784090242736714 " " y[1] (numeric) = 1.9784090242739365 " " absolute error = 2.6512125828048740000000000000E-13 " " relative error = 1.340073033572118400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.1299999999997663 " " y[1] (closed_form) = 1.9884076060636082 " " y[1] (numeric) = 1.9884076060638758 " " absolute error = 2.67563748934662700000000000000E-13 " " relative error = 1.34561821287915300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.139999999999765 " " y[1] (closed_form) = 1.9984073470832782 " " y[1] (numeric) = 1.9984073470835488 " " absolute error = 2.70672373403613160000000000000E-13 " " relative error = 1.354440443779721700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.149999999999764 " " y[1] (closed_form) = 2.008407247366913 " " y[1] (numeric) = 2.008407247367187 " " absolute error = 2.74003042477488630000000000000E-13 " " relative error = 1.364280291443458500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.159999999999763 " " y[1] (closed_form) = 2.0184063069328166 " " y[1] (numeric) = 2.018406306933093 " " absolute error = 2.76223488526738950000000000000E-13 " " relative error = 1.368522718037330800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.169999999999762 " " y[1] (closed_form) = 2.0284035258833657 " " y[1] (numeric) = 2.028403525883644 " " absolute error = 2.78443934575989260000000000000E-13 " " relative error = 1.37272456403726400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.179999999999761 " " y[1] (closed_form) = 2.038397904504996 " " y[1] (numeric) = 2.0383979045052776 " " absolute error = 2.8155255904493970000000000000E-13 " " relative error = 1.381244350883061900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.1899999999997597 " " y[1] (closed_form) = 2.0483884433681743 " " y[1] (numeric) = 2.048388443368458 " " absolute error = 2.83773005094190000000000000E-13 " " relative error = 1.385347618089373700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.1999999999997586 " " y[1] (closed_form) = 2.058374143427339 " " y[1] (numeric) = 2.0583741434276255 " " absolute error = 2.8643754035329040000000000000E-13 " " relative error = 1.391571795962961200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.2099999999997575 " " y[1] (closed_form) = 2.068354006120806 " " y[1] (numeric) = 2.0683540061210954 " " absolute error = 2.89546164822240800000000000000E-13 " " relative error = 1.3998868857332800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.2199999999997564 " " y[1] (closed_form) = 2.078327033470622 " " y[1] (numeric) = 2.0783270334709147 " " absolute error = 2.92654789291191260000000000000E-13 " " relative error = 1.408126750882336700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.2299999999997553 " " y[1] (closed_form) = 2.0882922281823637 " " y[1] (numeric) = 2.0882922281826586 " " absolute error = 2.9487523534044160000000000000E-13 " " relative error = 1.412040093627600600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.239999999999754 " " y[1] (closed_form) = 2.098248593744864 " " y[1] (numeric) = 2.0982485937451614 " " absolute error = 2.97539770599541950000000000000E-13 " " relative error = 1.418038698972774200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.249999999999753 " " y[1] (closed_form) = 2.108195134529863 " " y[1] (numeric) = 2.1081951345301633 " " absolute error = 3.00204305858642330000000000000E-13 " " relative error = 1.423987281545402400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.259999999999752 " " y[1] (closed_form) = 2.1181308558915712 " " y[1] (numeric) = 2.118130855891874 " " absolute error = 3.0286884111774270000000000000E-13 " " relative error = 1.4298873002832400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.269999999999751 " " y[1] (closed_form) = 2.1280547642661327 " " y[1] (numeric) = 2.1280547642664382 " " absolute error = 3.0553337637684310000000000000E-13 " " relative error = 1.43574019572850300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.27999999999975 " " y[1] (closed_form) = 2.1379658672709794 " " y[1] (numeric) = 2.137965867271287 " " absolute error = 3.0775382242609340000000000000E-13 " " relative error = 1.439470232604451400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.2899999999997487 " " y[1] (closed_form) = 2.14786317380407 " " y[1] (numeric) = 2.1478631738043803 " " absolute error = 3.10418357685193770000000000000E-13 " " relative error = 1.445242702007937300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.2999999999997476 " " y[1] (closed_form) = 2.1577456941429993 " " y[1] (numeric) = 2.1577456941433115 " " absolute error = 3.121947145245940000000000000E-13 " " relative error = 1.446855926405125600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3099999999997465 " " y[1] (closed_form) = 2.1676124400439685 " " y[1] (numeric) = 2.167612440044284 " " absolute error = 3.1574742820339450000000000000E-13 " " relative error = 1.456659974681589200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3199999999997454 " " y[1] (closed_form) = 2.1774624248406096 " " y[1] (numeric) = 2.177462424840928 " " absolute error = 3.1841196346249490000000000000E-13 " " relative error = 1.462307499913816600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3299999999997443 " " y[1] (closed_form) = 2.187294663542652 " " y[1] (numeric) = 2.187294663542972 " " absolute error = 3.20188320301895150000000000000E-13 " " relative error = 1.46385544498747200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.339999999999743 " " y[1] (closed_form) = 2.1971081729344184 " " y[1] (numeric) = 2.197108172934741 " " absolute error = 3.22408766351145460000000000000E-13 " " relative error = 1.467423271747890500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.349999999999742 " " y[1] (closed_form) = 2.2069019716731475 " " y[1] (numeric) = 2.206901971673473 " " absolute error = 3.2551739082009590000000000000E-13 " " relative error = 1.474997054687060300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.359999999999741 " " y[1] (closed_form) = 2.2166750803871267 " " y[1] (numeric) = 2.2166750803874558 " " absolute error = 3.2907010449889640000000000000E-13 " " relative error = 1.48452115247051300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.36999999999974 " " y[1] (closed_form) = 2.2264265217736297 " " y[1] (numeric) = 2.226426521773961 " " absolute error = 3.3129055054814670000000000000E-13 " " relative error = 1.487992293068050600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3799999999997388 " " y[1] (closed_form) = 2.236155320696643 " " y[1] (numeric) = 2.2361553206969775 " " absolute error = 3.34399175017097150000000000000E-13 " " relative error = 1.495420161211877300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3899999999997377 " " y[1] (closed_form) = 2.2458605042843827 " " y[1] (numeric) = 2.24586050428472 " " absolute error = 3.3750779948604760000000000000E-13 " " relative error = 1.502799478606043300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3999999999997366 " " y[1] (closed_form) = 2.2555411020265765 " " y[1] (numeric) = 2.255541102026917 " " absolute error = 3.40616423954998000000000000000E-13 " " relative error = 1.510131753524501500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4099999999997355 " " y[1] (closed_form) = 2.265196145871518 " " y[1] (numeric) = 2.2651961458718617 " " absolute error = 3.43725048423948460000000000000E-13 " " relative error = 1.51741847632229100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4199999999997344 " " y[1] (closed_form) = 2.2748246703228685 " " y[1] (numeric) = 2.2748246703232144 " " absolute error = 3.4594549447319880000000000000E-13 " " relative error = 1.520756737810911300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4299999999997333 " " y[1] (closed_form) = 2.2844257125362066 " " y[1] (numeric) = 2.2844257125365552 " " absolute error = 3.48610029732299150000000000000E-13 " " relative error = 1.526029180197182300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.439999999999732 " " y[1] (closed_form) = 2.2939983124153116 " " y[1] (numeric) = 2.293998312415663 " " absolute error = 3.51274564991399530000000000000E-13 " " relative error = 1.531276475184275600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.449999999999731 " " y[1] (closed_form) = 2.303541512708173 " " y[1] (numeric) = 2.303541512708527 " " absolute error = 3.5393910025049990000000000000E-13 " " relative error = 1.536499769150629000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.45999999999973 " " y[1] (closed_form) = 2.313054359102714 " " y[1] (numeric) = 2.3130543591030706 " " absolute error = 3.5660363550960030000000000000E-13 " " relative error = 1.541700194404142200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.469999999999729 " " y[1] (closed_form) = 2.3225359003222223 " " y[1] (numeric) = 2.322535900322582 " " absolute error = 3.5971225997855070000000000000E-13 " " relative error = 1.548790957025229200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4799999999997278 " " y[1] (closed_form) = 2.3319851882204774 " " y[1] (numeric) = 2.3319851882208398 " " absolute error = 3.6237679523765110000000000000E-13 " " relative error = 1.55394123885571700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4899999999997267 " " y[1] (closed_form) = 2.341401277876564 " " y[1] (numeric) = 2.341401277876929 " " absolute error = 3.65041330496751470000000000000E-13 " " relative error = 1.559072056319241700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4999999999997256 " " y[1] (closed_form) = 2.3507832276893628 " " y[1] (numeric) = 2.3507832276897305 " " absolute error = 3.67705865755851850000000000000E-13 " " relative error = 1.564184487215685000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5099999999997245 " " y[1] (closed_form) = 2.360130099471711 " " y[1] (numeric) = 2.3601300994720815 " " absolute error = 3.7037040101495220000000000000E-13 " " relative error = 1.569279596484344200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5199999999997234 " " y[1] (closed_form) = 2.36944095854422 " " y[1] (numeric) = 2.3694409585445926 " " absolute error = 3.72590847064202530000000000000E-13 " " relative error = 1.572484200210338400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5299999999997222 " " y[1] (closed_form) = 2.378714873828741 " " y[1] (numeric) = 2.3787148738291166 " " absolute error = 3.75699471533153000000000000000E-13 " " relative error = 1.579422047033460500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.539999999999721 " " y[1] (closed_form) = 2.387950917941473 " " y[1] (numeric) = 2.387950917941852 " " absolute error = 3.7880809600210340000000000000E-13 " " relative error = 1.586331164330018800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.54999999999972 " " y[1] (closed_form) = 2.397148167285703 " " y[1] (numeric) = 2.3971481672860846 " " absolute error = 3.8147263126120380000000000000E-13 " " relative error = 1.591360252433399500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.559999999999719 " " y[1] (closed_form) = 2.40630570214416 " " y[1] (numeric) = 2.4063057021445444 " " absolute error = 3.84581255730154200000000000000E-13 " " relative error = 1.59822276690559180000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.569999999999718 " " y[1] (closed_form) = 2.4154226067709894 " " y[1] (numeric) = 2.4154226067713767 " " absolute error = 3.8724579098925460000000000000E-13 " " relative error = 1.603221688427171600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5799999999997167 " " y[1] (closed_form) = 2.424497969483326 " " y[1] (numeric) = 2.4244979694837157 " " absolute error = 3.8946623703850490000000000000E-13 " " relative error = 1.60637889551007700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5899999999997156 " " y[1] (closed_form) = 2.4335308827524615 " " y[1] (numeric) = 2.4335308827528532 " " absolute error = 3.91686683087755200000000000000E-13 " " relative error = 1.609540630299030300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5999999999997145 " " y[1] (closed_form) = 2.4425204432945966 " " y[1] (numeric) = 2.442520443294991 " " absolute error = 3.9435121834685560000000000000E-13 " " relative error = 1.614525763456597700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6099999999997134 " " y[1] (closed_form) = 2.451465752161168 " " y[1] (numeric) = 2.451465752161565 " " absolute error = 3.970157536059560000000000000E-13 " " relative error = 1.619503569470445000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6199999999997123 " " y[1] (closed_form) = 2.460365914828743 " " y[1] (numeric) = 2.460365914829143 " " absolute error = 4.0012437807490640000000000000E-13 " " relative error = 1.626279959673224700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6299999999997112 " " y[1] (closed_form) = 2.469220041288472 " " y[1] (numeric) = 2.469220041288875 " " absolute error = 4.0278891333400680000000000000E-13 " " relative error = 1.631239446460292500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.63999999999971 " " y[1] (closed_form) = 2.4780272461350883 " " y[1] (numeric) = 2.4780272461354937 " " absolute error = 4.05453448593107170000000000000E-13 " " relative error = 1.63619447375117380000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.649999999999709 " " y[1] (closed_form) = 2.4867866486554453 " " y[1] (numeric) = 2.486786648655854 " " absolute error = 4.0856207306205760000000000000E-13 " " relative error = 1.64293174600627200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.659999999999708 " " y[1] (closed_form) = 2.4954973729165912 " " y[1] (numeric) = 2.4954973729170025 " " absolute error = 4.112266083211580000000000000E-13 " " relative error = 1.647874338735690300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.669999999999707 " " y[1] (closed_form) = 2.5041585478533586 " " y[1] (numeric) = 2.504158547853771 " " absolute error = 4.12558875950708170000000000000E-13 " " relative error = 1.647495029036265500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6799999999997057 " " y[1] (closed_form) = 2.5127693073554713 " " y[1] (numeric) = 2.512769307355886 " " absolute error = 4.1477932199995850000000000000E-13 " " relative error = 1.650686041037675600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6899999999997046 " " y[1] (closed_form) = 2.5213287903541546 " " y[1] (numeric) = 2.521328790354572 " " absolute error = 4.17443857259058860000000000000E-13 " " relative error = 1.65565022243855500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6999999999997035 " " y[1] (closed_form) = 2.529836140908242 " " y[1] (numeric) = 2.529836140908662 " " absolute error = 4.20108392518159230000000000000E-13 " " relative error = 1.660615032431844700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7099999999997024 " " y[1] (closed_form) = 2.5382905082897667 " " y[1] (numeric) = 2.5382905082901894 " " absolute error = 4.2277292777725960000000000000E-13 " " relative error = 1.66558132883738700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7199999999997013 " " y[1] (closed_form) = 2.5466910470690367 " " y[1] (numeric) = 2.5466910470694613 " " absolute error = 4.24549284616659860000000000000E-13 " " relative error = 1.667062383186487300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7299999999997 " " y[1] (closed_form) = 2.5550369171991747 " " y[1] (numeric) = 2.5550369171996015 " " absolute error = 4.26769730665910200000000000000E-13 " " relative error = 1.67030749259675700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.739999999999699 " " y[1] (closed_form) = 2.5633272841001213 " " y[1] (numeric) = 2.563327284100551 " " absolute error = 4.2987835513486060000000000000E-13 " " relative error = 1.677032651278368400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.749999999999698 " " y[1] (closed_form) = 2.571561318742096 " " y[1] (numeric) = 2.571561318742529 " " absolute error = 4.32986979603811050000000000000E-13 " " relative error = 1.68375133211138400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.759999999999697 " " y[1] (closed_form) = 2.579738197728496 " " y[1] (numeric) = 2.5797381977289313 " " absolute error = 4.35207425653061360000000000000E-13 " " relative error = 1.68702167544082200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.769999999999696 " " y[1] (closed_form) = 2.5878571033782367 " " y[1] (numeric) = 2.587857103378674 " " absolute error = 4.3742787170231170000000000000E-13 " " relative error = 1.69030921812214900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7799999999996947 " " y[1] (closed_form) = 2.5959172238075188 " " y[1] (numeric) = 2.5959172238079584 " " absolute error = 4.396483177515620000000000000E-13 " " relative error = 1.693614548720914500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7899999999996936 " " y[1] (closed_form) = 2.6039177530110162 " " y[1] (numeric) = 2.603917753011458 " " absolute error = 4.4186876380081230000000000000E-13 " " relative error = 1.696938251178868600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7999999999996925 " " y[1] (closed_form) = 2.611857890942476 " " y[1] (numeric) = 2.6118578909429204 " " absolute error = 4.4453329905991270000000000000E-13 " " relative error = 1.701981185888735400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.8099999999996914 " " y[1] (closed_form) = 2.619736843594721 " " y[1] (numeric) = 2.6197368435951685 " " absolute error = 4.4764192352886310000000000000E-13 " " relative error = 1.7087285870844300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.8199999999996903 " " y[1] (closed_form) = 2.6275538230790523 " " y[1] (numeric) = 2.627553823079502 " " absolute error = 4.49862369578113430000000000000E-13 " " relative error = 1.712095735686777500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.829999999999689 " " y[1] (closed_form) = 2.6353080477040356 " " y[1] (numeric) = 2.6353080477044877 " " absolute error = 4.52082815627363740000000000000E-13 " " relative error = 1.71548375918038400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.839999999999688 " " y[1] (closed_form) = 2.64299874205367 " " y[1] (numeric) = 2.6429987420541248 " " absolute error = 4.5474735088646410000000000000E-13 " " relative error = 1.72057346698967800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.849999999999687 " " y[1] (closed_form) = 2.65062513706493 " " y[1] (numeric) = 2.650625137065387 " " absolute error = 4.5696779693571443000000000000E-13 " " relative error = 1.724000087925373600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.859999999999686 " " y[1] (closed_form) = 2.6581864701046687 " " y[1] (numeric) = 2.6581864701051283 " " absolute error = 4.5963233219481480000000000000E-13 " " relative error = 1.729119974704845800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.869999999999685 " " y[1] (closed_form) = 2.665681985045884 " " y[1] (numeric) = 2.6656819850463465 " " absolute error = 4.6229686745391520000000000000E-13 " " relative error = 1.734253635832549200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.8799999999996837 " " y[1] (closed_form) = 2.6731109323433278 " " y[1] (numeric) = 2.6731109323437923 " " absolute error = 4.6451731350316550000000000000E-13 " " relative error = 1.737740502583467200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.8899999999996826 " " y[1] (closed_form) = 2.680472569108461 " " y[1] (numeric) = 2.680472569108928 " " absolute error = 4.6673775955241580000000000000E-13 " " relative error = 1.74125176631691890000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.8999999999996815 " " y[1] (closed_form) = 2.6877661591837425 " " y[1] (numeric) = 2.687766159184211 " " absolute error = 4.6851411639181606000000000000E-13 " " relative error = 1.743135706917676200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.9099999999996804 " " y[1] (closed_form) = 2.694990973216242 " " y[1] (numeric) = 2.694990973216713 " " absolute error = 4.7117865165091644000000000000E-13 " " relative error = 1.748349646932601300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.9199999999996793 " " y[1] (closed_form) = 2.702146288730577 " " y[1] (numeric) = 2.702146288731051 " " absolute error = 4.7384318691001680000000000000E-13 " " relative error = 1.753580806806060700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.929999999999678 " " y[1] (closed_form) = 2.7092313902011593 " " y[1] (numeric) = 2.7092313902016345 " " absolute error = 4.751754545395670000000000000E-13 " " relative error = 1.753912405777512400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.939999999999677 " " y[1] (closed_form) = 2.7162455691237453 " " y[1] (numeric) = 2.716245569124222 " " absolute error = 4.7695181137896725000000000000E-13 " " relative error = 1.755923016683763600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.949999999999676 " " y[1] (closed_form) = 2.7231881240862883 " " y[1] (numeric) = 2.723188124086768 " " absolute error = 4.7961634663806760000000000000E-13 " " relative error = 1.76123104531749300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.959999999999675 " " y[1] (closed_form) = 2.7300583608390774 " " y[1] (numeric) = 2.730058360839559 " " absolute error = 4.8183679268731794000000000000E-13 " " relative error = 1.764932206574611200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.969999999999674 " " y[1] (closed_form) = 2.7368555923641624 " " y[1] (numeric) = 2.736855592364647 " " absolute error = 4.8450132794641830000000000000E-13 " " relative error = 1.770284589724715200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.9799999999996727 " " y[1] (closed_form) = 2.743579138944056 " " y[1] (numeric) = 2.743579138944542 " " absolute error = 4.8627768478581856000000000000E-13 " " relative error = 1.772420842115661800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.9899999999996716 " " y[1] (closed_form) = 2.7502283282297015 " " y[1] (numeric) = 2.75022832823019 " " absolute error = 4.8849813083506890000000000000E-13 " " relative error = 1.776209363494960800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.9999999999996705 " " y[1] (closed_form) = 2.7568024953077126 " " y[1] (numeric) = 2.7568024953082033 " " absolute error = 4.9071857688431920000000000000E-13 " " relative error = 1.780028049595716300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.009999999999674 " " y[1] (closed_form) = 2.7633009827668626 " " y[1] (numeric) = 2.763300982767352 " " absolute error = 4.893863092547690000000000000E-13 " " relative error = 1.77102064634577700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.019999999999677 " " y[1] (closed_form) = 2.769723140763818 " " y[1] (numeric) = 2.7697231407643064 " " absolute error = 4.8849813083506890000000000000E-13 " " relative error = 1.763707439366498400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.0299999999996805 " " y[1] (closed_form) = 2.776068327088131 " " y[1] (numeric) = 2.7760683270886184 " " absolute error = 4.8760995241536875000000000000E-13 " " relative error = 1.756476768447669300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.039999999999684 " " y[1] (closed_form) = 2.782335907226456 " " y[1] (numeric) = 2.7823359072269436 " " absolute error = 4.8760995241536875000000000000E-13 " " relative error = 1.752520071889658900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.049999999999687 " " y[1] (closed_form) = 2.788525254426003 " " y[1] (numeric) = 2.78852525442649 " " absolute error = 4.8716586320551870000000000000E-13 " " relative error = 1.747037658820838600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.0599999999996905 " " y[1] (closed_form) = 2.794635749757209 " " y[1] (numeric) = 2.7946357497576955 " " absolute error = 4.8627768478581856000000000000E-13 " " relative error = 1.74003959130654200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.069999999999694 " " y[1] (closed_form) = 2.800666782175634 " " y[1] (numeric) = 2.80066678217612 " " absolute error = 4.8583359557596850000000000000E-13 " " relative error = 1.73470688718834230000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.079999999999697 " " y[1] (closed_form) = 2.8066177485830615 " " y[1] (numeric) = 2.806617748583547 " " absolute error = 4.8538950636611844000000000000E-13 " " relative error = 1.729446436413260600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.0899999999997005 " " y[1] (closed_form) = 2.81248805388781 " " y[1] (numeric) = 2.8124880538882953 " " absolute error = 4.8538950636611844000000000000E-13 " " relative error = 1.72583668647106230000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.099999999999704 " " y[1] (closed_form) = 2.81827711106424 " " y[1] (numeric) = 2.8182771110647256 " " absolute error = 4.8538950636611844000000000000E-13 " " relative error = 1.72229162441313400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.109999999999707 " " y[1] (closed_form) = 2.82398434121146 " " y[1] (numeric) = 2.8239843412119447 " " absolute error = 4.8494541715626840000000000000E-13 " " relative error = 1.71723833620207630000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.119999999999710 " " y[1] (closed_form) = 2.8296091736112094 " " y[1] (numeric) = 2.829609173611695 " " absolute error = 4.8538950636611844000000000000E-13 " " relative error = 1.715394164299565400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.129999999999714 " " y[1] (closed_form) = 2.835151045784936 " " y[1] (numeric) = 2.835151045785422 " " absolute error = 4.8583359557596850000000000000E-13 " " relative error = 1.713607450644525600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.139999999999717 " " y[1] (closed_form) = 2.8406094035500415 " " y[1] (numeric) = 2.8406094035505265 " " absolute error = 4.8494541715626840000000000000E-13 " " relative error = 1.707187959563217500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.149999999999720 " " y[1] (closed_form) = 2.8459837010752973 " " y[1] (numeric) = 2.8459837010757822 " " absolute error = 4.8494541715626840000000000000E-13 " " relative error = 1.7039641406696798000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.159999999999724 " " y[1] (closed_form) = 2.8512734009354297 " " y[1] (numeric) = 2.851273400935914 " " absolute error = 4.8450132794641830000000000000E-13 " " relative error = 1.699245424123361500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.169999999999727 " " y[1] (closed_form) = 2.8564779741648603 " " y[1] (numeric) = 2.8564779741653448 " " absolute error = 4.8450132794641830000000000000E-13 " " relative error = 1.696149357104951600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.179999999999730 " " y[1] (closed_form) = 2.861596900310604 " " y[1] (numeric) = 2.8615969003110884 " " absolute error = 4.8450132794641830000000000000E-13 " " relative error = 1.693115224907566200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.189999999999734 " " y[1] (closed_form) = 2.8666296674843115 " " y[1] (numeric) = 2.866629667484795 " " absolute error = 4.8361314952671820000000000000E-13 " " relative error = 1.68704438878959220000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.199999999999737 " " y[1] (closed_form) = 2.8715757724134594 " " y[1] (numeric) = 2.871575772413943 " " absolute error = 4.8361314952671820000000000000E-13 " " relative error = 1.68413856312855800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.209999999999740 " " y[1] (closed_form) = 2.8764347204916767 " " y[1] (numeric) = 2.8764347204921603 " " absolute error = 4.8361314952671820000000000000E-13 " " relative error = 1.681293672620016400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.219999999999744 " " y[1] (closed_form) = 2.881206025828204 " " y[1] (numeric) = 2.8812060258286887 " " absolute error = 4.8450132794641830000000000000E-13 " " relative error = 1.681592095820874700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.229999999999747 " " y[1] (closed_form) = 2.8858892112964853 " " y[1] (numeric) = 2.88588921129697 " " absolute error = 4.8450132794641830000000000000E-13 " " relative error = 1.678863228878963700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.239999999999750 " " y[1] (closed_form) = 2.890483808581875 " " y[1] (numeric) = 2.8904838085823608 " " absolute error = 4.8583359557596850000000000000E-13 " " relative error = 1.680803726121986300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.249999999999754 " " y[1] (closed_form) = 2.894989358228474 " " y[1] (numeric) = 2.8949893582289605 " " absolute error = 4.8672177399566860000000000000E-13 " " relative error = 1.681255831259799700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.259999999999757 " " y[1] (closed_form) = 2.8994054096850714 " " y[1] (numeric) = 2.899405409685559 " " absolute error = 4.8760995241536875000000000000E-13 " " relative error = 1.68175844187423320000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.269999999999760 " " y[1] (closed_form) = 2.903731521350203 " " y[1] (numeric) = 2.9037315213506902 " " absolute error = 4.8716586320551870000000000000E-13 " " relative error = 1.677723507230420600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.279999999999764 " " y[1] (closed_form) = 2.9079672606163065 " " y[1] (numeric) = 2.9079672606167946 " " absolute error = 4.8805404162521880000000000000E-13 " " relative error = 1.6783340315935400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.289999999999767 " " y[1] (closed_form) = 2.9121122039129848 " " y[1] (numeric) = 2.912112203913474 " " absolute error = 4.893863092547690000000000000E-13 " " relative error = 1.680520100143064700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.299999999999770 " " y[1] (closed_form) = 2.916165936749363 " " y[1] (numeric) = 2.916165936749853 " " absolute error = 4.9027448767446913000000000000E-13 " " relative error = 1.68122973214952200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.309999999999774 " " y[1] (closed_form) = 2.920128053755535 " " y[1] (numeric) = 2.9201280537560264 " " absolute error = 4.9116266609416925000000000000E-13 " " relative error = 1.68199016293991600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.319999999999777 " " y[1] (closed_form) = 2.9239981587231028 " " y[1] (numeric) = 2.9239981587235953 " " absolute error = 4.9249493372371944000000000000E-13 " " relative error = 1.684320259417638700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.329999999999780 " " y[1] (closed_form) = 2.9277758646447936 " " y[1] (numeric) = 2.9277758646452874 " " absolute error = 4.9382720135326963000000000000E-13 " " relative error = 1.686697425566701400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.339999999999784 " " y[1] (closed_form) = 2.931460793753164 " " y[1] (numeric) = 2.931460793753659 " " absolute error = 4.9515946898281980000000000000E-13 " " relative error = 1.689121921869078400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.349999999999787 " " y[1] (closed_form) = 2.935052577558374 " " y[1] (numeric) = 2.93505257755887 " " absolute error = 4.9604764740251994000000000000E-13 " " relative error = 1.69008095866948500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.359999999999790 " " y[1] (closed_form) = 2.9385508568850356 " " y[1] (numeric) = 2.9385508568855334 " " absolute error = 4.9782400424192020000000000000E-13 " " relative error = 1.694113964628234000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.369999999999794 " " y[1] (closed_form) = 2.9419552819081316 " " y[1] (numeric) = 2.9419552819086316 " " absolute error = 5.0004445029117050000000000000E-13 " " relative error = 1.699701057205890400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.379999999999797 " " y[1] (closed_form) = 2.9452655121879974 " " y[1] (numeric) = 2.9452655121884987 " " absolute error = 5.0137671792072070000000000000E-13 " " relative error = 1.7023141575723500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.389999999999800 " " y[1] (closed_form) = 2.9484812167043626 " " y[1] (numeric) = 2.9484812167048657 " " absolute error = 5.0315307476012090000000000000E-13 " " relative error = 1.706482211619837200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.399999999999804 " " y[1] (closed_form) = 2.9516020738894557 " " y[1] (numeric) = 2.95160207388996 " " absolute error = 5.0448534238967110000000000000E-13 " " relative error = 1.709191583962023400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.409999999999807 " " y[1] (closed_form) = 2.954627771660159 " " y[1] (numeric) = 2.954627771660665 " " absolute error = 5.0581761001922130000000000000E-13 " " relative error = 1.711950367727743400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.419999999999810 " " y[1] (closed_form) = 2.9575580074492165 " " y[1] (numeric) = 2.957558007449724 " " absolute error = 5.0759396685862160000000000000E-13 " " relative error = 1.716260393135627400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.429999999999814 " " y[1] (closed_form) = 2.9603924882354917 " " y[1] (numeric) = 2.960392488236001 " " absolute error = 5.0937032369802180000000000000E-13 " " relative error = 1.72061753879677700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.439999999999817 " " y[1] (closed_form) = 2.9631309305732674 " " y[1] (numeric) = 2.963130930573779 " " absolute error = 5.1159076974727210000000000000E-13 " " relative error = 1.726520973031375200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.449999999999820 " " y[1] (closed_form) = 2.9657730606205925 " " y[1] (numeric) = 2.965773060621106 " " absolute error = 5.1336712658667240000000000000E-13 " " relative error = 1.73097238424321500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.459999999999824 " " y[1] (closed_form) = 2.9683186141666633 " " y[1] (numeric) = 2.968318614167179 " " absolute error = 5.1558757263592270000000000000E-13 " " relative error = 1.736968431135451600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.4699999999998274 " " y[1] (closed_form) = 2.970767336658247 " " y[1] (numeric) = 2.970767336658764 " " absolute error = 5.1691984026547290000000000000E-13 " " relative error = 1.740021286375610400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.479999999999830 " " y[1] (closed_form) = 2.9731189832251346 " " y[1] (numeric) = 2.973118983225654 " " absolute error = 5.1958437552457330000000000000E-13 " " relative error = 1.747607070070725500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.489999999999834 " " y[1] (closed_form) = 2.97537331870463 " " y[1] (numeric) = 2.975373318705152 " " absolute error = 5.2180482157382360000000000000E-13 " " relative error = 1.753745717532341200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.4999999999998375 " " y[1] (closed_form) = 2.977530117665063 " " y[1] (numeric) = 2.977530117665587 " " absolute error = 5.2402526762307390000000000000E-13 " " relative error = 1.75993271911555700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.509999999999840 " " y[1] (closed_form) = 2.9795891644283348 " " y[1] (numeric) = 2.9795891644288615 " " absolute error = 5.2668980288217430000000000000E-13 " " relative error = 1.7676591429786098000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.519999999999844 " " y[1] (closed_form) = 2.981550253091486 " " y[1] (numeric) = 2.981550253092014 " " absolute error = 5.2802207051172450000000000000E-13 " " relative error = 1.77096485281183200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.5299999999998475 " " y[1] (closed_form) = 2.983413187547283 " " y[1] (numeric) = 2.9834131875478134 " " absolute error = 5.3024251656097480000000000000E-13 " " relative error = 1.777301644888472600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.539999999999850 " " y[1] (closed_form) = 2.985177781503834 " " y[1] (numeric) = 2.9851777815043663 " " absolute error = 5.3246296261022510000000000000E-13 " " relative error = 1.783689286143580500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.549999999999854 " " y[1] (closed_form) = 2.986843858503213 " " y[1] (numeric) = 2.986843858503747 " " absolute error = 5.3423931944962530000000000000E-13 " " relative error = 1.788641605515150200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.5599999999998575 " " y[1] (closed_form) = 2.988411251939109 " " y[1] (numeric) = 2.9884112519396457 " " absolute error = 5.3690385470872570000000000000E-13 " " relative error = 1.796619706743312300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.569999999999860 " " y[1] (closed_form) = 2.989879805073484 " " y[1] (numeric) = 2.989879805074023 " " absolute error = 5.391243007579760000000000000E-13 " " relative error = 1.803163792213799700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.579999999999864 " " y[1] (closed_form) = 2.991249371052249 " " y[1] (numeric) = 2.9912493710527897 " " absolute error = 5.4045656838752620000000000000E-13 " " relative error = 1.806792083661706300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.5899999999998675 " " y[1] (closed_form) = 2.992519812919947 " " y[1] (numeric) = 2.9925198129204906 " " absolute error = 5.4356519285647660000000000000E-13 " " relative error = 1.81641301257114700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.599999999999870 " " y[1] (closed_form) = 2.99369100363345 " " y[1] (numeric) = 2.993691003633996 " " absolute error = 5.457856389057270000000000000E-13 " " relative error = 1.823119481079729400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.609999999999874 " " y[1] (closed_form) = 2.9947628260746626 " " y[1] (numeric) = 2.9947628260752115 " " absolute error = 5.4889426337467740000000000000E-13 " " relative error = 1.832847191088356500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.6199999999998775 " " y[1] (closed_form) = 2.995735173062234 " " y[1] (numeric) = 2.995735173062786 " " absolute error = 5.5200288784362780000000000000E-13 " " relative error = 1.84262912425390280000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.629999999999880 " " y[1] (closed_form) = 2.9966079473622758 " " y[1] (numeric) = 2.996607947362831 " " absolute error = 5.5511151231257830000000000000E-13 " " relative error = 1.852466262065438600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.639999999999884 " " y[1] (closed_form) = 2.9973810616980847 " " y[1] (numeric) = 2.997381061698643 " " absolute error = 5.5822013678152870000000000000E-13 " " relative error = 1.862359590893272500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.649999999999888 " " y[1] (closed_form) = 2.9980544387588726 " " y[1] (numeric) = 2.9980544387594334 " " absolute error = 5.6088467204062910000000000000E-13 " " relative error = 1.870828844164760300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.659999999999891 " " y[1] (closed_form) = 2.9986280112074932 " " y[1] (numeric) = 2.9986280112080577 " " absolute error = 5.6443738571942960000000000000E-13 " " relative error = 1.882318792493841000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.669999999999894 " " y[1] (closed_form) = 2.9991017216871803 " " y[1] (numeric) = 2.9991017216877482 " " absolute error = 5.6799009939823010000000000000E-13 " " relative error = 1.89386740466642300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.679999999999898 " " y[1] (closed_form) = 2.9994755228272805 " " y[1] (numeric) = 2.999475522827852 " " absolute error = 5.7154281307703060000000000000E-13 " " relative error = 1.905475836449897500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.689999999999901 " " y[1] (closed_form) = 2.9997493772479915 " " y[1] (numeric) = 2.9997493772485666 " " absolute error = 5.7509552675583110000000000000E-13 " " relative error = 1.917145249258893600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.699999999999904 " " y[1] (closed_form) = 2.9999232575640997 " " y[1] (numeric) = 2.999923257564678 " " absolute error = 5.7820415122478150000000000000E-13 " " relative error = 1.92739647511608700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.709999999999908 " " y[1] (closed_form) = 2.9999971463877175 " " y[1] (numeric) = 2.9999971463882997 " " absolute error = 5.8220095411343210000000000000E-13 " " relative error = 1.940671693019633300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.719999999999911 " " y[1] (closed_form) = 2.999971036330025 " " y[1] (numeric) = 2.9999710363306105 " " absolute error = 5.8530957858238250000000000000E-13 " " relative error = 1.95105076513809700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.729999999999914 " " y[1] (closed_form) = 2.999844930002006 " " y[1] (numeric) = 2.999844930002595 " " absolute error = 5.888622922611830000000000000E-13 " " relative error = 1.962975773753709900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.739999999999918 " " y[1] (closed_form) = 2.999618840014188 " " y[1] (numeric) = 2.9996188400147807 " " absolute error = 5.9285909514983360000000000000E-13 " " relative error = 1.976448098142460600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.749999999999921 " " y[1] (closed_form) = 2.9992927889753807 " " y[1] (numeric) = 2.9992927889759784 " " absolute error = 5.9774407645818430000000000000E-13 " " relative error = 1.992950066946901400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.759999999999924 " " y[1] (closed_form) = 2.998866809490418 " " y[1] (numeric) = 2.998866809491019 " " absolute error = 6.0129679013698480000000000000E-13 " " relative error = 2.005080013003845400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.769999999999928 " " y[1] (closed_form) = 2.998340944156892 " " y[1] (numeric) = 2.9983409441574964 " " absolute error = 6.0440541460593520000000000000E-13 " " relative error = 2.0157994899939200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.779999999999931 " " y[1] (closed_form) = 2.997715245560898 " " y[1] (numeric) = 2.9977152455615057 " " absolute error = 6.0751403907488570000000000000E-13 " " relative error = 2.026590217247984700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.789999999999934 " " y[1] (closed_form) = 2.9969897762717745 " " y[1] (numeric) = 2.996989776272386 " " absolute error = 6.1151084196353620000000000000E-13 " " relative error = 2.040416843611157200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.799999999999938 " " y[1] (closed_form) = 2.996164608835846 " " y[1] (numeric) = 2.9961646088364615 " " absolute error = 6.1550764485218680000000000000E-13 " " relative error = 2.054318521208823600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.809999999999941 " " y[1] (closed_form) = 2.9952398257691684 " " y[1] (numeric) = 2.995239825769788 " " absolute error = 6.1950444774083730000000000000E-13 " " relative error = 2.068296643263784200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.819999999999944 " " y[1] (closed_form) = 2.9942155195492774 " " y[1] (numeric) = 2.994215519549902 " " absolute error = 6.243894290491880000000000000E-13 " " relative error = 2.08531892568367300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.829999999999948 " " y[1] (closed_form) = 2.9930917926059415 " " y[1] (numeric) = 2.99309179260657 " " absolute error = 6.2838623193783860000000000000E-13 " " relative error = 2.099455263918694500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.839999999999951 " " y[1] (closed_form) = 2.991868757310919 " " y[1] (numeric) = 2.9918687573115514 " " absolute error = 6.3238303482648920000000000000E-13 " " relative error = 2.113672377109458400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.849999999999954 " " y[1] (closed_form) = 2.9905465359667196 " " y[1] (numeric) = 2.990546535967357 " " absolute error = 6.3726801613483990000000000000E-13 " " relative error = 2.130941647189039700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.859999999999958 " " y[1] (closed_form) = 2.989125260794376 " " y[1] (numeric) = 2.989125260795018 " " absolute error = 6.4215299744319050000000000000E-13 " " relative error = 2.148297382735091500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.869999999999961 " " y[1] (closed_form) = 2.9876050739202213 " " y[1] (numeric) = 2.987605073920868 " " absolute error = 6.4659388954169120000000000000E-13 " " relative error = 2.164254891605386600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.879999999999964 " " y[1] (closed_form) = 2.9859861273616763 " " y[1] (numeric) = 2.9859861273623274 " " absolute error = 6.5103478164019180000000000000E-13 " " relative error = 2.180300757845200200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.889999999999968 " " y[1] (closed_form) = 2.9842685830120472 " " y[1] (numeric) = 2.9842685830127036 " " absolute error = 6.5636385215839250000000000000E-13 " " relative error = 2.199412800492370800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.899999999999971 " " y[1] (closed_form) = 2.982452612624338 " " y[1] (numeric) = 2.982452612624999 " " absolute error = 6.6124883346674320000000000000E-13 " " relative error = 2.217131064103959300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.909999999999974 " " y[1] (closed_form) = 2.980538397794074 " " y[1] (numeric) = 2.9805383977947404 " " absolute error = 6.665779039849440000000000000E-13 " " relative error = 2.236434546450685000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.919999999999978 " " y[1] (closed_form) = 2.978526129941143 " " y[1] (numeric) = 2.978526129941814 " " absolute error = 6.7101879608344460000000000000E-13 " " relative error = 2.252855159933427300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.929999999999981 " " y[1] (closed_form) = 2.976416010290654 " " y[1] (numeric) = 2.97641601029133 " " absolute error = 6.7590377739179530000000000000E-13 " " relative error = 2.270864607148083700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.939999999999984 " " y[1] (closed_form) = 2.9742082498528126 " " y[1] (numeric) = 2.9742082498534943 " " absolute error = 6.8167693711984610000000000000E-13 " " relative error = 2.291961019049627600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.949999999999988 " " y[1] (closed_form) = 2.9719030694018236 " " y[1] (numeric) = 2.9719030694025106 " " absolute error = 6.8700600763804690000000000000E-13 " " relative error = 2.311670305506718600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.959999999999991 " " y[1] (closed_form) = 2.969500699453811 " " y[1] (numeric) = 2.969500699454503 " " absolute error = 6.9189098894639760000000000000E-13 " " relative error = 2.329990995030441200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.969999999999994 " " y[1] (closed_form) = 2.9670013802437674 " " y[1] (numeric) = 2.967001380244465 " " absolute error = 6.9766414867444840000000000000E-13 " " relative error = 2.35141160809682100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.979999999999998 " " y[1] (closed_form) = 2.964405361701531 " " y[1] (numeric) = 2.9644053617022346 " " absolute error = 7.0343730840249920000000000000E-13 " " relative error = 2.37294574315145300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.990000000000001 " " y[1] (closed_form) = 2.9617129034267933 " " y[1] (numeric) = 2.9617129034275016 " " absolute error = 7.0832228971084990000000000000E-13 " " relative error = 2.391596730700329400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " "Finished!" "diff ( y , x , 2 ) = sin ( x ) ; " Iterations = 4900 "Total Elapsed Time "= 2 Minutes 27 Seconds "Elapsed Time(since restart) "= 2 Minutes 27 Seconds "Time to Timeout "= 32 Seconds Percent Done = 100.0204081632654 "%" (%o254) temp/diffeq.h2sin.max