(%i1) batch("temp/diffeq.div_lin_lin.max") read and interpret file: /home/dennis/src/mine/omni/testtar/omnisode0060dir/temp/diffeq.div_lin_lin.max (%i2) load("stringproc") (%i3) keepfloat:true (%i4) alias(convfloat,float) (%i5) alias(int_trunc,truncate) (%i6) alias(elapsed_time_seconds,elapsed_real_time) (%i7) alias(ln,log) (%i8) alias(arcsin,asin) (%i9) alias(arccos,acos) (%i10) alias(arctan,atan) (%i11) alias(float_abs,abs) (%i12) mode_declare(display_poles(),fixnum) (%i13) mode_declare(est_size_answer(),convfloat) (%i14) mode_declare(test_suggested_h(),convfloat) (%i15) mode_declare(reached_interval(),boolean) (%i16) mode_declare(display_alot([iter],fixnum),fixnum) (%i17) mode_declare(prog_report([x_start],convfloat,[x_end],convfloat),fixnum) (%i18) mode_declare(check_for_pole(),fixnum) (%i19) mode_declare(atomall(),fixnum) (%i20) mode_declare(log10([x],convfloat),convfloat) (%i21) mode_declare(logitem_timestr([fd],fixnum,[secs_in],number),fixnum) (%i22) mode_declare(omniout_timestr(secs_in,number),fixnum) (%i23) mode_declare(zero_ats_ar(ar,array([30],convfloat)),fixnum) (%i24) mode_declare(ats([mmm_ats],fixnum,[arr_a], completearray([30],convfloat),[arr_b], completearray([30],convfloat),[jjj_ats],fixnum), convfloat) (%i25) mode_declare(att([mmm_att],fixnum,[arr_a], completearray([30],convfloat),[arr_b], completearray([30],convfloat),[jjj_att],fixnum), convfloat) (%i26) mode_declare(logitem_ditto([file],fixnum),fixnum) (%i27) mode_declare(logitem_integer([file],fixnum,[n],fixnum),fixnum) (%i28) mode_declare(logitem_good_digits([file],fixnum,[relerror],convfloat),fixnum) (%i29) mode_declare(logitem_number([file],fixnum,[x],number),fixnum) (%i30) mode_declare(logitem_pole([file],fixnum,[pole],fixnum),fixnum) (%i31) mode_declare(logstart([file],fixnum),fixnum) (%i32) mode_declare(logend([file],fixnum),fixnum) (%i33) mode_declare(chk_data(),fixnum) (%i34) mode_declare(comp_expect_sec([t_end2],convfloat,[t_start2],convfloat, [t2],convfloat,[clock_sec2],convfloat), convfloat) (%i35) mode_declare(comp_percent([t_end2],convfloat,[start2],convfloat,[t2], convfloat),convfloat) (%i36) mode_declare(comp_rad_from_ratio([term1],convfloat,[term2],convfloat, [last_no],fixnum),convfloat) (%i37) mode_declare(comp_ord_from_ratio([term1],convfloat,[term2],convfloat, [last_no],fixnum),convfloat) (%i38) mode_declare(comp_rad_from_three_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [last_no],fixnum),convfloat) (%i39) mode_declare(comp_ord_from_three_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [last_no],fixnum),convfloat) (%i40) mode_declare(comp_rad_from_six_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [term4],convfloat,[term5], convfloat,[term6],convfloat, [last_no],fixnum),convfloat) (%i41) mode_declare(comp_ord_from_six_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [term4],convfloat,[term5], convfloat,[term6],convfloat, [last_no],fixnum),convfloat) (%i42) mode_declare(neg([nnn],convfloat),convfloat) (%i43) mode_declare(factorial_2([nnn],fixnum),convfloat) (%i44) mode_declare(factorial_1([nnn],fixnum),convfloat) (%i45) mode_declare(factorial_3([mmm],fixnum,[nnn],fixnum),convfloat) (%i46) mode_declare(convfloat([mmm],fixnum),convfloat) (%i47) mode_declare(elaped_time_seconds(),convfloat) (%i48) mode_declare(Si([x],convfloat),convfloat) (%i49) mode_declare(Ci([x],convfloat),convfloat) (%i50) mode_declare(estimated_needed_step_error([x_start],convfloat,[x_end], convfloat,[estimated_h], convfloat,[estimated_answer], convfloat),convfloat) (%i51) mode_declare(my_check_sign([x0],convfloat,[xf],convfloat),convfloat) (%i52) mode_declare(main_prog(),fixnum) (%i53) define_variable(always,1,fixnum) (%i54) define_variable(info,2,fixnum) (%i55) define_variable(debugl,3,fixnum) (%i56) define_variable(debugmassive,4,fixnum) (%i57) define_variable(glob_iolevel,5,fixnum) (%i58) define_variable(glob_yes_pole,4,fixnum) (%i59) define_variable(glob_no_pole,3,fixnum) (%i60) define_variable(glob_not_given,0,fixnum) (%i61) define_variable(glob_no_sing_tests,4,fixnum) (%i62) define_variable(glob_ratio_test,1,fixnum) (%i63) define_variable(glob_three_term_test,2,fixnum) (%i64) define_variable(glob_six_term_test,3,fixnum) (%i65) define_variable(ats_max_terms,30,fixnum) (%i66) define_variable(glob_log_10,0.0,convfloat) (%i67) define_variable(max_unchanged,10,fixnum) (%i68) define_variable(glob__small,1.0E-51,convfloat) (%i69) define_variable(glob_small_float,1.0E-51,convfloat) (%i70) define_variable(glob_smallish_float,1.0E-61,convfloat) (%i71) define_variable(glob_large_float,1.0E+100,convfloat) (%i72) define_variable(glob_larger_float,1.1E+100,convfloat) (%i73) define_variable(glob__m2,-2.0,convfloat) (%i74) define_variable(glob__m1,-1.0,convfloat) (%i75) define_variable(glob__0,0.0,convfloat) (%i76) define_variable(glob__1,1.0,convfloat) (%i77) define_variable(glob__2,2.0,convfloat) (%i78) define_variable(glob__3,3.0,convfloat) (%i79) define_variable(glob__4,4.0,convfloat) (%i80) define_variable(glob__5,5.0,convfloat) (%i81) define_variable(glob__8,8.0,convfloat) (%i82) define_variable(glob__10,10.0,convfloat) (%i83) define_variable(glob__100,100.0,convfloat) (%i84) define_variable(glob__pi,0.0,convfloat) (%i85) define_variable(glob__0_5,0.5,convfloat) (%i86) define_variable(glob__0_8,0.8,convfloat) (%i87) define_variable(glob__m0_8,-0.8,convfloat) (%i88) define_variable(glob__0_25,0.25,convfloat) (%i89) define_variable(glob__0_125,0.125,convfloat) (%i90) define_variable(glob_prec,1.0E-16,convfloat) (%i91) define_variable(glob_check_sign,1.0,convfloat) (%i92) define_variable(glob_desired_digits_correct,8.0,convfloat) (%i93) define_variable(glob_max_estimated_step_error,0.0,convfloat) (%i94) define_variable(glob_ratio_of_radius,0.1,convfloat) (%i95) define_variable(glob_percent_done,0.0,convfloat) (%i96) define_variable(glob_total_exp_sec,0.1,convfloat) (%i97) define_variable(glob_optimal_expect_sec,0.1,convfloat) (%i98) define_variable(glob_estimated_size_answer,100.0,convfloat) (%i99) define_variable(glob_almost_1,0.999,convfloat) (%i100) define_variable(glob_clock_sec,0.0,convfloat) (%i101) define_variable(glob_clock_start_sec,0.0,convfloat) (%i102) define_variable(glob_disp_incr,0.1,convfloat) (%i103) define_variable(glob_h,0.1,convfloat) (%i104) define_variable(glob_diff_rc_fm,0.1,convfloat) (%i105) define_variable(glob_diff_rc_fmm1,0.1,convfloat) (%i106) define_variable(glob_diff_rc_fmm2,0.1,convfloat) (%i107) define_variable(glob_diff_ord_fm,0.1,convfloat) (%i108) define_variable(glob_diff_ord_fmm1,0.1,convfloat) (%i109) define_variable(glob_diff_ord_fmm2,0.1,convfloat) (%i110) define_variable(glob_six_term_ord_save,0.1,convfloat) (%i111) define_variable(glob_guess_error_rc,0.1,convfloat) (%i112) define_variable(glob_guess_error_ord,0.1,convfloat) (%i113) define_variable(glob_least_given_sing,9.9E+200,convfloat) (%i114) define_variable(glob_least_ratio_sing,9.9E+200,convfloat) (%i115) define_variable(glob_least_3_sing,9.9E+100,convfloat) (%i116) define_variable(glob_least_6_sing,9.9E+100,convfloat) (%i117) define_variable(glob_last_good_h,0.1,convfloat) (%i118) define_variable(glob_max_h,0.1,convfloat) (%i119) define_variable(glob_min_h,1.0E-6,convfloat) (%i120) define_variable(glob_display_interval,0.1,convfloat) (%i121) define_variable(glob_abserr,1.0E-11,convfloat) (%i122) define_variable(glob_relerr,1.0E-11,convfloat) (%i123) define_variable(glob_min_pole_est,1.0E+9,convfloat) (%i124) define_variable(glob_max_rel_trunc_err,1.0E-11,convfloat) (%i125) define_variable(glob_max_trunc_err,1.0E-11,convfloat) (%i126) define_variable(glob_max_hours,0.0,convfloat) (%i127) define_variable(glob_optimal_clock_start_sec,0.0,convfloat) (%i128) define_variable(glob_optimal_start,0.0,convfloat) (%i129) define_variable(glob_upper_ratio_limit,1.0001,convfloat) (%i130) define_variable(glob_lower_ratio_limit,0.9999,convfloat) (%i131) define_variable(glob_max_sec,10000.0,convfloat) (%i132) define_variable(glob_orig_start_sec,0.0,convfloat) (%i133) define_variable(glob_normmax,0.0,convfloat) (%i134) define_variable(glob_max_minutes,0.0,convfloat) (%i135) define_variable(glob_next_display,0.0,convfloat) (%i136) define_variable(glob_est_digits,1,fixnum) (%i137) define_variable(glob_subiter_method,3,fixnum) (%i138) define_variable(glob_html_log,true,boolean) (%i139) define_variable(glob_min_good_digits,99999,fixnum) (%i140) define_variable(glob_good_digits,0,fixnum) (%i141) define_variable(glob_min_apfp_est_good_digits,99999,fixnum) (%i142) define_variable(glob_apfp_est_good_digits,0,fixnum) (%i143) define_variable(glob_max_opt_iter,10,fixnum) (%i144) define_variable(glob_dump,false,boolean) (%i145) define_variable(glob_djd_debug,true,boolean) (%i146) define_variable(glob_display_flag,true,boolean) (%i147) define_variable(glob_djd_debug2,true,boolean) (%i148) define_variable(glob_h_reason,0,fixnum) (%i149) define_variable(glob_sec_in_minute,60,fixnum) (%i150) define_variable(glob_min_in_hour,60,fixnum) (%i151) define_variable(glob_hours_in_day,24,fixnum) (%i152) define_variable(glob_days_in_year,365,fixnum) (%i153) define_variable(glob_sec_in_hour,3600,fixnum) (%i154) define_variable(glob_sec_in_day,86400,fixnum) (%i155) define_variable(glob_sec_in_year,31536000,fixnum) (%i156) define_variable(glob_not_yet_finished,true,boolean) (%i157) define_variable(glob_initial_pass,true,boolean) (%i158) define_variable(glob_not_yet_start_msg,true,boolean) (%i159) define_variable(glob_reached_optimal_h,false,boolean) (%i160) define_variable(glob_optimal_done,false,boolean) (%i161) define_variable(glob_type_given_pole,0,fixnum) (%i162) define_variable(glob_optimize,false,boolean) (%i163) define_variable(glob_look_poles,false,boolean) (%i164) define_variable(glob_dump_closed_form,false,boolean) (%i165) define_variable(glob_max_iter,1000,fixnum) (%i166) define_variable(glob_no_eqs,0,fixnum) (%i167) define_variable(glob_unchanged_h_cnt,0,fixnum) (%i168) define_variable(glob_warned,false,boolean) (%i169) define_variable(glob_warned2,false,boolean) (%i170) define_variable(glob_start,0,fixnum) (%i171) define_variable(glob_iter,0,fixnum) (%i172) completearray(array_y_init,[30],convfloat) (%i173) completearray(array_norms,[30],convfloat) (%i174) completearray(array_fact_1,[30],convfloat) (%i175) completearray(array_1st_rel_error,[2],convfloat) (%i176) completearray(array_last_rel_error,[2],convfloat) (%i177) completearray(array_est_rel_error,[2],convfloat) (%i178) completearray(array_max_est_error,[2],convfloat) (%i179) completearray(array_type_pole,[2],convfloat) (%i180) completearray(array_type_real_pole,[2],convfloat) (%i181) completearray(array_type_complex_pole,[2],convfloat) (%i182) completearray(array_est_digits,[2],convfloat) (%i183) completearray(array_y,[30],convfloat) (%i184) completearray(array_x,[30],convfloat) (%i185) completearray(array_tmp0,[30],convfloat) (%i186) completearray(array_tmp1,[30],convfloat) (%i187) completearray(array_tmp2,[30],convfloat) (%i188) completearray(array_tmp3,[30],convfloat) (%i189) completearray(array_tmp4,[30],convfloat) (%i190) completearray(array_tmp5,[30],convfloat) (%i191) completearray(array_tmp6,[30],convfloat) (%i192) completearray(array_m1,[30],convfloat) (%i193) completearray(array_y_higher,[2,30],convfloat) (%i194) completearray(array_y_higher_work,[2,30],convfloat) (%i195) completearray(array_y_higher_work2,[2,30],convfloat) (%i196) completearray(array_y_set_initial,[2,30],convfloat) (%i197) completearray(array_given_rad_poles,[2,3],convfloat) (%i198) completearray(array_given_ord_poles,[2,3],convfloat) (%i199) completearray(array_rad_test_poles,[2,4],convfloat) (%i200) completearray(array_ord_test_poles,[2,4],convfloat) (%i201) completearray(array_fact_2,[30,30],convfloat) (%i202) omniout_str(iolevel,str):=if glob_iolevel >= iolevel then printf(true,"~a~%",string(str)) (%i203) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel then printf(true,"~a",string(str)) (%i204) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel then printf(true,"~a = ~a~%",string(label), string(str)) (%i205) 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)) (%i206) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if glob_iolevel >= iolevel then (printf(true,"~a = ~d ~a~%",prelabel,value, postlabel),newline()) (%i207) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen, postlabel):=if glob_iolevel >= iolevel then (sprint(prelabel,"[",elemnt,"]=",value, postlabel),newline()) (%i208) 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) (%i209) 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) (%i210) 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) (%i211) 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) (%i212) 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) (%i213) logditto(file):=(printf(file,""),printf(file,"ditto"), printf(file,""),0) (%i214) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n), printf(file,""),0) (%i215) logitem_str(file,str):=(printf(file,""),printf(file,str), printf(file,""),0) (%i216) logitem_good_digits(file,rel_error):=( block(mode_declare([[good_digits],fixnum]), printf(file,""), printf(file,"~d",glob_min_good_digits), printf(file,"")),0) (%i217) log_revs(file,revs):=printf(file,revs) (%i218) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x), printf(file,""),0) (%i219) 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) (%i220) logstart(file):=(printf(file,""),0) (%i221) logend(file):=(printf(file,"~%"),0) (%i222) 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) (%i223) 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) (%i224) 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) (%i225) 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) (%i226) 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) (%i227) c(in_val):=(ret:in_val,ret) (%i228) 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) (%i229) 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) (%i230) 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) (%i231) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save (%i232) factorial_2(nnn):=block(mode_declare([[ret],convfloat]),ret:nnn!,ret) (%i233) 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) (%i234) factorial_1(in):=block(mode_declare([[ret],convfloat]),ret:in!,ret) (%i235) neg(in):=block(mode_declare([[ret],convfloat]),ret:-in,ret) (%i236) 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) (%i237) log10(x):=log(x)/glob_log_10 (%i238) c(x):=x (%i239) 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 (%i240) 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) (%i241) exact_soln_y(x):=block(c(0.25)*log(c(3.0)+c(2.0)*c(x))+c(0.5)*c(x)) (%o241) exact_soln_y(x) := block(c(0.25) log(c(3.0) + c(2.0) c(x)) + c(0.5) c(x)) (%i242) 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) (%i243) my_check_sign(x0,xf):=block([ret], if xf > x0 then ret:glob__1 else ret:glob__m1,ret) (%i244) 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) (%i245) 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) (%i246) 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)) (%i247) 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)) (%i248) 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(28) *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) (%i249) 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) (%i250) check_for_pole():=( block(mode_declare([cnt],fixnum,[dr1,dr2,ds1,ds2,hdrc], convfloat,[m,n],fixnum,[nr1,nr2], convfloat,[ord_no],fixnum, [term1,term2,term3,part1,part2, part3,part4,part5,part6,part7, part8,part9,part10,part11,part12, part13,part14,rad_c,rcs,rm0,rm1, rm2,rm3,rm4],convfloat, [found_sing],fixnum, [h_new,ratio,term,local_test, tmp_rad,tmp_ord,tmp_ratio, prev_tmp_rad],convfloat,[last_no], fixnum),tmp_rad:glob_larger_float, prev_tmp_rad:glob_larger_float, tmp_ratio:glob_larger_float, rad_c:glob_larger_float, array_rad_test_poles[1,1]:glob_larger_float, array_ord_test_poles[1,1]:glob_larger_float, found_sing:1,last_no:-10-1+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:-10-1+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:-10-1+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) (%i251) atomall():=( block(mode_declare([[kkk,order_d],fixnum, [adj2,adj3,temporary,term,temp,temp2], convfloat]), array_tmp1[1]:array_const_0D1[1]*array_x[1], array_tmp2[1]:array_const_0D2[1]+array_tmp1[1], array_tmp3[1]:array_const_0D2[1]*array_x[1], array_tmp4[1]:array_const_0D3[1]+array_tmp3[1], array_tmp5[1]:array_tmp2[1]/array_tmp4[1], array_tmp6[1]:array_tmp5[1]+array_const_0D0[1], if not array_y_set_initial[1,2] then (if 1 <= ats_max_terms then ( temporary :c(array_tmp6[1])*expt(glob_h,c(1)) *c(factorial_3(0,1)), if 2 <= ats_max_terms then (array_y[2]:temporary, array_y_higher[1,2]:temporary), temporary:c(temporary)*c(1)/c(glob_h), array_y_higher[2,1]:c(temporary),0)), kkk:2,array_tmp1[2]:array_const_0D1[1]*array_x[2], array_tmp2[2]:array_tmp1[2], array_tmp3[2]:array_const_0D2[1]*array_x[2], array_tmp4[2]:array_tmp3[2], array_tmp5[2]:(array_tmp2[2] -array_tmp5[1]*array_tmp4[2]) /array_tmp4[1], array_tmp6[2]:array_tmp5[2], if not array_y_set_initial[1,3] then (if 2 <= ats_max_terms then ( temporary :c(array_tmp6[2])*expt(glob_h,c(1)) *c(factorial_3(1,2)), 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),0)), kkk:3, array_tmp5[3]:neg(array_tmp5[2])*array_tmp4[2] /array_tmp4[1], array_tmp6[3]:array_tmp5[3], if not array_y_set_initial[1,4] then (if 3 <= ats_max_terms then ( temporary :c(array_tmp6[3])*expt(glob_h,c(1)) *c(factorial_3(2,3)), 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),0)), kkk:4, array_tmp5[4]:neg(array_tmp5[3])*array_tmp4[2] /array_tmp4[1], array_tmp6[4]:array_tmp5[4], if not array_y_set_initial[1,5] then (if 4 <= ats_max_terms then ( temporary :c(array_tmp6[4])*expt(glob_h,c(1)) *c(factorial_3(3,4)), 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),0)), kkk:5, array_tmp5[5]:neg(array_tmp5[4])*array_tmp4[2] /array_tmp4[1], array_tmp6[5]:array_tmp5[5], if not array_y_set_initial[1,6] then (if 5 <= ats_max_terms then ( temporary :c(array_tmp6[5])*expt(glob_h,c(1)) *c(factorial_3(4,5)), 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),0)), kkk:6, while kkk <= ats_max_terms do (array_tmp5[kkk] :neg(array_tmp5[kkk-1])*array_tmp4[2] /array_tmp4[1],array_tmp6[kkk]:array_tmp5[kkk], order_d:1, if order_d+kkk <= ats_max_terms then (if not array_y_set_initial[1,order_d+kkk] then ( temporary :c(array_tmp6[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) (%i252) exact_soln_y(x):=block(c(0.25)*log(c(3.0)+c(2.0)*c(x))+c(0.5)*c(x)) (%o252) exact_soln_y(x) := block(c(0.25) log(c(3.0) + c(2.0) c(x)) + c(0.5) c(x)) (%i253) main_prog():=block( mode_declare([[d1,d2,d3,d4,est_err_2,display_max],convfloat, [niii,done_once,term,ord,order_diff,term_no, html_log_file,iiif,jjjf,rows,r_order, sub_iter,calc_term,iii],fixnum,[temp_sum], convfloat,[current_iter],fixnum, [x_start,x_end],convfloat,[it,opt_iter], fixnum,[tmp],convfloat,[subiter],fixnum, [est_needed_step_err,estimated_step_error, min_value,est_answer,last_min_pole_est], convfloat,[repeat_it],fixnum],[found_h], boolean),Digits:32,max_terms:30, glob_html_log:true,term:1, while term <= 30 do (array_y_init[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_norms[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_fact_1[term]:c(0.0),term:1+term), term:1, while term <= 2 do (array_1st_rel_error[term]:c(0.0),term:1+term),term:1, while term <= 2 do (array_last_rel_error[term]:c(0.0),term:1+term), term:1, while term <= 2 do (array_est_rel_error[term]:c(0.0),term:1+term),term:1, while term <= 2 do (array_max_est_error[term]:c(0.0),term:1+term),term:1, while term <= 2 do (array_type_pole[term]:0,term:1+term), term:1, while term <= 2 do (array_type_real_pole[term]:0,term:1+term),term:1, while term <= 2 do (array_type_complex_pole[term]:0,term:1+term),term:1, while term <= 2 do (array_est_digits[term]:0,term:1+term), term:1, while term <= 30 do (array_y[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_x[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_tmp0[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_tmp1[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_tmp2[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_tmp3[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_tmp4[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_tmp5[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_tmp6[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_m1[term]:c(0.0),term:1+term), ord:1, while ord <= 2 do (term:1, while term <= 30 do (array_y_higher[ord,term]:c(0.0),term:1+term), ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 30 do (array_y_higher_work[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 30 do (array_y_higher_work2[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 30 do (array_y_set_initial[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 3 do (array_given_rad_poles[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 3 do (array_given_ord_poles[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 4 do (array_rad_test_poles[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 4 do (array_ord_test_poles[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 30 do (term:1, while term <= 30 do (array_fact_2[ord,term]:c(0.0),term:1+term), ord:1+ord),zero_ats_ar(array_y),zero_ats_ar(array_x), zero_ats_ar(array_tmp0),zero_ats_ar(array_tmp1), zero_ats_ar(array_tmp2),zero_ats_ar(array_tmp3), zero_ats_ar(array_tmp4),zero_ats_ar(array_tmp5), zero_ats_ar(array_tmp6),zero_ats_ar(array_m1), zero_ats_ar(array_const_1),array_const_1[1]:c(1), zero_ats_ar(array_const_0D0),array_const_0D0[1]:c(0.0), zero_ats_ar(array_const_0D1),array_const_0D1[1]:c(0.1), zero_ats_ar(array_const_0D2),array_const_0D2[1]:c(0.2), zero_ats_ar(array_const_0D3),array_const_0D3[1]:c(0.3), 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]:false, array_y_set_initial[1,3]:false, array_y_set_initial[1,4]:false, array_y_set_initial[1,5]:false, array_y_set_initial[1,6]:false, array_y_set_initial[1,7]:false, array_y_set_initial[1,8]:false, array_y_set_initial[1,9]:false, array_y_set_initial[1,10]:false, array_y_set_initial[1,11]:false, array_y_set_initial[1,12]:false, array_y_set_initial[1,13]:false, array_y_set_initial[1,14]:false, array_y_set_initial[1,15]:false, array_y_set_initial[1,16]:false, array_y_set_initial[1,17]:false, array_y_set_initial[1,18]:false, array_y_set_initial[1,19]:false, array_y_set_initial[1,20]:false, array_y_set_initial[1,21]:false, array_y_set_initial[1,22]:false, array_y_set_initial[1,23]:false, array_y_set_initial[1,24]:false, array_y_set_initial[1,25]:false, array_y_set_initial[1,26]:false, array_y_set_initial[1,27]:false, array_y_set_initial[1,28]:false, array_y_set_initial[1,29]:false, array_y_set_initial[1,30]:false,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/div_lin_linpostode.ode#################"), omniout_str(always, "diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) / ( 0.2 * x + 0.3 ) ; "), omniout_str(always,"!"), omniout_str(always,"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(always,"Digits:32,"), omniout_str(always,"max_terms:30,"),omniout_str(always,"!"), omniout_str(always,"/* END FIRST INPUT BLOCK */"), omniout_str(always,"/* BEGIN SECOND INPUT BLOCK */"), omniout_str(always,"x_start:c(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,"glob_look_poles:true,"), omniout_str(always,""),omniout_str(always,""), omniout_str(always,""),omniout_str(always,""), omniout_str(always,""),omniout_str(always,""), omniout_str(always,""),omniout_str(always,""), omniout_str(always,"glob_type_given_pole:1,"), omniout_str(always,""), omniout_str(always,"array_given_rad_poles[1,1]:c(-1.5),"), omniout_str(always,""), omniout_str(always,"array_given_rad_poles[1,2]:c(0.0),"), omniout_str(always,""), omniout_str(always,"array_given_ord_poles[1,1]:c(1.0),"), omniout_str(always,""), omniout_str(always,"array_given_ord_poles[1,2]:c(0.0),"), 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,""), omniout_str(always, " (c(0.5) * c(x) + c(0.25) * ln(c(2.0) * c(x) + c(3.0))) "), 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), glob_look_poles:true,glob_type_given_pole:1, array_given_rad_poles[1,1]:c(-1.5), array_given_rad_poles[1,2]:c(0.0), array_given_ord_poles[1,1]:c(1.0), array_given_ord_poles[1,2]:c(0.0), 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:1, 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:1, 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:2,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: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 , 1 ) = ( 0.1 * x + 0.2 ) / ( 0.2 * x + 0.3 ) ; "), omniout_int(info, "Iterations ",32, glob_iter,4," "), prog_report(x_start,x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2015-04-24T20:52:37-05:00"), logitem_str(html_log_file,"Maxima"), logitem_str(html_log_file, "div_lin_lin"), logitem_str(html_log_file, "diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) / ( 0.2 * x + 0.3 ) ; "), 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, "div_lin_lin diffeq.max"), logitem_str(html_log_file, "div_lin_lin maxima results"), logitem_str(html_log_file,"OK"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%i254) main():=(glob_iolevel:2,compile(all),main_prog()) (%i255) main() warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable secs in translation. warning: encountered undefined variable glob_sec_in_year in translation. warning: encountered undefined variable sec_temp in translation. warning: encountered undefined variable glob_sec_in_day in translation. warning: encountered undefined variable glob_sec_in_hour in translation. warning: encountered undefined variable glob_sec_in_minute in translation. warning: encountered undefined variable years_int in translation. warning: encountered undefined variable days_int in translation. warning: encountered undefined variable hours_int in translation. warning: encountered undefined variable minutes_int in translation. warning: encountered undefined variable sec_int in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob_sec_in_year in translation. warning: encountered undefined variable glob_sec_in_day in translation. warning: encountered undefined variable glob_sec_in_hour in translation. warning: encountered undefined variable glob_sec_in_minute in translation. warning: encountered undefined variable iii in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable glob__0 in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable iii_ats in translation. warning: encountered undefined variable ma_ats in translation. warning: encountered undefined variable ret_ats in translation. warning: encountered undefined variable lll_ats in translation. warning: encountered undefined variable ats_max_terms in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable iii_att in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable ma_att in translation. warning: encountered undefined variable lll_att in translation. warning: encountered undefined variable ret_att in translation. warning: encountered undefined variable al_att in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob_min_good_digits in translation. warning: encountered undefined variable glob_h_reason in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable always in translation. warning: encountered undefined variable glob_max_iter in translation. warning: encountered undefined variable errflag in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable sub1 in translation. warning: encountered undefined variable sub2 in translation. warning: encountered undefined variable rrr in translation. warning: encountered undefined variable ms2 in translation. warning: encountered undefined variable sec_left in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob__100 in translation. warning: encountered undefined variable glob_small_float in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable ret in translation. warning: encountered undefined variable glob__1 in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable glob__m2 in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable temp in translation. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable glob__4 in translation. warning: encountered undefined variable glob__3 in translation. warning: encountered undefined variable glob__2 in translation. warning: encountered undefined variable rm0 in translation. warning: encountered undefined variable glob__2 in translation. warning: encountered undefined variable rm1 in translation. warning: encountered undefined variable rm2 in translation. warning: encountered undefined variable rm3 in translation. warning: encountered undefined variable glob__m1 in translation. warning: encountered undefined variable glob__1 in translation. warning: encountered undefined variable rm4 in translation. warning: encountered undefined variable glob__3 in translation. warning: encountered undefined variable glob__8 in translation. warning: encountered undefined variable glob__5 in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable nr1 in translation. warning: encountered undefined variable dr2 in translation. warning: encountered undefined variable nr2 in translation. warning: encountered undefined variable dr1 in translation. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable ds1 in translation. warning: encountered undefined variable ds2 in translation. warning: encountered undefined variable rcs in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable ord_no in translation. warning: variable glob_six_term_ord_save (declared type convfloat) assigned type any. warning: encountered undefined variable rad_c in translation. warning: encountered undefined variable glob_six_term_ord_save in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable array_fact_2 in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable glob_log_10 in translation. warning: encountered undefined variable always in translation. warning: encountered undefined variable glob_desired_digits_correct in translation. warning: encountered undefined variable glob__10 in translation. warning: encountered undefined variable ats_max_terms in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable array_x in translation. warning: encountered undefined variable array_given_rad_poles in translation. warning: encountered undefined variable always in translation. warning: encountered undefined variable rad_given in translation. warning: encountered undefined variable array_given_ord_poles in translation. warning: variable glob_least_given_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_given_sing in translation. warning: encountered undefined variable glob_type_given_pole in translation. warning: encountered undefined variable array_rad_test_poles in translation. warning: variable glob_least_ratio_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_ratio_sing in translation. warning: encountered undefined variable array_ord_test_poles in translation. warning: encountered undefined variable glob_large_float in translation. warning: variable glob_least_3_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_3_sing in translation. warning: encountered undefined variable glob__small in translation. warning: variable glob_least_6_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_6_sing in translation. warning: encountered undefined variable glob__1 in translation. warning: encountered undefined variable glob__m1 in translation. warning: encountered undefined variable glob_estimated_size_answer in translation. warning: encountered undefined variable array_y in translation. warning: encountered undefined variable always in translation. warning: encountered undefined variable glob__1 in translation. warning: encountered undefined variable glob__small in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable glob__0_5 in translation. warning: encountered undefined variable glob__0_25 in translation. warning: encountered undefined variable glob__0_125 in translation. warning: encountered undefined variable always in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable glob__0_5 in translation. warning: encountered undefined variable glob__0_25 in translation. warning: encountered undefined variable glob__0_125 in translation. warning: encountered undefined variable glob_prec in translation. warning: encountered undefined variable array_max_est_error in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob_check_sign in translation. warning: encountered undefined variable glob_next_display in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob__10 in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable always in translation. warning: encountered undefined variable ind_var in translation. warning: encountered undefined variable closed_form_val_y in translation. warning: encountered undefined variable term_no in translation. warning: encountered undefined variable numeric_val in translation. warning: encountered undefined variable abserr in translation. warning: encountered undefined variable glob__100 in translation. warning: encountered undefined variable relerr in translation. warning: variable glob_good_digits (declared type fixnum) assigned type any. warning: encountered undefined variable glob_prec in translation. warning: encountered undefined variable glob__m1 in translation. warning: encountered undefined variable glob_good_digits in translation. warning: encountered undefined variable glob_min_good_digits in translation. warning: encountered undefined variable glob_apfp_est_good_digits in translation. warning: encountered undefined variable glob_min_apfp_est_good_digits in translation. warning: encountered undefined variable glob_iter in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable est_rel_err in translation. warning: variable glob_est_digits (declared type fixnum) assigned type any. warning: encountered undefined variable glob_est_digits in translation. warning: encountered undefined variable array_est_digits in translation. warning: encountered undefined variable array_1st_rel_error in translation. warning: encountered undefined variable array_last_rel_error in translation. warning: encountered undefined variable array_est_rel_error in translation. warning: encountered undefined variable info in translation. warning: encountered undefined variable glob_desired_digits_correct in translation. warning: encountered undefined variable glob_h in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable clock_sec1 in translation. warning: encountered undefined variable glob_orig_start_sec in translation. warning: encountered undefined variable glob_clock_start_sec in translation. warning: variable glob_clock_sec (declared type convfloat) assigned type any. warning: encountered undefined variable glob_max_sec in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob_optimal_clock_start_sec in translation. warning: encountered undefined variable opt_clock_sec in translation. warning: variable glob_optimal_expect_sec (declared type convfloat) assigned type any. warning: encountered undefined variable glob_optimal_expect_sec in translation. warning: encountered undefined variable total_clock_sec in translation. warning: variable glob_total_exp_sec (declared type convfloat) assigned type any. warning: encountered undefined variable percent_done in translation. warning: variable glob_percent_done (declared type convfloat) assigned type any. warning: encountered undefined variable info in translation. warning: encountered undefined variable glob_clock_sec in translation. warning: encountered undefined variable expect_sec in translation. warning: encountered undefined variable glob_total_exp_sec in translation. warning: encountered undefined variable glob__100 in translation. warning: encountered undefined variable left_sec in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable last_no in translation. warning: encountered undefined variable found_sing in translation. warning: encountered undefined variable array_y_higher in translation. warning: variable tmp_rad (declared type convfloat) assigned type any. warning: encountered undefined variable tmp_rad in translation. warning: encountered undefined variable prev_tmp_rad in translation. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable glob_large_float in translation. warning: encountered undefined variable cnt in translation. warning: encountered undefined variable tmp_ratio in translation. warning: encountered undefined variable glob_upper_ratio_limit in translation. warning: encountered undefined variable glob_lower_ratio_limit in translation. warning: variable tmp_ord (declared type convfloat) assigned type any. warning: encountered undefined variable tmp_ord in translation. warning: encountered undefined variable glob_min_pole_est in translation. warning: encountered undefined variable glob_check_sign in translation. warning: encountered undefined variable glob_ratio_of_radius in translation. warning: encountered undefined variable always in translation. warning: encountered undefined variable glob_min_h in translation. warning: encountered undefined variable h_new in translation. warning: variable ratio (declared type convfloat) assigned type any. warning: encountered undefined variable term in translation. warning: encountered undefined variable ratio in translation. warning: encountered undefined variable glob_h in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable array_const_0D1 in translation. warning: encountered undefined variable array_tmp1 in translation. warning: encountered undefined variable array_const_0D2 in translation. warning: encountered undefined variable array_tmp2 in translation. warning: encountered undefined variable array_tmp3 in translation. warning: encountered undefined variable array_const_0D3 in translation. warning: encountered undefined variable array_tmp4 in translation. warning: encountered undefined variable array_tmp5 in translation. warning: encountered undefined variable array_const_0D0 in translation. warning: encountered undefined variable array_tmp6 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_1 in translation. warning: encountered undefined variable glob__m1 in translation. warning: variable iiif (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable iiif in translation. warning: encountered undefined variable ats_max_terms in translation. warning: variable jjjf (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable jjjf in translation. warning: variable jjjf (declared type [found_h]) assigned type any. warning: variable iiif (declared type [found_h]) assigned type any. warning: variable glob_orig_start_sec (declared type convfloat) assigned type any. warning: variable opt_iter (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable always in translation. warning: encountered undefined variable glob__0 in translation. warning: variable glob_large_float (declared type convfloat) assigned type any. warning: variable glob_larger_float (declared type convfloat) assigned type any. warning: variable glob_almost_1 (declared type convfloat) assigned type any. warning: variable x_start (declared type [found_h]) assigned type any. warning: variable x_end (declared type [found_h]) assigned type any. warning: encountered undefined variable x_start in translation. warning: variable glob_upper_ratio_limit (declared type convfloat) assigned type any. warning: variable glob_lower_ratio_limit (declared type convfloat) assigned type any. warning: variable glob_h (declared type convfloat) assigned type any. warning: variable glob_display_interval (declared type convfloat) assigned type any. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob_max_minutes in translation. warning: encountered undefined variable glob_max_hours in translation. warning: encountered undefined variable x_end in translation. warning: variable glob_check_sign (declared type convfloat) assigned type any. warning: encountered undefined variable glob_larger_float in translation. warning: variable last_min_pole_est (declared type [found_h]) assigned type convfloat. warning: encountered undefined variable glob_min_h in translation. warning: encountered undefined variable glob_check_sign in translation. warning: encountered undefined variable glob_max_h in translation. warning: encountered undefined variable glob_display_interval in translation. warning: encountered undefined variable glob__10 in translation. warning: variable display_max (declared type [found_h]) assigned type any. warning: encountered undefined variable display_max in translation. warning: variable min_value (declared type [found_h]) assigned type convfloat. warning: variable est_answer (declared type [found_h]) assigned type any. warning: encountered undefined variable est_answer in translation. warning: variable est_needed_step_err (declared type [found_h]) assigned type any. warning: encountered undefined variable est_needed_step_err in translation. warning: encountered undefined variable glob_small_float in translation. warning: variable estimated_step_error (declared type [found_h]) assigned type convfloat. warning: encountered undefined variable opt_iter in translation. warning: encountered undefined variable found_h in translation. warning: variable glob_next_display (declared type convfloat) assigned type any. warning: variable order_diff (declared type [found_h]) assigned type fixnum. warning: variable term_no (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable order_diff in translation. warning: variable term_no (declared type [found_h]) assigned type any. warning: variable r_order (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable r_order in translation. warning: encountered undefined variable rows in translation. warning: variable it (declared type [found_h]) assigned type any. warning: encountered undefined variable it in translation. warning: variable r_order (declared type [found_h]) assigned type any. warning: encountered undefined variable glob_look_poles in translation. warning: variable estimated_step_error (declared type [found_h]) assigned type any. warning: encountered undefined variable estimated_step_error in translation. warning: encountered undefined variable glob__2 in translation. warning: variable opt_iter (declared type [found_h]) assigned type any. warning: encountered undefined variable glob_optimize in translation. warning: variable html_log_file (declared type [found_h]) assigned type any. warning: encountered undefined variable glob_html_log in translation. warning: variable current_iter (declared type [found_h]) assigned type fixnum. warning: variable glob_clock_start_sec (declared type convfloat) assigned type any. warning: variable glob_clock_sec (declared type convfloat) assigned type any. warning: encountered undefined variable debugl in translation. warning: variable glob_optimal_clock_start_sec (declared type convfloat) assigned type any. warning: encountered undefined variable glob_iter in translation. warning: encountered undefined variable glob_max_iter in translation. warning: encountered undefined variable glob_clock_sec in translation. warning: encountered undefined variable glob_orig_start_sec in translation. warning: encountered undefined variable glob_max_sec in translation. warning: encountered undefined variable info in translation. warning: encountered undefined variable current_iter in translation. warning: encountered undefined variable glob_next_display in translation. warning: variable calc_term (declared type [found_h]) assigned type fixnum. warning: variable iii (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable calc_term in translation. warning: variable iii (declared type [found_h]) assigned type any. warning: variable temp_sum (declared type [found_h]) assigned type convfloat. warning: encountered undefined variable temp_sum in translation. warning: variable temp_sum (declared type [found_h]) assigned type any. warning: encountered undefined variable html_log_file in translation. warning: encountered undefined variable glob_desired_digits_correct in translation. warning: encountered undefined variable glob_min_good_digits in translation. warning: encountered undefined variable glob_good_digits in translation. warning: encountered undefined variable glob_type_given_pole in translation. warning: encountered undefined variable glob_least_given_sing in translation. warning: encountered undefined variable glob_least_ratio_sing in translation. warning: encountered undefined variable glob_large_float in translation. warning: encountered undefined variable glob_least_3_sing in translation. warning: encountered undefined variable glob_least_6_sing in translation. warning: encountered undefined variable glob_total_exp_sec in translation. warning: encountered undefined variable glob_percent_done in translation. warning: encountered undefined variable glob__100 in translation. WARNING: in $MAIN_PROG : |$Digits| is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $MAX_TERMS is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_DISPLAY_FLAG is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_NO_EQS is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_UNCHANGED_H_CNT is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_WARNED is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_WARNED2 is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_SMALLISH_FLOAT is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_ALMOST_1 is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_SUBITER_METHOD is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_LAST_GOOD_H is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB__PI is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $LAST_MIN_POLE_EST is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $MIN_VALUE is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_REACHED_OPTIMAL_H is neither declared nor bound, it will be treated as if it were declared SPECIAL. "##############ECHO OF PROBLEM#################" "##############temp/div_lin_linpostode.ode#################" "diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) / ( 0.2 * x + 0.3 ) ; " "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:30," "!" "/* 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)," "glob_look_poles:true," "" "" "" "" "" "" "" "" "glob_type_given_pole:1," "" "array_given_rad_poles[1,1]:c(-1.5)," "" "array_given_rad_poles[1,2]:c(0.0)," "" "array_given_ord_poles[1,1]:c(1.0)," "" "array_given_ord_poles[1,2]:c(0.0)," "/* 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(0.5) * c(x) + c(0.25) * ln(c(2.0) * c(x) + c(3.0))) " "));" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Soultion" " " "TOP MAIN SOLVE Loop" x[1] = 0.1 " " y[1] (closed_form) = 0.3407877024514202 " " y[1] (numeric) = 0.3407877024514202 " " 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) = 0.34734533988907923 " " y[1] (numeric) = 0.34734533988907923 " " 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) = 0.35389333245105953 " " y[1] (numeric) = 0.35389333245105953 " " 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] = 0.13000000000000003 " " y[1] (closed_form) = 0.3604317988446541 " " y[1] (numeric) = 0.3604317988446541 " " 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] = 0.14000000000000004 " " y[1] (closed_form) = 0.3669608555990131 " " y[1] (numeric) = 0.3669608555990131 " " 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] = 0.15000000000000005 " " y[1] (closed_form) = 0.37348061711810865 " " y[1] (numeric) = 0.3734806171181087 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.48631946845324800000000000000E-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) = 0.37999119573209933 " " y[1] (numeric) = 0.3799911957320994 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.460853615945201800000000000000E-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) = 0.3864927017471523 " " y[1] (numeric) = 0.3864927017471524 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.872558833857299000000000000000E-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) = 0.3929852434937783 " " y[1] (numeric) = 0.3929852434937784 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.82510105151755800000000000000E-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) = 0.3994689273737319 " " y[1] (numeric) = 0.3994689273737321 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 4.16887127588698400000000000000E-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) = 0.405943857905529 " " y[1] (numeric) = 0.40594385790552917 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 4.102376485088463600000000000000E-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) = 0.4124101377686285 " " y[1] (numeric) = 0.4124101377686287 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 5.384072421847287000000000000000E-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) = 0.4188678678463268 " " y[1] (numeric) = 0.418867867846327 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 5.30106560970426300000000000000E-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) = 0.4253171472674083 " " y[1] (numeric) = 0.42531714726740855 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 5.22068311497974700000000000000E-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) = 0.43175807344659584 " " y[1] (numeric) = 0.4317580734465961 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 6.42850182141689500000000000000E-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) = 0.43819074212384207 " " y[1] (numeric) = 0.4381907421238424 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 7.60095719442231300000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2600000000000001 " " y[1] (closed_form) = 0.4446152474025015 " " y[1] (numeric) = 0.44461524740250175 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 4.99408435095836100000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.27000000000000013 " " y[1] (closed_form) = 0.45103168178642083 " " y[1] (numeric) = 0.45103168178642106 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 4.92303786832821900000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.28000000000000014 " " y[1] (closed_form) = 0.4574401362159849 " " y[1] (numeric) = 0.45744013621598506 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 3.64055185606063800000000000000E-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) = 0.4638407001031523 " " y[1] (numeric) = 0.4638407001031526 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 5.98385946068476300000000000000E-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) = 0.4702334613655162 " " y[1] (numeric) = 0.47023346136551636 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 3.54150581309494950000000000000E-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) = 0.47661850645942 " " y[1] (numeric) = 0.47661850645942005 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.164687280895252400000000000000E-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) = 0.48299592041216244 " " y[1] (numeric) = 0.4829959204121625 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.149308904801672700000000000000E-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) = 0.48936578685331883 " " y[1] (numeric) = 0.4893657868533188 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.134348839304873500000000000000E-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) = 0.49572818804521 " " y[1] (numeric) = 0.49572818804520985 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 3.359370270035678000000000000000E-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) = 0.5020832049125448 " " y[1] (numeric) = 0.5020832049125447 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.21123314574631220000000000000E-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) = 0.508430917071264 " " y[1] (numeric) = 0.5084309170712636 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 6.5508783239643700000000000000E-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) = 0.5147714028566103 " " y[1] (numeric) = 0.5147714028566099 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 6.47019056496273300000000000000E-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) = 0.5211047393504509 " " y[1] (numeric) = 0.5211047393504504 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 8.52207198122229800000000000000E-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) = 0.5274310024078742 " " y[1] (numeric) = 0.5274310024078738 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 8.41985411973637600000000000000E-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) = 0.5337502666830851 " " y[1] (numeric) = 0.5337502666830846 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 1.04002104909893450000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.41000000000000025 " " y[1] (closed_form) = 0.5400626056546212 " " y[1] (numeric) = 0.5400626056546205 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 1.23343813809819180000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.42000000000000026 " " y[1] (closed_form) = 0.5463680916499091 " " y[1] (numeric) = 0.5463680916499083 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 1.42240392349921560000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.43000000000000027 " " y[1] (closed_form) = 0.5526667958691851 " " y[1] (numeric) = 0.5526667958691842 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.60707758515377660000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4400000000000003 " " y[1] (closed_form) = 0.5589587884087956 " " y[1] (numeric) = 0.558958788408795 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 1.19174047995809580000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4500000000000003 " " y[1] (closed_form) = 0.5652441382839004 " " y[1] (numeric) = 0.5652441382838997 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 1.1784886735800530000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4600000000000003 " " y[1] (closed_form) = 0.571522913450593 " " y[1] (numeric) = 0.5715229134505925 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 9.71284788847869200000000000000E-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) = 0.5777951808274608 " " y[1] (numeric) = 0.5777951808274604 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 7.68592789600775500000000000000E-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) = 0.5840610063165975 " " y[1] (numeric) = 0.584061006316597 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 9.50434126416707100000000000000E-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) = 0.5903204548240868 " " y[1] (numeric) = 0.5903204548240863 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 7.52284977118740500000000000000E-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) = 0.5965735902799729 " " y[1] (numeric) = 0.5965735902799724 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 9.30499642218596300000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5100000000000003 " " y[1] (closed_form) = 0.6028204756577327 " " y[1] (numeric) = 0.6028204756577321 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 9.20857095484191100000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5200000000000004 " " y[1] (closed_form) = 0.6090611729932649 " " y[1] (numeric) = 0.6090611729932645 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 7.29137284630313200000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5300000000000004 " " y[1] (closed_form) = 0.6152957434034105 " " y[1] (numeric) = 0.6152957434034101 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 7.21749198838356800000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5400000000000004 " " y[1] (closed_form) = 0.6215242471040179 " " y[1] (numeric) = 0.6215242471040173 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 8.93145383947788500000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5500000000000004 " " y[1] (closed_form) = 0.6277467434275658 " " y[1] (numeric) = 0.6277467434275652 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 8.84292141894052400000000000000E-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) = 0.633963290840359 " " y[1] (numeric) = 0.6339632908403584 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 8.75620907918410200000000000000E-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) = 0.640173946959306 " " y[1] (numeric) = 0.6401739469593054 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 8.67126059954865800000000000000E-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) = 0.6463787685682932 " " y[1] (numeric) = 0.6463787685682927 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 8.58802205929707800000000000000E-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) = 0.6525778116341665 " " y[1] (numeric) = 0.652577811634166 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 8.50644172106440600000000000000E-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) = 0.658771131322331 " " y[1] (numeric) = 0.6587711313223303 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 1.01117639055916740000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6100000000000004 " " y[1] (closed_form) = 0.6649587820119804 " " y[1] (numeric) = 0.6649587820119798 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 1.00176707608787150000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6200000000000004 " " y[1] (closed_form) = 0.6711408173109669 " " y[1] (numeric) = 0.6711408173109662 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 9.92539564862208300000000000000E-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) = 0.67731729007032 " " y[1] (numeric) = 0.6773172900703195 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 8.19573810458826200000000000000E-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) = 0.6834882523984267 " " y[1] (numeric) = 0.6834882523984261 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 8.12174182020887800000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6500000000000005 " " y[1] (closed_form) = 0.6896537556748794 " " y[1] (numeric) = 0.689653755674879 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 6.43930677090980300000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6600000000000005 " " y[1] (closed_form) = 0.695813850564005 " " y[1] (numeric) = 0.6958138505640045 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 7.97787385034980600000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6700000000000005 " " y[1] (closed_form) = 0.7019685870280787 " " y[1] (numeric) = 0.7019685870280781 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 9.48951031548721700000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6800000000000005 " " y[1] (closed_form) = 0.7081180143402361 " " y[1] (numeric) = 0.7081180143402354 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 1.09749519359664540000000000000E-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) = 0.714262181097089 " " y[1] (numeric) = 0.7142621810970883 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 1.08805441167823980000000000000E-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) = 0.7204011352310542 " " y[1] (numeric) = 0.7204011352310535 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 9.24670689978083900000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7100000000000005 " " y[1] (closed_form) = 0.7265349240224019 " " y[1] (numeric) = 0.7265349240224015 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 6.11242756771276300000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7200000000000005 " " y[1] (closed_form) = 0.7326635941110337 " " y[1] (numeric) = 0.7326635941110331 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 7.57662202372856400000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7300000000000005 " " y[1] (closed_form) = 0.7387871915079935 " " y[1] (numeric) = 0.7387871915079932 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.508292932200127500000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7400000000000005 " " y[1] (closed_form) = 0.7449057616067238 " " y[1] (numeric) = 0.7449057616067235 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.471262333494891400000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7500000000000006 " " y[1] (closed_form) = 0.7510193491940689 " " y[1] (numeric) = 0.7510193491940685 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.43486453105324800000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7600000000000006 " " y[1] (closed_form) = 0.7571279984610353 " " y[1] (numeric) = 0.7571279984610351 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.93272214706584500000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7700000000000006 " " y[1] (closed_form) = 0.7632317530133145 " " y[1] (numeric) = 0.7632317530133141 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.36390265568178840000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7800000000000006 " " y[1] (closed_form) = 0.769330655881574 " " y[1] (numeric) = 0.7693306558815737 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.329307623987588000000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7900000000000006 " " y[1] (closed_form) = 0.7754247495315237 " " y[1] (numeric) = 0.7754247495315234 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.295283424842588600000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8000000000000006 " " y[1] (closed_form) = 0.7815140758737626 " " y[1] (numeric) = 0.7815140758737624 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.841210565232327000000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8100000000000006 " " y[1] (closed_form) = 0.7875986762734122 " " y[1] (numeric) = 0.787598676273412 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.819260768385919400000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8200000000000006 " " y[1] (closed_form) = 0.7936785915595413 " " y[1] (numeric) = 0.7936785915595411 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.797664032851434600000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8300000000000006 " " y[1] (closed_form) = 0.7997538620343889 " " y[1] (numeric) = 0.7997538620343887 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.776411786999079500000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8400000000000006 " " y[1] (closed_form) = 0.8058245274823892 " " y[1] (numeric) = 0.8058245274823891 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.377747867881100000000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8500000000000006 " " y[1] (closed_form) = 0.8118906271790036 " " y[1] (numeric) = 0.8118906271790035 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.367453924776468000000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8600000000000007 " " y[1] (closed_form) = 0.8179521998993664 " " y[1] (numeric) = 0.8179521998993664 " " 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] = 0.8700000000000007 " " y[1] (closed_form) = 0.8240092839267467 " " y[1] (numeric) = 0.8240092839267464 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.694685718429002400000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8800000000000007 " " y[1] (closed_form) = 0.8300619170608325 " " y[1] (numeric) = 0.8300619170608323 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.675036649208885600000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8900000000000007 " " y[1] (closed_form) = 0.8361101366258415 " " y[1] (numeric) = 0.8361101366258411 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.311372155374215000000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9000000000000007 " " y[1] (closed_form) = 0.8421539794784617 " " y[1] (numeric) = 0.8421539794784613 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.27325430588219700000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9100000000000007 " " y[1] (closed_form) = 0.8481934820156276 " " y[1] (numeric) = 0.8481934820156273 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.92677984975850550000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9200000000000007 " " y[1] (closed_form) = 0.8542286801821355 " " y[1] (numeric) = 0.8542286801821349 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 6.49839469443029400000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9300000000000007 " " y[1] (closed_form) = 0.860259609478101 " " y[1] (numeric) = 0.8602596094781004 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 6.45283709936528500000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9400000000000007 " " y[1] (closed_form) = 0.8662863049662644 " " y[1] (numeric) = 0.8662863049662637 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 7.68953417543678100000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9500000000000007 " " y[1] (closed_form) = 0.8723088012791457 " " y[1] (numeric) = 0.8723088012791448 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.01819266112838550000000000000E-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) = 0.8783271326260547 " " y[1] (numeric) = 0.8783271326260539 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 8.84813970068349900000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9700000000000008 " " y[1] (closed_form) = 0.8843413327999583 " " y[1] (numeric) = 0.8843413327999575 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 8.78796555598069700000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9800000000000008 " " y[1] (closed_form) = 0.8903514351842094 " " y[1] (numeric) = 0.8903514351842088 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 7.48169529975850500000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9900000000000008 " " y[1] (closed_form) = 0.8963574727591408 " " y[1] (numeric) = 0.8963574727591399 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 9.90875233031929800000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0000000000000007 " " y[1] (closed_form) = 0.9023594781085256 " " y[1] (numeric) = 0.9023594781085247 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 9.84284468936785800000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0099999999999996 " " y[1] (closed_form) = 0.9083574834259092 " " y[1] (numeric) = 0.9083574834259089 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.444462769080522600000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0199999999999985 " " y[1] (closed_form) = 0.9143515205208184 " " y[1] (numeric) = 0.9143515205208188 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.85687615630701450000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0299999999999974 " " y[1] (closed_form) = 0.920341620824842 " " y[1] (numeric) = 0.9203416208248429 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 9.65052975550653600000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0399999999999963 " " y[1] (closed_form) = 0.9263278153975953 " " y[1] (numeric) = 0.9263278153975972 " " absolute error = 1.887379141862766000000000000000E-15 " " relative error = 2.03748512188708430000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0499999999999952 " " y[1] (closed_form) = 0.9323101349325671 " " y[1] (numeric) = 0.9323101349325698 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 2.8579923774968924000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.059999999999994 " " y[1] (closed_form) = 0.9382886097628506 " " y[1] (numeric) = 0.9382886097628538 " " absolute error = 3.219646771412954000000000000000E-15 " " relative error = 3.43140344869656830000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.069999999999993 " " y[1] (closed_form) = 0.9442632698667642 " " y[1] (numeric) = 0.9442632698667683 " " absolute error = 4.107825191113079000000000000000E-15 " " relative error = 4.35029649272781150000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0799999999999919 " " y[1] (closed_form) = 0.950234144873363 " " y[1] (numeric) = 0.9502341448733678 " " absolute error = 4.773959005888173000000000000000E-15 " " relative error = 5.0239817540174750000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0899999999999908 " " y[1] (closed_form) = 0.9562012640678424 " " y[1] (numeric) = 0.9562012640678479 " " absolute error = 5.440092820663267000000000000000E-15 " " relative error = 5.6892759140687490000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0999999999999897 " " y[1] (closed_form) = 0.9621646563968393 " " y[1] (numeric) = 0.9621646563968453 " " absolute error = 5.995204332975845000000000000000E-15 " " relative error = 6.2309546428643270000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1099999999999886 " " y[1] (closed_form) = 0.9681243504736301 " " y[1] (numeric) = 0.9681243504736369 " " absolute error = 6.772360450213455000000000000000E-15 " " relative error = 6.9953415043225090000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1199999999999875 " " y[1] (closed_form) = 0.9740803745832303 " " y[1] (numeric) = 0.9740803745832377 " " absolute error = 7.438494264988549000000000000000E-15 " " relative error = 7.6364276081131190000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1299999999999863 " " y[1] (closed_form) = 0.9800327566873965 " " y[1] (numeric) = 0.9800327566874046 " " absolute error = 8.104628079763643000000000000000E-15 " " relative error = 8.2697522347702460000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1399999999999852 " " y[1] (closed_form) = 0.9859815244295338 " " y[1] (numeric) = 0.9859815244295427 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 9.0080635153280850000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1499999999999841 " " y[1] (closed_form) = 0.9919267051395096 " " y[1] (numeric) = 0.9919267051395193 " " absolute error = 9.658940314238862000000000000000E-15 " " relative error = 9.7375544626358050000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.159999999999983 " " y[1] (closed_form) = 0.9978683258383783 " " y[1] (numeric) = 0.9978683258383886 " " absolute error = 1.032507412901395600000000000000E-14 " " relative error = 1.0347130840473513000000000000E-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) = 1.0038064132430151 " " y[1] (numeric) = 1.0038064132430262 " " absolute error = 1.110223024625156500000000000000E-14 " " relative error = 1.106013081783707000000000000E-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) = 1.0097409937706663 " " y[1] (numeric) = 1.0097409937706778 " " absolute error = 1.154631945610162800000000000000E-14 " " relative error = 1.1434931856123139000000000000E-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) = 1.0156720935434111 " " y[1] (numeric) = 1.0156720935434234 " " absolute error = 1.221245327087672200000000000000E-14 " " relative error = 1.2024011832668066000000000000E-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) = 1.0215997383925446 " " y[1] (numeric) = 1.021599738392557 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 1.2171594616270212000000000000E-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) = 1.0275239538628753 " " y[1] (numeric) = 1.0275239538628884 " " absolute error = 1.310063169057684700000000000000E-14 " " relative error = 1.2749709280573274000000000000E-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) = 1.033444765216949 " " y[1] (numeric) = 1.033444765216963 " " absolute error = 1.398881011027697200000000000000E-14 " " relative error = 1.353609847483269200000000000E-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) = 1.039362197439189 " " y[1] (numeric) = 1.0393621974392033 " " absolute error = 1.443289932012703500000000000000E-14 " " relative error = 1.3886303884908685000000000000E-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) = 1.0452762752399658 " " y[1] (numeric) = 1.045276275239981 " " absolute error = 1.50990331349021300000000000000E-14 " " relative error = 1.444501658801719000000000000E-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) = 1.0511870230595903 " " y[1] (numeric) = 1.0511870230596059 " " absolute error = 1.55431223447521920000000000000E-14 " " relative error = 1.478625782452327000000000000E-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) = 1.0570944650722345 " " y[1] (numeric) = 1.0570944650722502 " " absolute error = 1.576516694967722300000000000000E-14 " " relative error = 1.4913678455974075000000000000E-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) = 1.062998625189781 " " y[1] (numeric) = 1.062998625189797 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 1.5039729286336564000000000000E-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) = 1.068899527065605 " " y[1] (numeric) = 1.0688995270656216 " " absolute error = 1.665334536937734800000000000000E-14 " " relative error = 1.557989778056589000000000000E-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) = 1.0747971940982866 " " y[1] (numeric) = 1.0747971940983037 " " absolute error = 1.70974345792274100000000000000E-14 " " relative error = 1.5907591379201078000000000000E-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) = 1.0806916494352568 " " y[1] (numeric) = 1.0806916494352745 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.643722185073357200000000000E-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) = 1.0865829159763802 " " y[1] (numeric) = 1.0865829159763989 " " absolute error = 1.86517468137026300000000000000E-14 " " relative error = 1.7165507150406990000000000000E-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) = 1.0924710163774716 " " y[1] (numeric) = 1.092471016377491 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 1.7885989596497728000000000000E-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) = 1.098355973053752 " " y[1] (numeric) = 1.0983559730537718 " " absolute error = 1.976196983832778600000000000000E-14 " " relative error = 1.7992317903442280000000000000E-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) = 1.1042378081832434 " " y[1] (numeric) = 1.1042378081832638 " " absolute error = 2.04281036531028800000000000000E-14 " " relative error = 1.84997321244708970000000000E-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) = 1.110116543710104 " " y[1] (numeric) = 1.110116543710125 " " absolute error = 2.109423746787797400000000000000E-14 " " relative error = 1.9001822454946252000000000000E-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) = 1.1159922013479038 " " y[1] (numeric) = 1.1159922013479253 " " absolute error = 2.153832667772803700000000000000E-14 " " relative error = 1.929971074324165200000000000E-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) = 1.1218648025828453 " " y[1] (numeric) = 1.1218648025828672 " " absolute error = 2.1982415887578100000000000000E-14 " " relative error = 1.9594532101344525000000000000E-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) = 1.127734368676926 " " y[1] (numeric) = 1.1277343686769483 " " absolute error = 2.242650509742816200000000000000E-14 " " relative error = 1.988633646391327000000000000E-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) = 1.1336009206710467 " " y[1] (numeric) = 1.1336009206710698 " " absolute error = 2.309263891220325600000000000000E-14 " " relative error = 2.0371048127354494000000000000E-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) = 1.139464479388068 " " y[1] (numeric) = 1.1394644793880917 " " absolute error = 2.37587727269783500000000000000E-14 " " relative error = 2.085082348485109100000000000E-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) = 1.1453250654358107 " " y[1] (numeric) = 1.1453250654358347 " " absolute error = 2.39808173319033800000000000000E-14 " " relative error = 2.093800097073609000000000000E-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) = 1.1511826992100072 " " y[1] (numeric) = 1.151182699210032 " " absolute error = 2.486899575160350700000000000000E-14 " " relative error = 2.1602996438940336000000000000E-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) = 1.157037400897203 " " y[1] (numeric) = 1.1570374008972286 " " absolute error = 2.5535129566378600000000000000E-14 " " relative error = 2.2069407217586792000000000000E-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) = 1.162889190477606 " " y[1] (numeric) = 1.1628891904776322 " " absolute error = 2.620126338115369400000000000000E-14 " " relative error = 2.2531178031152455000000000000E-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) = 1.16873808772789 " " y[1] (numeric) = 1.1687380877279168 " " absolute error = 2.686739719592879000000000000000E-14 " " relative error = 2.2988381638319774000000000000E-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) = 1.1745841122239493 " " y[1] (numeric) = 1.1745841122239766 " " absolute error = 2.73114864057788500000000000000E-14 " " relative error = 2.3252048211402648000000000000E-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) = 1.1804272833436085 " " y[1] (numeric) = 1.1804272833436364 " " absolute error = 2.797762022055394500000000000000E-14 " " relative error = 2.370126530903809100000000000E-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) = 1.1862676202692841 " " y[1] (numeric) = 1.186267620269313 " " absolute error = 2.88657986402540700000000000000E-14 " " relative error = 2.4333293893414626000000000000E-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) = 1.192105141990604 " " y[1] (numeric) = 1.1921051419906339 " " absolute error = 2.997602166487922700000000000000E-14 " " relative error = 2.5145451193025303000000000000E-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) = 1.197939867306982 " " y[1] (numeric) = 1.1979398673070125 " " absolute error = 3.04201108747292900000000000000E-14 " " relative error = 2.5393687700798323000000000000E-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) = 1.2037718148301502 " " y[1] (numeric) = 1.203771814830181 " " absolute error = 3.08642000845793500000000000000E-14 " " relative error = 2.5639576956646250000000000000E-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) = 1.209601002986648 " " y[1] (numeric) = 1.209601002986679 " " absolute error = 3.10862446895043830000000000000E-14 " " relative error = 2.569958574170224000000000000E-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) = 1.2154274500202722 " " y[1] (numeric) = 1.2154274500203037 " " absolute error = 3.153033389935444600000000000000E-14 " " relative error = 2.5941765507129655000000000000E-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) = 1.2212511739944847 " " y[1] (numeric) = 1.2212511739945169 " " absolute error = 3.21964677141295400000000000000E-14 " " relative error = 2.6363510144126130000000000000E-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) = 1.2270721927947816 " " y[1] (numeric) = 1.2270721927948143 " " absolute error = 3.2640556923979600000000000000E-14 " " relative error = 2.660035580273188000000000000E-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) = 1.2328905241310233 " " y[1] (numeric) = 1.2328905241310566 " " absolute error = 3.330669073875469600000000000000E-14 " " relative error = 2.7015124284640124000000000000E-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) = 1.2387061855397268 " " y[1] (numeric) = 1.2387061855397605 " " absolute error = 3.37507799486047600000000000000E-14 " " relative error = 2.7246800203794036000000000000E-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) = 1.2445191943863203 " " y[1] (numeric) = 1.2445191943863545 " " absolute error = 3.41948691584548200000000000000E-14 " " relative error = 2.7476369438654186000000000000E-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) = 1.2503295678673625 " " y[1] (numeric) = 1.2503295678673974 " " absolute error = 3.486100297322991500000000000000E-14 " " relative error = 2.788145131422505000000000000E-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) = 1.2561373230127235 " " y[1] (numeric) = 1.2561373230127588 " " absolute error = 3.53050921830799800000000000000E-14 " " relative error = 2.8106076888475967000000000000E-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) = 1.2619424766877334 " " y[1] (numeric) = 1.2619424766877694 " " absolute error = 3.59712259978550700000000000000E-14 " " relative error = 2.8504647923628080000000000000E-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) = 1.2677450455952948 " " y[1] (numeric) = 1.2677450455953312 " " absolute error = 3.641531520770513500000000000000E-14 " " relative error = 2.8724478422714400000000000000E-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) = 1.2735450462779618 " " y[1] (numeric) = 1.2735450462779991 " " absolute error = 3.73034936274052600000000000000E-14 " " relative error = 2.9291067274320390000000000000E-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) = 1.2793424951199863 " " y[1] (numeric) = 1.2793424951200245 " " absolute error = 3.819167204710538500000000000000E-14 " " relative error = 2.985257833049897000000000000E-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) = 1.2851374083493305 " " y[1] (numeric) = 1.2851374083493694 " " absolute error = 3.88578058618804800000000000000E-14 " " relative error = 3.0236304390042323000000000000E-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) = 1.2909298020396498 " " y[1] (numeric) = 1.2909298020396893 " " absolute error = 3.95239396766555730000000000000E-14 " " relative error = 3.061664516088198000000000000E-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) = 1.2967196921122413 " " y[1] (numeric) = 1.2967196921122812 " " absolute error = 3.996802888650563500000000000000E-14 " " relative error = 3.082241222187446000000000000E-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) = 1.3025070943379649 " " y[1] (numeric) = 1.302507094338005 " " absolute error = 4.019007349143066700000000000000E-14 " " relative error = 3.0855934425338677000000000000E-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) = 1.308292024339131 " " y[1] (numeric) = 1.3082920243391718 " " absolute error = 4.08562073062057600000000000000E-14 " " relative error = 3.122866038019594000000000000E-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) = 1.3140744975913623 " " y[1] (numeric) = 1.314074497591404 " " absolute error = 4.174438572590588600000000000000E-14 " " relative error = 3.1767137861986830000000000000E-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) = 1.3198545294254227 " " y[1] (numeric) = 1.3198545294254653 " " absolute error = 4.26325641456060100000000000000E-14 " " relative error = 3.230095680632729000000000000E-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) = 1.32563213502902 " " y[1] (numeric) = 1.3256321350290636 " " absolute error = 4.352074256530613600000000000000E-14 " " relative error = 3.283018072306568000000000000E-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) = 1.3314073294485815 " " y[1] (numeric) = 1.3314073294486253 " " absolute error = 4.37427871702311700000000000000E-14 " " relative error = 3.2854548869238814000000000000E-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) = 1.3371801275909991 " " y[1] (numeric) = 1.3371801275910438 " " absolute error = 4.46309655899312930000000000000E-14 " " relative error = 3.3376928559607255000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.749999999999918 " " y[1] (closed_form) = 1.3429505442253507 " " y[1] (numeric) = 1.3429505442253955 " " absolute error = 4.485301019485632400000000000000E-14 " " relative error = 3.3398854773709274000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.759999999999917 " " y[1] (closed_form) = 1.3487185939845925 " " y[1] (numeric) = 1.348718593984638 " " absolute error = 4.55191440096314200000000000000E-14 " " relative error = 3.3749919525578526000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7699999999999159 " " y[1] (closed_form) = 1.3544842913672284 " " y[1] (numeric) = 1.354484291367274 " " absolute error = 4.57411886145564500000000000000E-14 " " relative error = 3.3770187595446305000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7799999999999148 " " y[1] (closed_form) = 1.3602476507389503 " " y[1] (numeric) = 1.3602476507389967 " " absolute error = 4.640732242933154300000000000000E-14 " " relative error = 3.4116818657338550000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7899999999999137 " " y[1] (closed_form) = 1.3660086863342569 " " y[1] (numeric) = 1.3660086863343037 " " absolute error = 4.685141163918160600000000000000E-14 " " relative error = 3.4298033466323985000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7999999999999126 " " y[1] (closed_form) = 1.3717674122580448 " " y[1] (numeric) = 1.371767412258092 " " absolute error = 4.72955008490316700000000000000E-14 " " relative error = 3.4477784226685550000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8099999999999115 " " y[1] (closed_form) = 1.3775238424871783 " " y[1] (numeric) = 1.3775238424872265 " " absolute error = 4.818367926873179400000000000000E-14 " " relative error = 3.4978472083455264000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8199999999999104 " " y[1] (closed_form) = 1.383277990872034 " " y[1] (numeric) = 1.3832779908720831 " " absolute error = 4.90718576884319200000000000000E-14 " " relative error = 3.547505130006186600000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8299999999999093 " " y[1] (closed_form) = 1.3890298711380222 " " y[1] (numeric) = 1.3890298711380722 " " absolute error = 4.996003610813204400000000000000E-14 " " relative error = 3.596757502932615000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8399999999999082 " " y[1] (closed_form) = 1.394779496887086 " " y[1] (numeric) = 1.3947794968871363 " " absolute error = 5.04041253179821100000000000000E-14 " " relative error = 3.6137701644220950000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.849999999999907 " " y[1] (closed_form) = 1.4005268815991767 " " y[1] (numeric) = 1.4005268815992276 " " absolute error = 5.08482145278321700000000000000E-14 " " relative error = 3.630648950470103000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.859999999999906 " " y[1] (closed_form) = 1.4062720386337104 " " y[1] (numeric) = 1.4062720386337622 " " absolute error = 5.173639294753230000000000000000E-14 " " relative error = 3.678974730792326000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8699999999999048 " " y[1] (closed_form) = 1.4120149812309992 " " y[1] (numeric) = 1.4120149812310512 " " absolute error = 5.195843755245733000000000000000E-14 " " relative error = 3.679736988849778000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8799999999999037 " " y[1] (closed_form) = 1.417755722513663 " " y[1] (numeric) = 1.4177557225137154 " " absolute error = 5.24025267623073900000000000000E-14 " " relative error = 3.696160483090724000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8899999999999026 " " y[1] (closed_form) = 1.4234942754880202 " " y[1] (numeric) = 1.423494275488073 " " absolute error = 5.28466159721574500000000000000E-14 " " relative error = 3.712457217577493000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8999999999999015 " " y[1] (closed_form) = 1.4292306530454588 " " y[1] (numeric) = 1.4292306530455121 " " absolute error = 5.329070518200751000000000000000E-14 " " relative error = 3.7286287604071230000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9099999999999004 " " y[1] (closed_form) = 1.4349648679637856 " " y[1] (numeric) = 1.4349648679638396 " " absolute error = 5.39568389967826100000000000000E-14 " " relative error = 3.760150523639462000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9199999999998993 " " y[1] (closed_form) = 1.440696932908557 " " y[1] (numeric) = 1.4406969329086114 " " absolute error = 5.44009282066326700000000000000E-14 " " relative error = 3.776014716488993000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9299999999998982 " " y[1] (closed_form) = 1.4464268604343902 " " y[1] (numeric) = 1.4464268604344452 " " absolute error = 5.506706202140776000000000000000E-14 " " relative error = 3.807110025934533000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9399999999998971 " " y[1] (closed_form) = 1.452154662986254 " " y[1] (numeric) = 1.4521546629863096 " " absolute error = 5.55111512312578300000000000000E-14 " " relative error = 3.822674860066423000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.949999999999896 " " y[1] (closed_form) = 1.457880352900744 " " y[1] (numeric) = 1.4578803529008 " " absolute error = 5.59552404411078900000000000000E-14 " " relative error = 3.838122952255565000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.959999999999895 " " y[1] (closed_form) = 1.4636039424073344 " " y[1] (numeric) = 1.4636039424073914 " " absolute error = 5.70654634657330500000000000000E-14 " " relative error = 3.8989689636850683000000000000E-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) = 1.4693254436296175 " " y[1] (numeric) = 1.4693254436296748 " " absolute error = 5.72875080706580800000000000000E-14 " " relative error = 3.8988985264655174000000000000E-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) = 1.4750448685865207 " " y[1] (numeric) = 1.4750448685865782 " " absolute error = 5.75095526755831100000000000000E-14 " " relative error = 3.898834123648884400000000000E-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) = 1.4807622291935083 " " y[1] (numeric) = 1.4807622291935665 " " absolute error = 5.8175686490358200000000000000E-14 " " relative error = 3.9287662356192987000000000000E-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) = 1.4864775372637657 " " y[1] (numeric) = 1.4864775372638246 " " absolute error = 5.8841820305133300000000000000E-14 " " relative error = 3.958473561157634400000000000E-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) = 1.492190804509367 " " y[1] (numeric) = 1.492190804509426 " " absolute error = 5.90638649100583300000000000000E-14 " " relative error = 3.958197888069586000000000000E-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) = 1.497902042542424 " " y[1] (numeric) = 1.4979020425424843 " " absolute error = 6.01740879346834800000000000000E-14 " " relative error = 4.017224506386853000000000000E-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) = 1.5036112628762235 " " y[1] (numeric) = 1.503611262876284 " " absolute error = 6.06181771445335500000000000000E-14 " " relative error = 4.031505924515252000000000000E-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) = 1.5093184769263424 " " y[1] (numeric) = 1.5093184769264034 " " absolute error = 6.10622663543836100000000000000E-14 " " relative error = 4.0456846774137495000000000000E-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) = 1.515023696011752 " " y[1] (numeric) = 1.515023696011814 " " absolute error = 6.19504447740837300000000000000E-14 " " relative error = 4.089074311983777000000000000E-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) = 1.520726931355905 " " y[1] (numeric) = 1.5207269313559675 " " absolute error = 6.2394533983933800000000000000E-14 " " relative error = 4.102941343210237400000000000E-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) = 1.5264281940878066 " " y[1] (numeric) = 1.5264281940878697 " " absolute error = 6.30606677987088900000000000000E-14 " " relative error = 4.131256749774197000000000000E-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) = 1.5321274952430712 " " y[1] (numeric) = 1.532127495243135 " " absolute error = 6.37268016134839900000000000000E-14 " " relative error = 4.1593667505701776000000000000E-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) = 1.5378248457649653 " " y[1] (numeric) = 1.5378248457650294 " " absolute error = 6.41708908233340500000000000000E-14 " " relative error = 4.172834832266825000000000000E-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) = 1.543520256505434 " " y[1] (numeric) = 1.5435202565054986 " " absolute error = 6.46149800331841100000000000000E-14 " " relative error = 4.186208749827096000000000000E-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) = 1.5492137382261146 " " y[1] (numeric) = 1.54921373822618 " " absolute error = 6.5281113847959200000000000000E-14 " " relative error = 4.21382229173281000000000000E-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) = 1.5549053015993366 " " y[1] (numeric) = 1.5549053015994025 " " absolute error = 6.5947247662734300000000000000E-14 " " relative error = 4.241238845536292000000000000E-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) = 1.5605949572091058 " " y[1] (numeric) = 1.5605949572091724 " " absolute error = 6.66133814775093900000000000000E-14 " " relative error = 4.2684606386680635000000000000E-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) = 1.5662827155520778 " " y[1] (numeric) = 1.5662827155521448 " " absolute error = 6.70574706873594600000000000000E-14 " " relative error = 4.281313330060166000000000000E-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) = 1.571968587038515 " " y[1] (numeric) = 1.5719685870385827 " " absolute error = 6.77236045021345500000000000000E-14 " " relative error = 4.308203424708463300000000000E-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) = 1.577652581993233 " " y[1] (numeric) = 1.5776525819933014 " " absolute error = 6.83897383169096400000000000000E-14 " " relative error = 4.334904851517112000000000000E-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) = 1.5833347106565334 " " y[1] (numeric) = 1.5833347106566025 " " absolute error = 6.90558721316847400000000000000E-14 " " relative error = 4.361419709105635600000000000E-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) = 1.5890149831851228 " " y[1] (numeric) = 1.5890149831851923 " " absolute error = 6.9499961341534800000000000000E-14 " " relative error = 4.3737763379817010000000000000E-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) = 1.5946934096530214 " " y[1] (numeric) = 1.5946934096530914 " " absolute error = 6.99440505513848600000000000000E-14 " " relative error = 4.38605001613467000000000000E-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) = 1.6003700000524566 " " y[1] (numeric) = 1.6003700000525272 " " absolute error = 7.06101843661599600000000000000E-14 " " relative error = 4.412116220864269500000000000E-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) = 1.6060447642947473 " " y[1] (numeric) = 1.6060447642948183 " " absolute error = 7.10542735760100200000000000000E-14 " " relative error = 4.424177654052604000000000000E-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) = 1.6117177122111745 " " y[1] (numeric) = 1.6117177122112465 " " absolute error = 7.19424519957101400000000000000E-14 " " relative error = 4.4637129350033430000000000000E-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) = 1.617388853553841 " " y[1] (numeric) = 1.6173888535539134 " " absolute error = 7.23865412055602100000000000000E-14 " " relative error = 4.4755187379032196000000000000E-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) = 1.6230581979965195 " " y[1] (numeric) = 1.6230581979965928 " " absolute error = 7.32747196252603300000000000000E-14 " " relative error = 4.5146082694822426000000000000E-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) = 1.6287257551354886 " " y[1] (numeric) = 1.6287257551355623 " " absolute error = 7.3718808835110390000000000000E-14 " " relative error = 4.526164616889598000000000000E-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) = 1.634391534490359 " " y[1] (numeric) = 1.634391534490433 " " absolute error = 7.39408534400354300000000000000E-14 " " relative error = 4.52405998683124000000000000E-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) = 1.6400555455048875 " " y[1] (numeric) = 1.640055545504962 " " absolute error = 7.43849426498854900000000000000E-14 " " relative error = 4.5355136204844965000000000000E-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) = 1.645717797547781 " " y[1] (numeric) = 1.645717797547856 " " absolute error = 7.50510764646605800000000000000E-14 " " relative error = 4.560385539762116000000000000E-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) = 1.6513782999134903 " " y[1] (numeric) = 1.6513782999135658 " " absolute error = 7.54951656745106400000000000000E-14 " " relative error = 4.5716457385001100000000000000E-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) = 1.6570370618229908 " " y[1] (numeric) = 1.657037061823067 " " absolute error = 7.61612994892857400000000000000E-14 " " relative error = 4.596233919203763000000000000E-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) = 1.6626940924245577 " " y[1] (numeric) = 1.6626940924246345 " " absolute error = 7.68274333040608300000000000000E-14 " " relative error = 4.620659546100286000000000000E-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) = 1.6683494007945256 " " y[1] (numeric) = 1.6683494007946034 " " absolute error = 7.77156117237609600000000000000E-14 " " relative error = 4.658233562271195000000000000E-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) = 1.6740029959380427 " " y[1] (numeric) = 1.6740029959381206 " " absolute error = 7.79376563286859900000000000000E-14 " " relative error = 4.655765641865708000000000000E-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) = 1.6796548867898125 " " y[1] (numeric) = 1.679654886789891 " " absolute error = 7.86037901434610800000000000000E-14 " " relative error = 4.679758369511853000000000000E-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) = 1.6853050822148261 " " y[1] (numeric) = 1.6853050822149056 " " absolute error = 7.94919685631612100000000000000E-14 " " relative error = 4.7167702395279650000000000000E-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) = 1.6909535910090872 " " y[1] (numeric) = 1.6909535910091673 " " absolute error = 8.0158102377936300000000000000E-14 " " relative error = 4.740408181758641000000000000E-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) = 1.6966004219003241 " " y[1] (numeric) = 1.696600421900405 " " absolute error = 8.0824236192711400000000000000E-14 " " relative error = 4.763893439457122000000000000E-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) = 1.7022455835486965 " " y[1] (numeric) = 1.7022455835487778 " " absolute error = 8.12683254025614600000000000000E-14 " " relative error = 4.7741833603786000000000000E-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) = 1.7078890845474892 " " y[1] (numeric) = 1.7078890845475712 " " absolute error = 8.19344592173365500000000000000E-14 " " relative error = 4.797411023857287000000000000E-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) = 1.7135309334238 " " y[1] (numeric) = 1.7135309334238829 " " absolute error = 8.28226376370366800000000000000E-14 " " relative error = 4.8334486423042894000000000000E-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) = 1.7191711386392179 " " y[1] (numeric) = 1.7191711386393014 " " absolute error = 8.34887714518117700000000000000E-14 " " relative error = 4.8563385910431206000000000000E-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) = 1.7248097085904914 " " y[1] (numeric) = 1.7248097085905754 " " absolute error = 8.39328606616618300000000000000E-14 " " relative error = 4.866209892235097000000000000E-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) = 1.7304466516101904 " " y[1] (numeric) = 1.730446651610275 " " absolute error = 8.45989944764369300000000000000E-14 " " relative error = 4.88885308297237000000000000E-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) = 1.736081975967358 " " y[1] (numeric) = 1.7360819759674428 " " absolute error = 8.48210390813619600000000000000E-14 " " relative error = 4.8857738433750536000000000000E-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) = 1.7417156898681545 " " y[1] (numeric) = 1.7417156898682402 " " absolute error = 8.57092175010620800000000000000E-14 " " relative error = 4.920964885351073000000000000E-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) = 1.7473478014564936 " " y[1] (numeric) = 1.74734780145658 " " absolute error = 8.63753513158371800000000000000E-14 " " relative error = 4.9432260276883294000000000000E-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) = 1.7529783188146704 " " y[1] (numeric) = 1.7529783188147574 " " absolute error = 8.70414851306122700000000000000E-14 " " relative error = 4.965348641018448000000000000E-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) = 1.7586072499639815 " " y[1] (numeric) = 1.758607249964069 " " absolute error = 8.74855743404623400000000000000E-14 " " relative error = 4.974707931077513000000000000E-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) = 1.7642346028653375 " " y[1] (numeric) = 1.7642346028654257 " " absolute error = 8.81517081552374300000000000000E-14 " " relative error = 4.9965978454377913000000000000E-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) = 1.7698603854198667 " " y[1] (numeric) = 1.7698603854199553 " " absolute error = 8.85957973650874900000000000000E-14 " " relative error = 5.00580713003923000000000000E-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) = 1.7754846054695128 " " y[1] (numeric) = 1.7754846054696023 " " absolute error = 8.94839757847876200000000000000E-14 " " relative error = 5.0399747488164960000000000000E-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) = 1.7811072707976252 " " y[1] (numeric) = 1.7811072707977151 " " absolute error = 8.99280649946376800000000000000E-14 " " relative error = 5.048997692001201000000000000E-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) = 1.78672838912954 " " y[1] (numeric) = 1.7867283891296306 " " absolute error = 9.05941988094127700000000000000E-14 " " relative error = 5.070395666212508000000000000E-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) = 1.7923479681331562 " " y[1] (numeric) = 1.7923479681332475 " " absolute error = 9.12603326241878700000000000000E-14 " " relative error = 5.091663797808261000000000000E-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) = 1.7979660154195027 " " y[1] (numeric) = 1.7979660154195947 " " absolute error = 9.19264664389629600000000000000E-14 " " relative error = 5.112803337248540000000000000E-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) = 1.8035825385433006 " " y[1] (numeric) = 1.803582538543393 " " absolute error = 9.23705556488130200000000000000E-14 " " relative error = 5.1215042103600060000000000000E-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) = 1.8091975450035158 " " y[1] (numeric) = 1.8091975450036084 " " absolute error = 9.25926002537380600000000000000E-14 " " relative error = 5.117882262744178000000000000E-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) = 1.8148110422439068 " " y[1] (numeric) = 1.8148110422440002 " " absolute error = 9.34807786734381800000000000000E-14 " " relative error = 5.150992389701063000000000000E-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) = 1.8204230376535662 " " y[1] (numeric) = 1.8204230376536605 " " absolute error = 9.4368957093138310000000000000E-14 " " relative error = 5.183902595232762000000000000E-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) = 1.8260335385674535 " " y[1] (numeric) = 1.8260335385675492 " " absolute error = 9.5701224722688490000000000000E-14 " " relative error = 5.240934665294665000000000000E-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) = 1.8316425522669233 " " y[1] (numeric) = 1.8316425522670197 " " absolute error = 9.63673585374635900000000000000E-14 " " relative error = 5.2612535354234380000000000000E-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) = 1.8372500859802456 " " y[1] (numeric) = 1.8372500859803427 " " absolute error = 9.70334923522386800000000000000E-14 " " relative error = 5.281452595522262000000000000E-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) = 1.8428561468831215 " " y[1] (numeric) = 1.8428561468832192 " " absolute error = 9.76996261670137800000000000000E-14 " " relative error = 5.301532967304915000000000000E-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) = 1.8484607420991912 " " y[1] (numeric) = 1.8484607420992896 " " absolute error = 9.83657599817888700000000000000E-14 " " relative error = 5.32149575814526000000000000E-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) = 1.8540638787005368 " " y[1] (numeric) = 1.8540638787006356 " " absolute error = 9.88098491916389300000000000000E-14 " " relative error = 5.32936595803225900000000000E-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) = 1.8596655637081774 " " y[1] (numeric) = 1.8596655637082766 " " absolute error = 9.925393840148900000000000000E-14 " " relative error = 5.3371928984680670000000000000E-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) = 1.8652658040925614 " " y[1] (numeric) = 1.8652658040926613 " " absolute error = 9.99200722162640900000000000000E-14 " " relative error = 5.356881147825175000000000000E-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) = 1.8708646067740495 " " y[1] (numeric) = 1.87086460677415 " " absolute error = 1.00364161426114150000000000000E-13 " " relative error = 5.364587103883112000000000000E-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) = 1.8764619786233943 " " y[1] (numeric) = 1.8764619786234953 " " absolute error = 1.01030295240889250000000000000E-13 " " relative error = 5.384084324213532000000000000E-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) = 1.8820579264622128 " " y[1] (numeric) = 1.8820579264623147 " " absolute error = 1.01918473660589370000000000000E-13 " " relative error = 5.415267629523498000000000000E-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) = 1.8876524570634539 " " y[1] (numeric) = 1.8876524570635567 " " absolute error = 1.0280665208028950000000000000E-13 " " relative error = 5.446270138106976000000000000E-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) = 1.893245577151861 " " y[1] (numeric) = 1.893245577151964 " " absolute error = 1.03028696685214530000000000000E-13 " " relative error = 5.441908748056217000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7299999999998104 " " y[1] (closed_form) = 1.8988372934044269 " " y[1] (numeric) = 1.8988372934045306 " " absolute error = 1.03694830499989620000000000000E-13 " " relative error = 5.4609644997057680000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7399999999998093 " " y[1] (closed_form) = 1.9044276124508464 " " y[1] (numeric) = 1.904427612450951 " " absolute error = 1.04583008919689750000000000000E-13 " " relative error = 5.491571758146258000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.749999999999808 " " y[1] (closed_form) = 1.9100165408739604 " " y[1] (numeric) = 1.9100165408740657 " " absolute error = 1.05249142734464840000000000000E-13 " " relative error = 5.5103786005071100000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.759999999999807 " " y[1] (closed_form) = 1.9156040852101983 " " y[1] (numeric) = 1.915604085210304 " " absolute error = 1.0569323194431490000000000000E-13 " " relative error = 5.517488334898661000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.769999999999806 " " y[1] (closed_form) = 1.9211902519500113 " " y[1] (numeric) = 1.9211902519501178 " " absolute error = 1.06581410364015030000000000000E-13 " " relative error = 5.54767599178867000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.779999999999805 " " y[1] (closed_form) = 1.9267750475383036 " " y[1] (numeric) = 1.926775047538411 " " absolute error = 1.07247544178790120000000000000E-13 " " relative error = 5.566168417834365000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7899999999998037 " " y[1] (closed_form) = 1.9323584783748582 " " y[1] (numeric) = 1.9323584783749657 " " absolute error = 1.07469588783715150000000000000E-13 " " relative error = 5.5615761768022800000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7999999999998026 " " y[1] (closed_form) = 1.9379405508147554 " " y[1] (numeric) = 1.9379405508148633 " " absolute error = 1.07913677993565220000000000000E-13 " " relative error = 5.568472053912892000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8099999999998015 " " y[1] (closed_form) = 1.9435212711687897 " " y[1] (numeric) = 1.943521271168898 " " absolute error = 1.08357767203415280000000000000E-13 " " relative error = 5.5753321978437300000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8199999999998004 " " y[1] (closed_form) = 1.9491006457038798 " " y[1] (numeric) = 1.9491006457039888 " " absolute error = 1.09023901018190370000000000000E-13 " " relative error = 5.5935490688228940000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8299999999997993 " " y[1] (closed_form) = 1.954678680643474 " " y[1] (numeric) = 1.9546786806435834 " " absolute error = 1.09467990228040430000000000000E-13 " " relative error = 5.600306143002692000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8399999999997982 " " y[1] (closed_form) = 1.9602553821679523 " " y[1] (numeric) = 1.960255382168062 " " absolute error = 1.09690034832965470000000000000E-13 " " relative error = 5.5957012453986130000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.849999999999797 " " y[1] (closed_form) = 1.9658307564150215 " " y[1] (numeric) = 1.965830756415132 " " absolute error = 1.10578213252665590000000000000E-13 " " relative error = 5.6250118628890030000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.859999999999796 " " y[1] (closed_form) = 1.9714048094801084 " " y[1] (numeric) = 1.9714048094802197 " " absolute error = 1.11244347067440690000000000000E-13 " " relative error = 5.642897213828835000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.869999999999795 " " y[1] (closed_form) = 1.9769775474167468 " " y[1] (numeric) = 1.9769775474168585 " " absolute error = 1.11688436277290750000000000000E-13 " " relative error = 5.649453956785218000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.879999999999794 " " y[1] (closed_form) = 1.9825489762369601 " " y[1] (numeric) = 1.9825489762370727 " " absolute error = 1.12576614696990870000000000000E-13 " " relative error = 5.678377485063217000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8899999999997927 " " y[1] (closed_form) = 1.9881191019116409 " " y[1] (numeric) = 1.9881191019117541 " " absolute error = 1.13242748511765970000000000000E-13 " " relative error = 5.695974069303967000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8999999999997916 " " y[1] (closed_form) = 1.9936879303709243 " " y[1] (numeric) = 1.9936879303710378 " " absolute error = 1.134647931166910000000000000E-13 " " relative error = 5.69120128522727000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9099999999997905 " " y[1] (closed_form) = 1.9992554675045584 " " y[1] (numeric) = 1.9992554675046728 " " absolute error = 1.14352971536391120000000000000E-13 " " relative error = 5.7197778570602000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9199999999997894 " " y[1] (closed_form) = 2.004821719162271 " " y[1] (numeric) = 2.0048217191623854 " " absolute error = 1.14575016141316150000000000000E-13 " " relative error = 5.714972810110625000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9299999999997883 " " y[1] (closed_form) = 2.0103866911541295 " " y[1] (numeric) = 2.0103866911542445 " " absolute error = 1.15019105351166220000000000000E-13 " " relative error = 5.721242876172029000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9399999999997872 " " y[1] (closed_form) = 2.0159503892509014 " " y[1] (numeric) = 2.015950389251017 " " absolute error = 1.15463194561016280000000000000E-13 " " relative error = 5.727481944827063000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.949999999999786 " " y[1] (closed_form) = 2.0215128191844047 " " y[1] (numeric) = 2.0215128191845206 " " absolute error = 1.15907283770866340000000000000E-13 " " relative error = 5.733690267550717000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.959999999999785 " " y[1] (closed_form) = 2.02707398664786 " " y[1] (numeric) = 2.0270739866479768 " " absolute error = 1.16795462190566470000000000000E-13 " " relative error = 5.761775986465558000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.969999999999784 " " y[1] (closed_form) = 2.0326338972962357 " " y[1] (numeric) = 2.0326338972963525 " " absolute error = 1.16795462190566470000000000000E-13 " " relative error = 5.746015666959268000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.979999999999783 " " y[1] (closed_form) = 2.038192556746589 " " y[1] (numeric) = 2.0381925567467056 " " absolute error = 1.16795462190566470000000000000E-13 " " relative error = 5.730344849114656000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9899999999997817 " " y[1] (closed_form) = 2.0437499705784057 " " y[1] (numeric) = 2.043749970578523 " " absolute error = 1.17239551400416530000000000000E-13 " " relative error = 5.736491894223066000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9999999999997806 " " y[1] (closed_form) = 2.049306144333933 " " y[1] (numeric) = 2.04930614433405 " " absolute error = 1.17239551400416530000000000000E-13 " " relative error = 5.720938851648338000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0099999999997795 " " y[1] (closed_form) = 2.0548610835185106 " " y[1] (numeric) = 2.054861083518628 " " absolute error = 1.17239551400416530000000000000E-13 " " relative error = 5.705473345169828000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0199999999997784 " " y[1] (closed_form) = 2.060414793600898 " " y[1] (numeric) = 2.0604147936010158 " " absolute error = 1.1768364061026660000000000000E-13 " " relative error = 5.711648012611867000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0299999999997773 " " y[1] (closed_form) = 2.065967280013598 " " y[1] (numeric) = 2.0659672800137163 " " absolute error = 1.18127729820116660000000000000E-13 " " relative error = 5.717792869369118000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.039999999999776 " " y[1] (closed_form) = 2.0715185481531764 " " y[1] (numeric) = 2.0715185481532954 " " absolute error = 1.19015908239816780000000000000E-13 " " relative error = 5.745346009376705000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.049999999999775 " " y[1] (closed_form) = 2.0770686033805763 " " y[1] (numeric) = 2.0770686033806958 " " absolute error = 1.19459997449666840000000000000E-13 " " relative error = 5.751374665970937000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.059999999999774 " " y[1] (closed_form) = 2.0826174510214344 " " y[1] (numeric) = 2.0826174510215547 " " absolute error = 1.20348175869366970000000000000E-13 " " relative error = 5.778698138265448000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.069999999999773 " " y[1] (closed_form) = 2.0881650963663887 " " y[1] (numeric) = 2.0881650963665086 " " absolute error = 1.1990408665951690000000000000E-13 " " relative error = 5.742078864748852000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.079999999999772 " " y[1] (closed_form) = 2.0937115446713834 " " y[1] (numeric) = 2.0937115446715038 " " absolute error = 1.20348175869366970000000000000E-13 " " relative error = 5.7480781522010530000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0899999999997707 " " y[1] (closed_form) = 2.0992568011579724 " " y[1] (numeric) = 2.0992568011580937 " " absolute error = 1.2123635428906710000000000000E-13 " " relative error = 5.775203596920196000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0999999999997696 " " y[1] (closed_form) = 2.104800871013621 " " y[1] (numeric) = 2.104800871013743 " " absolute error = 1.22124532708767220000000000000E-13 " " relative error = 5.8021893847827520000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.1099999999997685 " " y[1] (closed_form) = 2.1103437593919976 " " y[1] (numeric) = 2.11034375939212 " " absolute error = 1.22568621918617280000000000000E-13 " " relative error = 5.807993194148142000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.1199999999997674 " " y[1] (closed_form) = 2.1158854714132693 " " y[1] (numeric) = 2.115885471413392 " " absolute error = 1.22568621918617280000000000000E-13 " " relative error = 5.7927814891015660000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.1299999999997663 " " y[1] (closed_form) = 2.1214260121643926 " " y[1] (numeric) = 2.121426012164515 " " absolute error = 1.22568621918617280000000000000E-13 " " relative error = 5.7776524477309580000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.139999999999765 " " y[1] (closed_form) = 2.126965386699397 " " y[1] (numeric) = 2.1269653866995206 " " absolute error = 1.2345680033831741000000000000E-13 " " relative error = 5.804363395395746000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.149999999999764 " " y[1] (closed_form) = 2.132503600039672 " " y[1] (numeric) = 2.1325036000397963 " " absolute error = 1.24344978758017530000000000000E-13 " " relative error = 5.830938749913682000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.159999999999763 " " y[1] (closed_form) = 2.1380406571742436 " " y[1] (numeric) = 2.138040657174369 " " absolute error = 1.25233157177717660000000000000E-13 " " relative error = 5.8573795946066310000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.169999999999762 " " y[1] (closed_form) = 2.143576563060056 " " y[1] (numeric) = 2.143576563060182 " " absolute error = 1.26121335597417780000000000000E-13 " " relative error = 5.883687001007963000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.179999999999761 " " y[1] (closed_form) = 2.1491113226222427 " " y[1] (numeric) = 2.1491113226223697 " " absolute error = 1.2700951401711790000000000000E-13 " " relative error = 5.90986202902449000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.1899999999997597 " " y[1] (closed_form) = 2.1546449407544004 " " y[1] (numeric) = 2.154644940754528 " " absolute error = 1.27453603226967970000000000000E-13 " " relative error = 5.915294943321054000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.1999999999997586 " " y[1] (closed_form) = 2.160177422318856 " " y[1] (numeric) = 2.160177422318984 " " absolute error = 1.27897692436818030000000000000E-13 " " relative error = 5.92070313833414000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.2099999999997575 " " y[1] (closed_form) = 2.165708772146934 " " y[1] (numeric) = 2.1657087721470623 " " absolute error = 1.2834178164666810000000000000E-13 " " relative error = 5.926086798800696000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.2199999999997564 " " y[1] (closed_form) = 2.1712389950392175 " " y[1] (numeric) = 2.171238995039347 " " absolute error = 1.29674049276218280000000000000E-13 " " relative error = 5.972352632413738000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.2299999999997553 " " y[1] (closed_form) = 2.1767680957658113 " " y[1] (numeric) = 2.176768095765941 " " absolute error = 1.29674049276218280000000000000E-13 " " relative error = 5.957182555572026000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.239999999999754 " " y[1] (closed_form) = 2.182296079066597 " " y[1] (numeric) = 2.182296079066727 " " absolute error = 1.30118138486068350000000000000E-13 " " relative error = 5.962442023069664000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.249999999999753 " " y[1] (closed_form) = 2.1878229496514874 " " y[1] (numeric) = 2.187822949651619 " " absolute error = 1.31450406115618530000000000000E-13 " " relative error = 6.008274396086672000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.259999999999752 " " y[1] (closed_form) = 2.1933487122006814 " " y[1] (numeric) = 2.193348712200814 " " absolute error = 1.32782673745168720000000000000E-13 " " relative error = 6.053878847743374000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.269999999999751 " " y[1] (closed_form) = 2.198873371364911 " " y[1] (numeric) = 2.1988733713650452 " " absolute error = 1.3411494137471890000000000000E-13 " " relative error = 6.099257152378423000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.27999999999975 " " y[1] (closed_form) = 2.2043969317656895 " " y[1] (numeric) = 2.204396931765824 " " absolute error = 1.34559030584568970000000000000E-13 " " relative error = 6.1041198454576500000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.2899999999997487 " " y[1] (closed_form) = 2.2099193979955536 " " y[1] (numeric) = 2.2099193979956886 " " absolute error = 1.35003119794419040000000000000E-13 " " relative error = 6.108961255187402000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.2999999999997476 " " y[1] (closed_form) = 2.2154407746183082 " " y[1] (numeric) = 2.215440774618444 " " absolute error = 1.35891298214119160000000000000E-13 " " relative error = 6.133826720668327000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3099999999997465 " " y[1] (closed_form) = 2.220961066169264 " " y[1] (numeric) = 2.2209610661694 " " absolute error = 1.36335387423969220000000000000E-13 " " relative error = 6.138576200217768000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3199999999997454 " " y[1] (closed_form) = 2.2264802771554733 " " y[1] (numeric) = 2.226480277155609 " " absolute error = 1.35891298214119160000000000000E-13 " " relative error = 6.103413518117141000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3299999999997443 " " y[1] (closed_form) = 2.2319984120559657 " " y[1] (numeric) = 2.231998412056102 " " absolute error = 1.36335387423969220000000000000E-13 " " relative error = 6.1082206280956220000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.339999999999743 " " y[1] (closed_form) = 2.2375154753219797 " " y[1] (numeric) = 2.2375154753221165 " " absolute error = 1.36779476633819290000000000000E-13 " " relative error = 6.113006955365823000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.349999999999742 " " y[1] (closed_form) = 2.243031471377192 " " y[1] (numeric) = 2.2430314713773303 " " absolute error = 1.38111744263369470000000000000E-13 " " relative error = 6.1573698820449740000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.359999999999741 " " y[1] (closed_form) = 2.248546404617944 " " y[1] (numeric) = 2.2485464046180828 " " absolute error = 1.38555833473219540000000000000E-13 " " relative error = 6.1620179680820020000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.36999999999974 " " y[1] (closed_form) = 2.2540602794134674 " " y[1] (numeric) = 2.254060279413607 " " absolute error = 1.39444011892919660000000000000E-13 " " relative error = 6.186347950251118000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3799999999997388 " " y[1] (closed_form) = 2.259573100106106 " " y[1] (numeric) = 2.259573100106246 " " absolute error = 1.39888101102769720000000000000E-13 " " relative error = 6.190908410805599000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3899999999997377 " " y[1] (closed_form) = 2.265084871011537 " " y[1] (numeric) = 2.265084871011677 " " absolute error = 1.39888101102769720000000000000E-13 " " relative error = 6.175843691026853000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3999999999997366 " " y[1] (closed_form) = 2.2705955964189863 " " y[1] (numeric) = 2.2705955964191262 " " absolute error = 1.39888101102769720000000000000E-13 " " relative error = 6.160854945873707000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4099999999997355 " " y[1] (closed_form) = 2.276105280591448 " " y[1] (numeric) = 2.2761052805915885 " " absolute error = 1.40332190312619800000000000000E-13 " " relative error = 6.165452517036221000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4199999999997344 " " y[1] (closed_form) = 2.2816139277658944 " " y[1] (numeric) = 2.2816139277660348 " " absolute error = 1.40332190312619800000000000000E-13 " " relative error = 6.1505668686914950000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4299999999997333 " " y[1] (closed_form) = 2.287121542153489 " " y[1] (numeric) = 2.287121542153631 " " absolute error = 1.41664457942169970000000000000E-13 " " relative error = 6.194006541899069000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.439999999999732 " " y[1] (closed_form) = 2.2926281279397966 " " y[1] (numeric) = 2.292628127939939 " " absolute error = 1.4255263636187010000000000000E-13 " " relative error = 6.217869990540981000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.449999999999731 " " y[1] (closed_form) = 2.298133689284988 " " y[1] (numeric) = 2.298133689285131 " " absolute error = 1.42996725571720160000000000000E-13 " " relative error = 6.222297955877855000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.45999999999973 " " y[1] (closed_form) = 2.303638230324047 " " y[1] (numeric) = 2.303638230324191 " " absolute error = 1.44328993201270350000000000000E-13 " " relative error = 6.265262978422091000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.469999999999729 " " y[1] (closed_form) = 2.3091417551669715 " " y[1] (numeric) = 2.3091417551671167 " " absolute error = 1.45217171620970480000000000000E-13 " " relative error = 6.288794150295463000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4799999999997278 " " y[1] (closed_form) = 2.314644267898977 " " y[1] (numeric) = 2.3146442678991224 " " absolute error = 1.45217171620970480000000000000E-13 " " relative error = 6.2738440474391080000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4899999999997267 " " y[1] (closed_form) = 2.320145772580693 " " y[1] (numeric) = 2.3201457725808385 " " absolute error = 1.45661260830820540000000000000E-13 " " relative error = 6.278108149592767000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4999999999997256 " " y[1] (closed_form) = 2.3256462732483607 " " y[1] (numeric) = 2.3256462732485064 " " absolute error = 1.45661260830820540000000000000E-13 " " relative error = 6.263259486463832000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5099999999997245 " " y[1] (closed_form) = 2.331145773914028 " " y[1] (numeric) = 2.3311457739141748 " " absolute error = 1.46549439250520660000000000000E-13 " " relative error = 6.286584086265098000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5199999999997234 " " y[1] (closed_form) = 2.3366442785657435 " " y[1] (numeric) = 2.336644278565891 " " absolute error = 1.4743761767022080000000000000E-13 " " relative error = 6.309801582666212000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5299999999997222 " " y[1] (closed_form) = 2.3421417911677453 " " y[1] (numeric) = 2.3421417911678937 " " absolute error = 1.48325796089920900000000000000E-13 " " relative error = 6.332912748889068000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.539999999999721 " " y[1] (closed_form) = 2.347638315660652 " " y[1] (numeric) = 2.347638315660801 " " absolute error = 1.48769885299770980000000000000E-13 " " relative error = 6.337001926887764000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.54999999999972 " " y[1] (closed_form) = 2.3531338559616497 " " y[1] (numeric) = 2.3531338559617985 " " absolute error = 1.48769885299770980000000000000E-13 " " relative error = 6.322202407774781000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.559999999999719 " " y[1] (closed_form) = 2.3586284159646755 " " y[1] (numeric) = 2.3586284159648243 " " absolute error = 1.48769885299770980000000000000E-13 " " relative error = 6.307474475114568000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.569999999999718 " " y[1] (closed_form) = 2.3641219995406044 " " y[1] (numeric) = 2.3641219995407536 " " absolute error = 1.49213974509621040000000000000E-13 " " relative error = 6.311602131303556000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5799999999997167 " " y[1] (closed_form) = 2.3696146105374285 " " y[1] (numeric) = 2.3696146105375786 " " absolute error = 1.50102152929321160000000000000E-13 " " relative error = 6.334454229891755000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5899999999997156 " " y[1] (closed_form) = 2.375106252780438 " " y[1] (numeric) = 2.3751062527805886 " " absolute error = 1.50546242139171230000000000000E-13 " " relative error = 6.338505570558497000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5999999999997145 " " y[1] (closed_form) = 2.3805969300723997 " " y[1] (numeric) = 2.380596930072551 " " absolute error = 1.51434420558871350000000000000E-13 " " relative error = 6.3611953223121180000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6099999999997134 " " y[1] (closed_form) = 2.3860866461937325 " " y[1] (numeric) = 2.3860866461938848 " " absolute error = 1.52322598978571480000000000000E-13 " " relative error = 6.383783221852205000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6199999999997123 " " y[1] (closed_form) = 2.3915754049026825 " " y[1] (numeric) = 2.3915754049028366 " " absolute error = 1.54098955817971730000000000000E-13 " " relative error = 6.443407784762792000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6299999999997112 " " y[1] (closed_form) = 2.3970632099354976 " " y[1] (numeric) = 2.397063209935652 " " absolute error = 1.5454304502782180000000000000E-13 " " relative error = 6.4471827187227320000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.63999999999971 " " y[1] (closed_form) = 2.402550065006596 " " y[1] (numeric) = 2.4025500650067504 " " absolute error = 1.5454304502782180000000000000E-13 " " relative error = 6.432458881034703000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.649999999999709 " " y[1] (closed_form) = 2.408035973808738 " " y[1] (numeric) = 2.408035973808893 " " absolute error = 1.54987134237671850000000000000E-13 " " relative error = 6.436246631005769000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.659999999999708 " " y[1] (closed_form) = 2.413520940013194 " " y[1] (numeric) = 2.4135209400133495 " " absolute error = 1.55431223447521920000000000000E-13 " " relative error = 6.440019677089366000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.669999999999707 " " y[1] (closed_form) = 2.41900496726991 " " y[1] (numeric) = 2.4190049672700664 " " absolute error = 1.56319401867222040000000000000E-13 " " relative error = 6.4621364561993500000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6799999999997057 " " y[1] (closed_form) = 2.4244880592076727 " " y[1] (numeric) = 2.42448805920783 " " absolute error = 1.57207580286922170000000000000E-13 " " relative error = 6.4841556835011960000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6899999999997046 " " y[1] (closed_form) = 2.429970219434274 " " y[1] (numeric) = 2.429970219434431 " " absolute error = 1.57207580286922170000000000000E-13 " " relative error = 6.469527034924814000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6999999999997035 " " y[1] (closed_form) = 2.4354514515366694 " " y[1] (numeric) = 2.435451451536827 " " absolute error = 1.57651669496772230000000000000E-13 " " relative error = 6.4732010731439760000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7099999999997024 " " y[1] (closed_form) = 2.440931759081142 " " y[1] (numeric) = 2.440931759081301 " " absolute error = 1.58983937126322420000000000000E-13 " " relative error = 6.513247924070189000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7199999999997013 " " y[1] (closed_form) = 2.4464111456134594 " " y[1] (numeric) = 2.4464111456136197 " " absolute error = 1.6031620475587260000000000000E-13 " " relative error = 6.553117820907896000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7299999999997 " " y[1] (closed_form) = 2.45188961465903 " " y[1] (numeric) = 2.4518896146591906 " " absolute error = 1.60760293965722670000000000000E-13 " " relative error = 6.556587743778941000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.739999999999699 " " y[1] (closed_form) = 2.4573671697230592 " " y[1] (numeric) = 2.457367169723221 " " absolute error = 1.6164847238542280000000000000E-13 " " relative error = 6.578116383138637000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.749999999999698 " " y[1] (closed_form) = 2.462843814290704 " " y[1] (numeric) = 2.4628438142908653 " " absolute error = 1.61204383175572730000000000000E-13 " " relative error = 6.545457013562160000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.759999999999697 " " y[1] (closed_form) = 2.468319551827225 " " y[1] (numeric) = 2.4683195518273875 " " absolute error = 1.62536650805122920000000000000E-13 " " relative error = 6.584911207497497000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.769999999999696 " " y[1] (closed_form) = 2.4737943857781377 " " y[1] (numeric) = 2.4737943857783002 " " absolute error = 1.62536650805122920000000000000E-13 " " relative error = 6.570337928630905000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7799999999996947 " " y[1] (closed_form) = 2.479268319569362 " " y[1] (numeric) = 2.4792683195695253 " " absolute error = 1.63424829224823040000000000000E-13 " " relative error = 6.591655608022662000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7899999999996936 " " y[1] (closed_form) = 2.484741356607371 " " y[1] (numeric) = 2.484741356607535 " " absolute error = 1.64313007644523170000000000000E-13 " " relative error = 6.612881747534227000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7999999999996925 " " y[1] (closed_form) = 2.490213500279337 " " y[1] (numeric) = 2.4902135002795025 " " absolute error = 1.65645275274073360000000000000E-13 " " relative error = 6.6518503435746500000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.8099999999996914 " " y[1] (closed_form) = 2.495684753953279 " " y[1] (numeric) = 2.4956847539534452 " " absolute error = 1.66089364483923420000000000000E-13 " " relative error = 6.6550618711289660000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.8199999999996903 " " y[1] (closed_form) = 2.501155120978205 " " y[1] (numeric) = 2.501155120978371 " " absolute error = 1.66089364483923420000000000000E-13 " " relative error = 6.6405063440833560000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.829999999999689 " " y[1] (closed_form) = 2.5066246046842546 " " y[1] (numeric) = 2.506624604684421 " " absolute error = 1.66533453693773480000000000000E-13 " " relative error = 6.6437333050415330000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.839999999999688 " " y[1] (closed_form) = 2.512093208382842 " " y[1] (numeric) = 2.512093208383009 " " absolute error = 1.6742163211347360000000000000E-13 " " relative error = 6.664626597245218000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.849999999999687 " " y[1] (closed_form) = 2.5175609353667943 " " y[1] (numeric) = 2.517560935366962 " " absolute error = 1.67865721323323670000000000000E-13 " " relative error = 6.667791788676869000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.859999999999686 " " y[1] (closed_form) = 2.5230277889104924 " " y[1] (numeric) = 2.5230277889106616 " " absolute error = 1.69197988952873860000000000000E-13 " " relative error = 6.706148449753614000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.869999999999685 " " y[1] (closed_form) = 2.528493772270007 " " y[1] (numeric) = 2.5284937722701777 " " absolute error = 1.70530256582424040000000000000E-13 " " relative error = 6.744341570172309000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.8799999999996837 " " y[1] (closed_form) = 2.5339588886832365 " " y[1] (numeric) = 2.533958888683408 " " absolute error = 1.71418435002124170000000000000E-13 " " relative error = 6.764846729269598000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.8899999999996826 " " y[1] (closed_form) = 2.5394231413700394 " " y[1] (numeric) = 2.5394231413702113 " " absolute error = 1.71862524211974230000000000000E-13 " " relative error = 6.767778138748984000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.8999999999996815 " " y[1] (closed_form) = 2.5448865335323694 " " y[1] (numeric) = 2.5448865335325426 " " absolute error = 1.73194791841524420000000000000E-13 " " relative error = 6.8055997609105780000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.9099999999996804 " " y[1] (closed_form) = 2.5503490683544094 " " y[1] (numeric) = 2.5503490683545835 " " absolute error = 1.74082970261224550000000000000E-13 " " relative error = 6.825848760128749000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.9199999999996793 " " y[1] (closed_form) = 2.5558107490027 " " y[1] (numeric) = 2.555810749002875 " " absolute error = 1.74971148680924670000000000000E-13 " " relative error = 6.846013490991067000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.929999999999678 " " y[1] (closed_form) = 2.561271578626272 " " y[1] (numeric) = 2.5612715786264477 " " absolute error = 1.7585932710062480000000000000E-13 " " relative error = 6.866094504314387000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.939999999999677 " " y[1] (closed_form) = 2.566731560356773 " " y[1] (numeric) = 2.5667315603569496 " " absolute error = 1.76747505520324920000000000000E-13 " " relative error = 6.886092346008992000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.949999999999676 " " y[1] (closed_form) = 2.5721906973085975 " " y[1] (numeric) = 2.5721906973087743 " " absolute error = 1.76747505520324920000000000000E-13 " " relative error = 6.871477519348159000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.959999999999675 " " y[1] (closed_form) = 2.5776489925790123 " " y[1] (numeric) = 2.5776489925791894 " " absolute error = 1.77191594730174980000000000000E-13 " " relative error = 6.874155295787178000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.969999999999674 " " y[1] (closed_form) = 2.5831064492482807 " " y[1] (numeric) = 2.5831064492484583 " " absolute error = 1.77635683940025050000000000000E-13 " " relative error = 6.8768239880984960000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.9799999999996727 " " y[1] (closed_form) = 2.588563070379789 " " y[1] (numeric) = 2.588563070379968 " " absolute error = 1.78967951569575230000000000000E-13 " " relative error = 6.913795287333580000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.9899999999996716 " " y[1] (closed_form) = 2.594018859020167 " " y[1] (numeric) = 2.5940188590203466 " " absolute error = 1.7941204077942530000000000000E-13 " " relative error = 6.916373801815543000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.9999999999996705 " " y[1] (closed_form) = 2.599473818199413 " " y[1] (numeric) = 2.5994738181995927 " " absolute error = 1.79856129989275360000000000000E-13 " " relative error = 6.918943700454616000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.009999999999674 " " y[1] (closed_form) = 2.6049279509310144 " " y[1] (numeric) = 2.604927950931192 " " absolute error = 1.77635683940025050000000000000E-13 " " relative error = 6.819216780123887000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.019999999999677 " " y[1] (closed_form) = 2.610381260212061 " " y[1] (numeric) = 2.610381260212237 " " absolute error = 1.7585932710062480000000000000E-13 " " relative error = 6.736921145623701000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.0299999999996805 " " y[1] (closed_form) = 2.615833749023373 " " y[1] (numeric) = 2.615833749023546 " " absolute error = 1.73194791841524420000000000000E-13 " " relative error = 6.62101679459511000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.039999999999684 " " y[1] (closed_form) = 2.6212854203296123 " " y[1] (numeric) = 2.621285420329783 " " absolute error = 1.70530256582424040000000000000E-13 " " relative error = 6.5055966534533580000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.049999999999687 " " y[1] (closed_form) = 2.6267362770794014 " " y[1] (numeric) = 2.6267362770795715 " " absolute error = 1.70086167372573980000000000000E-13 " " relative error = 6.475190100229182000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.0599999999996905 " " y[1] (closed_form) = 2.6321863222054405 " " y[1] (numeric) = 2.632186322205608 " " absolute error = 1.6742163211347360000000000000E-13 " " relative error = 6.36055398894389000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.069999999999694 " " y[1] (closed_form) = 2.6376355586246176 " " y[1] (numeric) = 2.6376355586247837 " " absolute error = 1.66089364483923420000000000000E-13 " " relative error = 6.2969034497900810000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.079999999999697 " " y[1] (closed_form) = 2.6430839892381264 " " y[1] (numeric) = 2.64308398923829 " " absolute error = 1.63424829224823040000000000000E-13 " " relative error = 6.183111467143749000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.0899999999997005 " " y[1] (closed_form) = 2.6485316169315753 " " y[1] (numeric) = 2.6485316169317374 " " absolute error = 1.62092561595272850000000000000E-13 " " relative error = 6.120091622053705000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.099999999999704 " " y[1] (closed_form) = 2.6539784445751007 " " y[1] (numeric) = 2.653978444575262 " " absolute error = 1.61204383175572730000000000000E-13 " " relative error = 6.074065277549057000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.109999999999707 " " y[1] (closed_form) = 2.659424475023478 " " y[1] (numeric) = 2.6594244750236373 " " absolute error = 1.59428026336172480000000000000E-13 " " relative error = 5.994831883118810000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.119999999999710 " " y[1] (closed_form) = 2.6648697111162285 " " y[1] (numeric) = 2.6648697111163857 " " absolute error = 1.57207580286922170000000000000E-13 " " relative error = 5.8992595259403110000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.129999999999714 " " y[1] (closed_form) = 2.6703141556777306 " " y[1] (numeric) = 2.6703141556778855 " " absolute error = 1.54987134237671850000000000000E-13 " " relative error = 5.804078666479444000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.139999999999717 " " y[1] (closed_form) = 2.6757578115173244 " " y[1] (numeric) = 2.675757811517478 " " absolute error = 1.53654866608121670000000000000E-13 " " relative error = 5.742480352546915000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.149999999999720 " " y[1] (closed_form) = 2.681200681429422 " " y[1] (numeric) = 2.681200681429574 " " absolute error = 1.52322598978571480000000000000E-13 " " relative error = 5.681133830585336000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.159999999999724 " " y[1] (closed_form) = 2.686642768193609 " " y[1] (numeric) = 2.68664276819376 " " absolute error = 1.5099033134902130000000000000E-13 " " relative error = 5.620037510626734000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.169999999999727 " " y[1] (closed_form) = 2.692084074574753 " " y[1] (numeric) = 2.6920840745749026 " " absolute error = 1.4965806371947110000000000000E-13 " " relative error = 5.5591898162805850000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.179999999999730 " " y[1] (closed_form) = 2.697524603323105 " " y[1] (numeric) = 2.6975246033232523 " " absolute error = 1.4743761767022080000000000000E-13 " " relative error = 5.4656635008478160000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.189999999999734 " " y[1] (closed_form) = 2.7029643571744018 " " y[1] (numeric) = 2.702964357174547 " " absolute error = 1.45217171620970480000000000000E-13 " " relative error = 5.372515225201717000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.199999999999737 " " y[1] (closed_form) = 2.7084033388499695 " " y[1] (numeric) = 2.7084033388501134 " " absolute error = 1.4388490399142030000000000000E-13 " " relative error = 5.312536058699295000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.209999999999740 " " y[1] (closed_form) = 2.713841551056825 " " y[1] (numeric) = 2.713841551056967 " " absolute error = 1.42108547152020040000000000000E-13 " " relative error = 5.236434938387619000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.219999999999744 " " y[1] (closed_form) = 2.7192789964877737 " " y[1] (numeric) = 2.719278996487914 " " absolute error = 1.40332190312619800000000000000E-13 " " relative error = 5.16063965830182000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.229999999999747 " " y[1] (closed_form) = 2.724715677821511 " " y[1] (numeric) = 2.7247156778216493 " " absolute error = 1.38111744263369470000000000000E-13 " " relative error = 5.068849766144914000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.239999999999750 " " y[1] (closed_form) = 2.7301515977227195 " " y[1] (numeric) = 2.730151597722856 " " absolute error = 1.36335387423969220000000000000E-13 " " relative error = 4.993692934036689000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.249999999999754 " " y[1] (closed_form) = 2.7355867588421674 " " y[1] (numeric) = 2.7355867588423024 " " absolute error = 1.35003119794419040000000000000E-13 " " relative error = 4.935069939129216300000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.259999999999757 " " y[1] (closed_form) = 2.7410211638168045 " " y[1] (numeric) = 2.7410211638169377 " " absolute error = 1.33226762955018780000000000000E-13 " " relative error = 4.860479178843837000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.269999999999760 " " y[1] (closed_form) = 2.7464548152698582 " " y[1] (numeric) = 2.74645481526999 " " absolute error = 1.3189449532546860000000000000E-13 " " relative error = 4.802354460454105000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.279999999999764 " " y[1] (closed_form) = 2.7518877158109296 " " y[1] (numeric) = 2.7518877158110597 " " absolute error = 1.30118138486068350000000000000E-13 " " relative error = 4.728322952222088000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.289999999999767 " " y[1] (closed_form) = 2.757319868036086 " " y[1] (numeric) = 2.7573198680362134 " " absolute error = 1.27453603226967970000000000000E-13 " " relative error = 4.622372786866668000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.299999999999770 " " y[1] (closed_form) = 2.762751274527955 " " y[1] (numeric) = 2.7627512745280804 " " absolute error = 1.25233157177717660000000000000E-13 " " relative error = 4.532914646799504000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.309999999999774 " " y[1] (closed_form) = 2.7681819378558186 " " y[1] (numeric) = 2.7681819378559425 " " absolute error = 1.23900889548167470000000000000E-13 " " relative error = 4.475894010208691400000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.319999999999777 " " y[1] (closed_form) = 2.773611860575702 " " y[1] (numeric) = 2.773611860575824 " " absolute error = 1.22124532708767220000000000000E-13 " " relative error = 4.403086619460105400000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.329999999999780 " " y[1] (closed_form) = 2.7790410452304677 " " y[1] (numeric) = 2.779041045230588 " " absolute error = 1.20348175869366970000000000000E-13 " " relative error = 4.330564893091977000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.339999999999784 " " y[1] (closed_form) = 2.784469494349903 " " y[1] (numeric) = 2.784469494350022 " " absolute error = 1.19015908239816780000000000000E-13 " " relative error = 4.2742758892247706000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.349999999999787 " " y[1] (closed_form) = 2.789897210450812 " " y[1] (numeric) = 2.7898972104509294 " " absolute error = 1.17239551400416530000000000000E-13 " " relative error = 4.202289280094018000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.359999999999790 " " y[1] (closed_form) = 2.795324196037103 " " y[1] (numeric) = 2.795324196037218 " " absolute error = 1.15019105351166220000000000000E-13 " " relative error = 4.114696446094782000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.369999999999794 " " y[1] (closed_form) = 2.8007504535998757 " " y[1] (numeric) = 2.800750453599988 " " absolute error = 1.12354570092065840000000000000E-13 " " relative error = 4.011588035187271000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.379999999999797 " " y[1] (closed_form) = 2.8061759856175104 " " y[1] (numeric) = 2.8061759856176205 " " absolute error = 1.10134124042815530000000000000E-13 " " relative error = 3.924704815638285000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.389999999999800 " " y[1] (closed_form) = 2.811600794555752 " " y[1] (numeric) = 2.811600794555861 " " absolute error = 1.08801856413265340000000000000E-13 " " relative error = 3.869747676268408500000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.399999999999804 " " y[1] (closed_form) = 2.8170248828677984 " " y[1] (numeric) = 2.8170248828679054 " " absolute error = 1.07025499573865090000000000000E-13 " " relative error = 3.7992387012538764000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.409999999999807 " " y[1] (closed_form) = 2.8224482529943837 " " y[1] (numeric) = 2.8224482529944885 " " absolute error = 1.04805053524614780000000000000E-13 " " relative error = 3.7132674943969400000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.419999999999810 " " y[1] (closed_form) = 2.827870907363862 " " y[1] (numeric) = 2.8278709073639656 " " absolute error = 1.03472785895064590000000000000E-13 " " relative error = 3.659034987262619000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.429999999999814 " " y[1] (closed_form) = 2.833292848392294 " " y[1] (numeric) = 2.8332928483923956 " " absolute error = 1.01696429055664340000000000000E-13 " " relative error = 3.589337018704944000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.439999999999817 " " y[1] (closed_form) = 2.838714078483526 " " y[1] (numeric) = 2.838714078483626 " " absolute error = 9.99200722162640900000000000000E-14 " " relative error = 3.5199061777170090000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.449999999999820 " " y[1] (closed_form) = 2.8441346000292738 " " y[1] (numeric) = 2.8441346000293715 " " absolute error = 9.76996261670137800000000000000E-14 " " relative error = 3.435126669673375700000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.459999999999824 " " y[1] (closed_form) = 2.8495544154092056 " " y[1] (numeric) = 2.8495544154093015 " " absolute error = 9.59232693276135300000000000000E-14 " " relative error = 3.366255047066319000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.4699999999998274 " " y[1] (closed_form) = 2.8549735269910204 " " y[1] (numeric) = 2.8549735269911145 " " absolute error = 9.41469124882132700000000000000E-14 " " relative error = 3.2976457258936040000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.479999999999830 " " y[1] (closed_form) = 2.8603919371305295 " " y[1] (numeric) = 2.8603919371306223 " " absolute error = 9.28146448586630900000000000000E-14 " " relative error = 3.244822629159425700000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.489999999999834 " " y[1] (closed_form) = 2.865809648171736 " " y[1] (numeric) = 2.8658096481718274 " " absolute error = 9.1482377229112900000000000000E-14 " " relative error = 3.1922000572325090000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.4999999999998375 " " y[1] (closed_form) = 2.871226662446912 " " y[1] (numeric) = 2.8712266624470018 " " absolute error = 8.97060203897126500000000000000E-14 " " relative error = 3.1243099530590020000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.509999999999840 " " y[1] (closed_form) = 2.876642982276679 " " y[1] (numeric) = 2.876642982276767 " " absolute error = 8.7929663550312400000000000000E-14 " " relative error = 3.0566762748125836000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.519999999999844 " " y[1] (closed_form) = 2.8820586099700845 " " y[1] (numeric) = 2.88205860997017 " " absolute error = 8.57092175010620800000000000000E-14 " " relative error = 2.9738887753553260000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.5299999999998475 " " y[1] (closed_form) = 2.887473547824677 " " y[1] (numeric) = 2.8874735478247615 " " absolute error = 8.4376949871511900000000000000E-14 " " relative error = 2.9221722199006310000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.539999999999850 " " y[1] (closed_form) = 2.8928877981265866 " " y[1] (numeric) = 2.892887798126669 " " absolute error = 8.26005930321116500000000000000E-14 " " relative error = 2.8552988845818080000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.549999999999854 " " y[1] (closed_form) = 2.898301363150595 " " y[1] (numeric) = 2.8983013631506758 " " absolute error = 8.0824236192711400000000000000E-14 " " relative error = 2.7886760576495573000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.5599999999998575 " " y[1] (closed_form) = 2.9037142451602147 " " y[1] (numeric) = 2.9037142451602946 " " absolute error = 7.99360577730112700000000000000E-14 " " relative error = 2.7528899548654020000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.569999999999860 " " y[1] (closed_form) = 2.909126446407763 " " y[1] (numeric) = 2.90912644640784 " " absolute error = 7.7271522513910900000000000000E-14 " " relative error = 2.6561761386936970000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.579999999999864 " " y[1] (closed_form) = 2.9145379691344315 " " y[1] (numeric) = 2.9145379691345075 " " absolute error = 7.59392548843607100000000000000E-14 " " relative error = 2.605533216193213000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.5899999999998675 " " y[1] (closed_form) = 2.919948815570366 " " y[1] (numeric) = 2.919948815570439 " " absolute error = 7.28306304154102700000000000000E-14 " " relative error = 2.494243393139202700000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.599999999999870 " " y[1] (closed_form) = 2.925358987934733 " " y[1] (numeric) = 2.9253589879348043 " " absolute error = 7.14983627858600800000000000000E-14 " " relative error = 2.4440885060857792000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.609999999999874 " " y[1] (closed_form) = 2.9307684884357945 " " y[1] (numeric) = 2.930768488435864 " " absolute error = 6.92779167366097700000000000000E-14 " " relative error = 2.3638140306873806000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.6199999999998775 " " y[1] (closed_form) = 2.936177319270979 " " y[1] (numeric) = 2.9361773192710467 " " absolute error = 6.79456491070595800000000000000E-14 " " relative error = 2.314085346995655700000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.629999999999880 " " y[1] (closed_form) = 2.941585482626952 " " y[1] (numeric) = 2.9415854826270174 " " absolute error = 6.5281113847959200000000000000E-14 " " relative error = 2.219249252945748000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.639999999999884 " " y[1] (closed_form) = 2.9469929806796866 " " y[1] (numeric) = 2.9469929806797506 " " absolute error = 6.39488462184090200000000000000E-14 " " relative error = 2.1699694107740977000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.649999999999888 " " y[1] (closed_form) = 2.952399815594532 " " y[1] (numeric) = 2.952399815594595 " " absolute error = 6.30606677987088900000000000000E-14 " " relative error = 2.1359121981251786000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.659999999999891 " " y[1] (closed_form) = 2.9578059895262845 " " y[1] (numeric) = 2.957805989526346 " " absolute error = 6.1728400169158700000000000000E-14 " " relative error = 2.086965824930423800000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.669999999999894 " " y[1] (closed_form) = 2.9632115046192533 " " y[1] (numeric) = 2.9632115046193133 " " absolute error = 5.99520433297584500000000000000E-14 " " relative error = 2.0232117496945853000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.679999999999898 " " y[1] (closed_form) = 2.968616363007331 " " y[1] (numeric) = 2.9686163630073885 " " absolute error = 5.77315972805081400000000000000E-14 " " relative error = 1.944730818030783000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.689999999999901 " " y[1] (closed_form) = 2.974020566814059 " " y[1] (numeric) = 2.9740205668141155 " " absolute error = 5.63993296509579500000000000000E-14 " " relative error = 1.8964001217845017000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.699999999999904 " " y[1] (closed_form) = 2.979424118152696 " " y[1] (numeric) = 2.979424118152751 " " absolute error = 5.506706202140776000000000000000E-14 " " relative error = 1.8482451587171306000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.709999999999908 " " y[1] (closed_form) = 2.9848270191262833 " " y[1] (numeric) = 2.984827019126337 " " absolute error = 5.373479439185758000000000000000E-14 " " relative error = 1.8002649415706104000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.719999999999911 " " y[1] (closed_form) = 2.9902292718277104 " " y[1] (numeric) = 2.9902292718277623 " " absolute error = 5.195843755245733000000000000000E-14 " " relative error = 1.7376071474512356000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.729999999999914 " " y[1] (closed_form) = 2.9956308783397807 " " y[1] (numeric) = 2.99563087833983 " " absolute error = 4.92939022933569500000000000000E-14 " " relative error = 1.6455265783839265000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.739999999999918 " " y[1] (closed_form) = 3.001031840735276 " " y[1] (numeric) = 3.0010318407353234 " " absolute error = 4.7517545453956700000000000000E-14 " " relative error = 1.5833735853437175000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.749999999999921 " " y[1] (closed_form) = 3.0064321610770213 " " y[1] (numeric) = 3.0064321610770666 " " absolute error = 4.52970994047063870000000000000E-14 " " relative error = 1.5066729258404155000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.759999999999924 " " y[1] (closed_form) = 3.0118318414179472 " " y[1] (numeric) = 3.011831841417991 " " absolute error = 4.3964831775156200000000000000E-14 " " relative error = 1.4597372658912422000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.769999999999928 " " y[1] (closed_form) = 3.0172308838011546 " " y[1] (numeric) = 3.0172308838011968 " " absolute error = 4.21884749357559500000000000000E-14 " " relative error = 1.398251461704722000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.779999999999931 " " y[1] (closed_form) = 3.022629290259976 " " y[1] (numeric) = 3.0226292902600167 " " absolute error = 4.08562073062057600000000000000E-14 " " relative error = 1.3516777408946410000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.789999999999934 " " y[1] (closed_form) = 3.028027062818038 " " y[1] (numeric) = 3.0280270628180768 " " absolute error = 3.86357612569554500000000000000E-14 " " relative error = 1.2759384396320095000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.799999999999938 " " y[1] (closed_form) = 3.033424203489324 " " y[1] (numeric) = 3.0334242034893615 " " absolute error = 3.73034936274052600000000000000E-14 " " relative error = 1.2297486643805157000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.809999999999941 " " y[1] (closed_form) = 3.038820714278235 " " y[1] (numeric) = 3.03882071427827 " " absolute error = 3.508304757815494700000000000000E-14 " " relative error = 1.1544954729745446000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.819999999999944 " " y[1] (closed_form) = 3.0442165971796475 " " y[1] (numeric) = 3.0442165971796813 " " absolute error = 3.37507799486047600000000000000E-14 " " relative error = 1.1086852354682512000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.829999999999948 " " y[1] (closed_form) = 3.049611854178979 " " y[1] (numeric) = 3.0496118541790103 " " absolute error = 3.10862446895043830000000000000E-14 " " relative error = 1.0193508608941797000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.839999999999951 " " y[1] (closed_form) = 3.0550064872522436 " " y[1] (numeric) = 3.0550064872522724 " " absolute error = 2.88657986402540700000000000000E-14 " " relative error = 9.4486865283931890000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.849999999999954 " " y[1] (closed_form) = 3.0604004983661115 " " y[1] (numeric) = 3.0604004983661395 " " absolute error = 2.797762022055394500000000000000E-14 " " relative error = 9.1418166463803190000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.859999999999958 " " y[1] (closed_form) = 3.065793889477971 " " y[1] (numeric) = 3.065793889477997 " " absolute error = 2.575717417130363000000000000000E-14 " " relative error = 8.4014696029319310000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.869999999999961 " " y[1] (closed_form) = 3.0711866625359834 " " y[1] (numeric) = 3.071186662536007 " " absolute error = 2.35367281220533200000000000000E-14 " " relative error = 7.6637243867874320000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.879999999999964 " " y[1] (closed_form) = 3.076578819479142 " " y[1] (numeric) = 3.0765788194791632 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 6.9285668671449160000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.889999999999968 " " y[1] (closed_form) = 3.08197036223733 " " y[1] (numeric) = 3.0819703622373495 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 6.3400756453796380000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.899999999999971 " " y[1] (closed_form) = 3.0873612927313774 " " y[1] (numeric) = 3.087361292731395 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 5.7536409605910230000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.909999999999974 " " y[1] (closed_form) = 3.0927516128731174 " " y[1] (numeric) = 3.0927516128731325 " " absolute error = 1.50990331349021300000000000000E-14 " " relative error = 4.8820710567426934000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.919999999999978 " " y[1] (closed_form) = 3.0981413245654417 " " y[1] (numeric) = 3.0981413245654554 " " absolute error = 1.376676550535194000000000000000E-14 " " relative error = 4.443556333661740000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.929999999999981 " " y[1] (closed_form) = 3.1035304297023583 " " y[1] (numeric) = 3.10353042970237 " " absolute error = 1.154631945610162800000000000000E-14 " " relative error = 3.7203822284445810000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.939999999999984 " " y[1] (closed_form) = 3.1089189301690436 " " y[1] (numeric) = 3.1089189301690534 " " absolute error = 9.769962616701378000000000000000E-15 " " relative error = 3.1425594671811363000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.949999999999988 " " y[1] (closed_form) = 3.1143068278419 " " y[1] (numeric) = 3.1143068278419084 " " absolute error = 8.43769498715119000000000000000E-15 " " relative error = 2.7093332332312940000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.959999999999991 " " y[1] (closed_form) = 3.119694124588609 " " y[1] (numeric) = 3.1196941245886154 " " absolute error = 6.217248937900877000000000000000E-15 " " relative error = 1.99290337116647230000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.969999999999994 " " y[1] (closed_form) = 3.1250808222681856 " " y[1] (numeric) = 3.1250808222681896 " " absolute error = 3.9968028886505635000000000000000E-15 " " relative error = 1.27894384688255260000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.979999999999998 " " y[1] (closed_form) = 3.130466922731031 " " y[1] (numeric) = 3.1304669227310336 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 8.51162246677190800000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.990000000000001 " " y[1] (closed_form) = 3.1358524278189863 " " y[1] (numeric) = 3.1358524278189877 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 4.24850231385662470000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " "Finished!" "diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) / ( 0.2 * x + 0.3 ) ; " Iterations = 4900 "Total Elapsed Time "= 1 Minutes 5 Seconds "Elapsed Time(since restart) "= 1 Minutes 5 Seconds "Time to Timeout "= 1 Minutes 54 Seconds Percent Done = 100.0204081632654 "%" (%o255) temp/diffeq.div_lin_lin.max