##############ECHO OF PROBLEM################# ##############temp/lin_lnpostode.ode################# diff ( y , x , 1 ) = ln (0.1 * x + 0.2) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits = 32; max_terms = 30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start = 20.0; x_end = 30.0 ; array_y_init[0 + 1] = exact_soln_y(x_start); glob_h = 0.00001 ; glob_look_poles = true; glob_max_iter = 20; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_h = 0.005 ; glob_display_interval = 0.1; glob_look_poles = true; glob_max_iter = 10000; glob_max_minutes = 10; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(10.0* (0.1 * x + 0.2) * ln(0.1 * x + 0.2) - x - 2.0); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 20 y[1] (analytic) = -4.653938071986054 y[1] (numeric) = -4.653938071986054 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 20.10499999999998 y[1] (analytic) = -4.570899878648641 y[1] (numeric) = -4.570899878648624 absolute error = 1.687538997430238e-14 relative error = 3.691918532963248e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 20.20499999999996 y[1] (analytic) = -4.49135215237084 y[1] (numeric) = -4.491352152370807 absolute error = 3.375077994860476e-14 relative error = 7.514614486594824e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 20.30499999999994 y[1] (analytic) = -4.41135407555025 y[1] (numeric) = -4.411354075550204 absolute error = 4.618527782440651e-14 relative error = 1.046963744769129e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 20.40499999999992 y[1] (analytic) = -4.330907667256886 y[1] (numeric) = -4.330907667256826 absolute error = 6.039613253960852e-14 relative error = 1.394537523767212e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 20.5049999999999 y[1] (analytic) = -4.250014928537194 y[1] (numeric) = -4.250014928537118 absolute error = 7.638334409421077e-14 relative error = 1.797248842147033e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 20.60499999999988 y[1] (analytic) = -4.168677842654321 y[1] (numeric) = -4.168677842654229 absolute error = 9.237055564881302e-14 relative error = 2.215823796784401e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 20.70499999999986 y[1] (analytic) = -4.086898375324114 y[1] (numeric) = -4.086898375324006 absolute error = 1.074695887837152e-13 relative error = 2.62961245703087e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 20.80499999999984 y[1] (analytic) = -4.00467847494699 y[1] (numeric) = -4.004678474946869 absolute error = 1.216804434989172e-13 relative error = 3.038457250941421e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 20.90499999999982 y[1] (analytic) = -3.922020072835719 y[1] (numeric) = -3.922020072835577 absolute error = 1.412203687323199e-13 relative error = 3.6007048946645e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 21.0049999999998 y[1] (analytic) = -3.838925083439217 y[1] (numeric) = -3.838925083439061 absolute error = 1.56319401867222e-13 relative error = 4.071957604527635e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 21.10499999999978 y[1] (analytic) = -3.755395404562492 y[1] (numeric) = -3.75539540456232 absolute error = 1.723066134218243e-13 relative error = 4.588241579368344e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 21.20499999999976 y[1] (analytic) = -3.671432917582738 y[1] (numeric) = -3.671432917582549 absolute error = 1.887379141862766e-13 relative error = 5.140715312607188e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 21.30499999999974 y[1] (analytic) = -3.587039487661722 y[1] (numeric) = -3.587039487661515 absolute error = 2.065014825802791e-13 relative error = 5.756877873538296e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 21.40499999999972 y[1] (analytic) = -3.502216963954524 y[1] (numeric) = -3.502216963954301 absolute error = 2.224886941348814e-13 relative error = 6.352795855447475e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 21.5049999999997 y[1] (analytic) = -3.416967179814713 y[1] (numeric) = -3.416967179814475 absolute error = 2.384759056894836e-13 relative error = 6.979168752285619e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 21.60499999999968 y[1] (analytic) = -3.331291952996031 y[1] (numeric) = -3.331291952995773 absolute error = 2.575717417130363e-13 relative error = 7.731887368244221e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 21.70499999999966 y[1] (analytic) = -3.24519308585064 y[1] (numeric) = -3.245193085850366 absolute error = 2.744471316873387e-13 relative error = 8.45703551150639e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 21.80499999999964 y[1] (analytic) = -3.158672365524064 y[1] (numeric) = -3.158672365523771 absolute error = 2.926547892911913e-13 relative error = 9.265120133554468e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 21.90499999999962 y[1] (analytic) = -3.071731564146808 y[1] (numeric) = -3.0717315641465 absolute error = 3.086420008457935e-13 relative error = 1.004781812474296e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 22.0049999999996 y[1] (analytic) = -2.984372439022814 y[1] (numeric) = -2.984372439022486 absolute error = 3.272937476594961e-13 relative error = 1.096692032736582e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 22.10499999999958 y[1] (analytic) = -2.896596732814739 y[1] (numeric) = -2.896596732814394 absolute error = 3.446132268436486e-13 relative error = 1.189717653616125e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 22.20499999999956 y[1] (analytic) = -2.80840617372619 y[1] (numeric) = -2.808406173725828 absolute error = 3.61488616817951e-13 relative error = 1.287166436962814e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 22.30499999999954 y[1] (analytic) = -2.719802475680924 y[1] (numeric) = -2.719802475680544 absolute error = 3.792521852119535e-13 relative error = 1.394410765498714e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 22.40499999999952 y[1] (analytic) = -2.630787338499112 y[1] (numeric) = -2.630787338498715 absolute error = 3.961275751862559e-13 relative error = 1.505737728737323e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 22.5049999999995 y[1] (analytic) = -2.541362448070715 y[1] (numeric) = -2.541362448070299 absolute error = 4.156675004196586e-13 relative error = 1.635608886623843e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 22.60499999999948 y[1] (analytic) = -2.45152947652601 y[1] (numeric) = -2.451529476525577 absolute error = 4.329869796038111e-13 relative error = 1.766191203286628e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 22.70499999999946 y[1] (analytic) = -2.361290082403378 y[1] (numeric) = -2.361290082402927 absolute error = 4.503064587879635e-13 relative error = 1.907035743484895e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 22.80499999999944 y[1] (analytic) = -2.270645910814344 y[1] (numeric) = -2.270645910813874 absolute error = 4.694022948115162e-13 relative error = 2.067263295328905e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 22.90499999999942 y[1] (analytic) = -2.179598593605965 y[1] (numeric) = -2.17959859360548 absolute error = 4.849454171562684e-13 relative error = 2.224929941590605e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 23.0049999999994 y[1] (analytic) = -2.08814974952063 y[1] (numeric) = -2.088149749520127 absolute error = 5.03597163969971e-13 relative error = 2.411690847773634e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 23.10499999999938 y[1] (analytic) = -1.996300984353264 y[1] (numeric) = -1.996300984352743 absolute error = 5.204725539442734e-13 relative error = 2.607184778365921e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 23.20499999999936 y[1] (analytic) = -1.904053891106065 y[1] (numeric) = -1.904053891105525 absolute error = 5.404565683875262e-13 relative error = 2.838452057013863e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 23.30499999999934 y[1] (analytic) = -1.811410050140762 y[1] (numeric) = -1.811410050140202 absolute error = 5.597744490160039e-13 relative error = 3.090269091598033e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 23.40499999999932 y[1] (analytic) = -1.718371029328476 y[1] (numeric) = -1.718371029327899 absolute error = 5.768718835952313e-13 relative error = 3.357085715188459e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 23.5049999999993 y[1] (analytic) = -1.624938384197223 y[1] (numeric) = -1.624938384196627 absolute error = 5.964118088286341e-13 relative error = 3.670365686655145e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 23.60499999999928 y[1] (analytic) = -1.531113658077094 y[1] (numeric) = -1.531113658076479 absolute error = 6.150635556423367e-13 relative error = 4.017099268873267e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 23.70499999999926 y[1] (analytic) = -1.436898382243176 y[1] (numeric) = -1.436898382242543 absolute error = 6.330491686412643e-13 relative error = 4.405664147613529e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 23.80499999999924 y[1] (analytic) = -1.34229407605625 y[1] (numeric) = -1.342294076055597 absolute error = 6.52589093874667e-13 relative error = 4.861744572337066e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 23.90499999999922 y[1] (analytic) = -1.247302247101292 y[1] (numeric) = -1.247302247100622 absolute error = 6.701306176637445e-13 relative error = 5.372640185817961e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 24.0049999999992 y[1] (analytic) = -1.151924391323864 y[1] (numeric) = -1.151924391323174 absolute error = 6.903366767119223e-13 relative error = 5.992899203380387e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 24.10499999999918 y[1] (analytic) = -1.056161993164373 y[1] (numeric) = -1.056161993163665 absolute error = 7.083222897108499e-13 relative error = 6.706568635258699e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 24.20499999999916 y[1] (analytic) = -0.9600165256903077 y[1] (numeric) = -0.9600165256895791 absolute error = 7.286393710614902e-13 relative error = 7.589862794680082e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 24.30499999999914 y[1] (analytic) = -0.8634894507264197 y[1] (numeric) = -0.8634894507256728 absolute error = 7.468470286653428e-13 relative error = 8.649173745400709e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 24.40499999999912 y[1] (analytic) = -0.7665822189829662 y[1] (numeric) = -0.7665822189821984 absolute error = 7.678302438307583e-13 relative error = 1.001628037824107e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 24.5049999999991 y[1] (analytic) = -0.6692962701819662 y[1] (numeric) = -0.6692962701811794 absolute error = 7.868150575518484e-13 relative error = 1.175585600287197e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 24.60499999999908 y[1] (analytic) = -0.5716330331815932 y[1] (numeric) = -0.5716330331807865 absolute error = 8.066880496926387e-13 relative error = 1.411199148521521e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 24.70499999999906 y[1] (analytic) = -0.4735939260986642 y[1] (numeric) = -0.4735939260978373 absolute error = 8.268941087408166e-13 relative error = 1.745998128718714e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 24.80499999999904 y[1] (analytic) = -0.3751803564293118 y[1] (numeric) = -0.3751803564284664 absolute error = 8.453793221008254e-13 relative error = 2.253261151907095e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 24.90499999999902 y[1] (analytic) = -0.276393721167857 y[1] (numeric) = -0.2763937211669916 absolute error = 8.654188476953095e-13 relative error = 3.131108926927218e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 25.004999999999 y[1] (analytic) = -0.1772354069238997 y[1] (numeric) = -0.1772354069230142 absolute error = 8.854583732897936e-13 relative error = 4.995945159366416e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 25.10499999999898 y[1] (analytic) = -0.07770679003768774 y[1] (numeric) = -0.07770679003678443 absolute error = 9.03305208410643e-13 relative error = 1.16245338145166e-09 % Correct digits = 10 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 25.20499999999896 y[1] (analytic) = 0.02219076330621311 y[1] (numeric) = 0.02219076330713596 absolute error = 9.228451336440457e-13 relative error = 4.158690356476659e-09 % Correct digits = 10 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 25.30499999999894 y[1] (analytic) = 0.122455896966939 y[1] (numeric) = 0.1224558969678817 absolute error = 9.426626146336048e-13 relative error = 7.697976479549265e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 25.40499999999892 y[1] (analytic) = 0.2230872647369677 y[1] (numeric) = 0.223087264737933 absolute error = 9.652834087603424e-13 relative error = 4.326931929074773e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 25.5049999999989 y[1] (analytic) = 0.3240835302333914 y[1] (numeric) = 0.3240835302343752 absolute error = 9.838241332715825e-13 relative error = 3.035711603619824e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 25.60499999999888 y[1] (analytic) = 0.4254433667907331 y[1] (numeric) = 0.4254433667917399 absolute error = 1.006805749881323e-12 relative error = 2.366485949648265e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 25.70499999999886 y[1] (analytic) = 0.527165457355373 y[1] (numeric) = 0.5271654573563984 absolute error = 1.025401985543795e-12 relative error = 1.945123625299581e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 25.80499999999885 y[1] (analytic) = 0.6292484943814339 y[1] (numeric) = 0.6292484943824804 absolute error = 1.046496223011673e-12 relative error = 1.663088958266643e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 25.90499999999883 y[1] (analytic) = 0.7316911797282233 y[1] (numeric) = 0.7316911797292902 absolute error = 1.066924326664775e-12 relative error = 1.458162071956464e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 26.00499999999881 y[1] (analytic) = 0.8344922245591084 y[1] (numeric) = 0.8344922245601926 absolute error = 1.084132783546465e-12 relative error = 1.299152648329648e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 26.10499999999879 y[1] (analytic) = 0.9376503492418358 y[1] (numeric) = 0.9376503492429437 absolute error = 1.107891556273444e-12 relative error = 1.181561503357047e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 26.20499999999877 y[1] (analytic) = 1.041164283250315 y[1] (numeric) = 1.04116428325144 absolute error = 1.125100013155134e-12 relative error = 1.080617181414241e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 26.30499999999875 y[1] (analytic) = 1.145032765067712 y[1] (numeric) = 1.14503276506886 absolute error = 1.147748562857487e-12 relative error = 1.002371807927797e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 26.40499999999873 y[1] (analytic) = 1.249254542091008 y[1] (numeric) = 1.249254542092178 absolute error = 1.16995302334999e-12 relative error = 9.365209282262983e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 26.50499999999871 y[1] (analytic) = 1.353828370536826 y[1] (numeric) = 1.353828370538017 absolute error = 1.191269305422793e-12 relative error = 8.799263860532229e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 26.60499999999869 y[1] (analytic) = 1.458753015348619 y[1] (numeric) = 1.458753015349829 absolute error = 1.210365141446346e-12 relative error = 8.297258882834856e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 26.70499999999867 y[1] (analytic) = 1.564027250105136 y[1] (numeric) = 1.564027250106365 absolute error = 1.229238932864973e-12 relative error = 7.859447031900129e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 26.80499999999865 y[1] (analytic) = 1.66964985693018 y[1] (numeric) = 1.669649856931434 absolute error = 1.253663839406727e-12 relative error = 7.508543388322834e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 26.90499999999863 y[1] (analytic) = 1.775619626403623 y[1] (numeric) = 1.775619626404896 absolute error = 1.27364785384998e-12 relative error = 7.172976885987979e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 27.00499999999861 y[1] (analytic) = 1.881935357473613 y[1] (numeric) = 1.881935357474908 absolute error = 1.295408225132633e-12 relative error = 6.883383214988011e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 27.10499999999859 y[1] (analytic) = 1.988595857370044 y[1] (numeric) = 1.988595857371362 absolute error = 1.317834730230061e-12 relative error = 6.626961055691439e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 27.20499999999857 y[1] (analytic) = 2.095599941519185 y[1] (numeric) = 2.095599941520522 absolute error = 1.336708521648688e-12 relative error = 6.378643629278088e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 27.30499999999855 y[1] (analytic) = 2.20294643345947 y[1] (numeric) = 2.202946433460832 absolute error = 1.361577517400292e-12 relative error = 6.180710963825359e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 27.40499999999853 y[1] (analytic) = 2.310634164758487 y[1] (numeric) = 2.310634164759866 absolute error = 1.379341085794294e-12 relative error = 5.969534714027161e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 27.50499999999851 y[1] (analytic) = 2.418661974931009 y[1] (numeric) = 2.418661974932412 absolute error = 1.403321903126198e-12 relative error = 5.802058814631288e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 27.60499999999849 y[1] (analytic) = 2.527028711358242 y[1] (numeric) = 2.527028711359667 absolute error = 1.425526363618701e-12 relative error = 5.641116609444856e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 27.70499999999847 y[1] (analytic) = 2.635733229208073 y[1] (numeric) = 2.635733229209521 absolute error = 1.448174913321054e-12 relative error = 5.494391075974596e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 27.80499999999845 y[1] (analytic) = 2.74477439135645 y[1] (numeric) = 2.744774391357919 absolute error = 1.469935284603707e-12 relative error = 5.355395653765462e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 27.90499999999843 y[1] (analytic) = 2.854151068309785 y[1] (numeric) = 2.854151068311274 absolute error = 1.48858703141741e-12 relative error = 5.215515912754205e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 28.00499999999841 y[1] (analytic) = 2.963862138128402 y[1] (numeric) = 2.963862138129915 absolute error = 1.513011937959163e-12 relative error = 5.104866108632802e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 28.10499999999839 y[1] (analytic) = 3.073906486351032 y[1] (numeric) = 3.073906486352571 absolute error = 1.538325022920617e-12 relative error = 5.004462659326794e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 28.20499999999837 y[1] (analytic) = 3.184283005920276 y[1] (numeric) = 3.184283005921835 absolute error = 1.55875312657372e-12 relative error = 4.895146328626124e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 28.30499999999835 y[1] (analytic) = 3.294990597109058 y[1] (numeric) = 3.294990597110634 absolute error = 1.576516694967722e-12 relative error = 4.784586324315822e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 28.40499999999833 y[1] (analytic) = 3.406028167448061 y[1] (numeric) = 3.406028167449663 absolute error = 1.601385690719326e-12 relative error = 4.701621983118099e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 28.50499999999831 y[1] (analytic) = 3.517394631654148 y[1] (numeric) = 3.517394631655771 absolute error = 1.622701972792129e-12 relative error = 4.613363420154565e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 28.60499999999829 y[1] (analytic) = 3.629088911559644 y[1] (numeric) = 3.629088911561291 absolute error = 1.647570968543732e-12 relative error = 4.539902462284037e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 28.70499999999827 y[1] (analytic) = 3.741109936042622 y[1] (numeric) = 3.741109936044288 absolute error = 1.665778626147585e-12 relative error = 4.452632118877692e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 28.80499999999825 y[1] (analytic) = 3.853456640958034 y[1] (numeric) = 3.853456640959721 absolute error = 1.687094908220388e-12 relative error = 4.37813388189817e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 28.90499999999823 y[1] (analytic) = 3.966127969069789 y[1] (numeric) = 3.966127969071499 absolute error = 1.710631636342441e-12 relative error = 4.313102475973943e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 29.00499999999821 y[1] (analytic) = 4.079122869983677 y[1] (numeric) = 4.07912286998541 absolute error = 1.732836096834944e-12 relative error = 4.248060556317291e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 29.10499999999819 y[1] (analytic) = 4.192440300081166 y[1] (numeric) = 4.192440300082919 absolute error = 1.753264200488047e-12 relative error = 4.181965812259995e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 29.20499999999817 y[1] (analytic) = 4.306079222454048 y[1] (numeric) = 4.306079222455827 absolute error = 1.779021374659351e-12 relative error = 4.13141812482837e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 29.30499999999815 y[1] (analytic) = 4.42003860683994 y[1] (numeric) = 4.420038606841746 absolute error = 1.805666727250355e-12 relative error = 4.085183157577207e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 29.40499999999813 y[1] (analytic) = 4.534317429558588 y[1] (numeric) = 4.534317429560415 absolute error = 1.826983009323158e-12 relative error = 4.029234912874224e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 29.50499999999811 y[1] (analytic) = 4.648914673448984 y[1] (numeric) = 4.648914673450831 absolute error = 1.84652293455656e-12 relative error = 3.971944129459884e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 29.60499999999809 y[1] (analytic) = 4.763829327807286 y[1] (numeric) = 4.763829327809161 absolute error = 1.874944643986964e-12 relative error = 3.935793066814112e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 29.70499999999807 y[1] (analytic) = 4.879060388325554 y[1] (numeric) = 4.879060388327448 absolute error = 1.894484569220367e-12 relative error = 3.882888135087288e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 29.80499999999805 y[1] (analytic) = 4.994606857031183 y[1] (numeric) = 4.994606857033098 absolute error = 1.91491267287347e-12 relative error = 3.833960765455928e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 29.90499999999803 y[1] (analytic) = 5.110467742227186 y[1] (numeric) = 5.110467742229125 absolute error = 1.938893490205373e-12 relative error = 3.793964834538583e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 30.00499999999801 y[1] (analytic) = 5.226642058433161 y[1] (numeric) = 5.226642058435122 absolute error = 1.961097950697877e-12 relative error = 3.75211833673143e-11 % Correct digits = 12 h = 0.005 Finished! diff ( y , x , 1 ) = ln (0.1 * x + 0.2) ; Iterations = 2001 Total Elapsed Time = 1 Minutes 37 Seconds Elapsed Time(since restart) = 1 Minutes 37 Seconds Time to Timeout = 8 Minutes 23 Seconds Percent Done = 100.1 %