##############ECHO OF PROBLEM################# ##############temp/diff0postode.ode################# diff ( y , x , 1 ) = y - 1.0; ! // BEGIN FIRST INPUT BLOCK Digits = 32; max_terms = 30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start = 1.1; x_end = 5.0 ; array_y_init[0 + 1] = exact_soln_y(x_start); glob_h = 0.01 ; glob_look_poles = true; glob_max_iter = 100; // 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(1.0 + exp(x)); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 1.1 y[1] (analytic) = 4.004166023946434 y[1] (numeric) = 4.004166023946434 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 1.204999999999998 y[1] (analytic) = 4.336759078067407 y[1] (numeric) = 4.336759078067471 absolute error = 6.306066779870889e-14 relative error = 1.454096634457514e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 1.233e-09 Order of pole = 0.5 Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 1.304999999999996 y[1] (analytic) = 4.687689093705001 y[1] (numeric) = 4.687689093705134 absolute error = 1.332267629550188e-13 relative error = 2.842056294516763e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 1.404999999999994 y[1] (analytic) = 5.0755267412675 y[1] (numeric) = 5.075526741267721 absolute error = 2.211564265053312e-13 relative error = 4.357309847413045e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 1.504999999999991 y[1] (analytic) = 5.504153630288446 y[1] (numeric) = 5.504153630288767 absolute error = 3.215205879314453e-13 relative error = 5.841417400891043e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.604999999999989 y[1] (analytic) = 5.977859602739632 y[1] (numeric) = 5.977859602740078 absolute error = 4.458655666894629e-13 relative error = 7.458615563422136e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.704999999999987 y[1] (analytic) = 6.501385667211426 y[1] (numeric) = 6.501385667212018 absolute error = 5.924150059399835e-13 relative error = 9.112134493539163e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 1.804999999999985 y[1] (analytic) = 7.079971448520248 y[1] (numeric) = 7.079971448521012 absolute error = 7.638334409421077e-13 relative error = 1.078865143025051e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 1.904999999999983 y[1] (analytic) = 7.719407627634833 y[1] (numeric) = 7.719407627635798 absolute error = 9.64561763794336e-13 relative error = 1.249528215534681e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 2.004999999999981 y[1] (analytic) = 8.426093896757681 y[1] (numeric) = 8.426093896758879 absolute error = 1.197264509755769e-12 relative error = 1.420900982620749e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 2.104999999999979 y[1] (analytic) = 9.207103009595635 y[1] (numeric) = 9.207103009597105 absolute error = 1.470823463023407e-12 relative error = 1.597487789036917e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 2.204999999999977 y[1] (analytic) = 10.0702515678562 y[1] (numeric) = 10.07025156785799 absolute error = 1.794120407794253e-12 relative error = 1.78160435785041e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used x[1] = 2.304999999999974 y[1] (analytic) = 11.0241782524247 y[1] (numeric) = 11.02417825242686 absolute error = 2.163602630389505e-12 relative error = 1.962597647505958e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used x[1] = 2.404999999999972 y[1] (analytic) = 12.07843028218612 y[1] (numeric) = 12.07843028218871 absolute error = 2.589928271845565e-12 relative error = 2.144258990065392e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used x[1] = 2.50499999999997 y[1] (analytic) = 13.24355896580066 y[1] (numeric) = 13.24355896580374 absolute error = 3.083755473198835e-12 relative error = 2.328494539241402e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used x[1] = 2.604999999999968 y[1] (analytic) = 14.53122530274721 y[1] (numeric) = 14.53122530275086 absolute error = 3.646860591288714e-12 relative error = 2.509671769110382e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 2.704999999999966 y[1] (analytic) = 15.95431669052554 y[1] (numeric) = 15.95431669052983 absolute error = 4.293454480830405e-12 relative error = 2.691092676742508e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 2.804999999999964 y[1] (analytic) = 17.52707590606206 y[1] (numeric) = 17.52707590606709 absolute error = 5.030642569181509e-12 relative error = 2.870212119890216e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used x[1] = 2.904999999999962 y[1] (analytic) = 19.26524365220848 y[1] (numeric) = 19.26524365221437 absolute error = 5.890399279451231e-12 relative error = 3.057526489562971e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 9.527e-10 Order of pole = 0.5 Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 3.004999999999959 y[1] (analytic) = 21.1862160959866 y[1] (numeric) = 21.18621609599346 absolute error = 6.860290113763767e-12 relative error = 3.238091258336284e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used x[1] = 3.104999999999957 y[1] (analytic) = 23.30921897527488 y[1] (numeric) = 23.30921897528286 absolute error = 7.979394922585925e-12 relative error = 3.423278545304338e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 1.233e-09 Order of pole = 0.5 Complex estimate of poles used Complex estimate of poles used x[1] = 3.204999999999955 y[1] (analytic) = 25.65550001645514 y[1] (numeric) = 25.6555000164644 absolute error = 9.261924560632906e-12 relative error = 3.610112667729109e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.304999999999953 y[1] (analytic) = 28.24854158879982 y[1] (numeric) = 28.24854158881054 absolute error = 1.071853716894111e-11 relative error = 3.794368334112821e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 3.404999999999951 y[1] (analytic) = 31.1142957239163 y[1] (numeric) = 31.11429572392867 absolute error = 1.237765445694095e-11 relative error = 3.978124578737209e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 3.504999999999949 y[1] (analytic) = 34.28144385240205 y[1] (numeric) = 34.28144385241633 absolute error = 1.428190898877801e-11 relative error = 4.166075691055615e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 3.604999999999947 y[1] (analytic) = 37.78168385724221 y[1] (numeric) = 37.78168385725866 absolute error = 1.644195890548872e-11 relative error = 4.35183327657246e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 1.233e-09 Order of pole = 0.5 Complex estimate of poles used x[1] = 3.704999999999945 y[1] (analytic) = 41.65004731687652 y[1] (numeric) = 41.65004731689541 absolute error = 1.889333134386106e-11 relative error = 4.536208854726924e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used x[1] = 3.804999999999942 y[1] (analytic) = 45.92525011301084 y[1] (numeric) = 45.92525011303253 absolute error = 2.169286972275586e-11 relative error = 4.723516947512533e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used x[1] = 3.90499999999994 y[1] (analytic) = 50.65007991217418 y[1] (numeric) = 50.65007991219905 absolute error = 2.486899575160351e-11 relative error = 4.909961799611304e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used x[1] = 4.004999999999939 y[1] (analytic) = 55.87182439906672 y[1] (numeric) = 55.87182439909515 absolute error = 2.843592028511921e-11 relative error = 5.089491991887453e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 4.104999999999936 y[1] (analytic) = 61.64274454760216 y[1] (numeric) = 61.64274454763465 absolute error = 3.249311930630938e-11 relative error = 5.27119931871582e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 6.495e-10 Order of pole = 0.5 Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 4.204999999999934 y[1] (analytic) = 68.0205976663003 y[1] (numeric) = 68.02059766633739 absolute error = 3.709033080667723e-11 relative error = 5.452808719593628e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 3.039e-08 Order of pole = 0.5 Complex estimate of poles used x[1] = 4.304999999999932 y[1] (analytic) = 75.06921545284355 y[1] (numeric) = 75.06921545288587 absolute error = 4.231992534187157e-11 relative error = 5.637454059774449e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used x[1] = 4.40499999999993 y[1] (analytic) = 82.85914284316188 y[1] (numeric) = 82.85914284321011 absolute error = 4.82316409033956e-11 relative error = 5.820919605056718e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 4.504999999999928 y[1] (analytic) = 91.4683440488626 y[1] (numeric) = 91.46834404891749 absolute error = 5.488232091011014e-11 relative error = 6.000143708821478e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used x[1] = 4.604999999999926 y[1] (analytic) = 100.9829828492648 y[1] (numeric) = 100.9829828493273 absolute error = 6.24424956185976e-11 relative error = 6.183467140379899e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used x[1] = 4.704999999999924 y[1] (analytic) = 111.4982849474635 y[1] (numeric) = 111.4982849475345 absolute error = 7.099743015714921e-11 relative error = 6.367580469116834e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.152e-08 Order of pole = 0.5 Complex estimate of poles used Complex estimate of poles used x[1] = 4.804999999999922 y[1] (analytic) = 123.1194910211725 y[1] (numeric) = 123.1194910212531 absolute error = 8.064660050877137e-11 relative error = 6.550270784899754e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used x[1] = 4.904999999999919 y[1] (analytic) = 135.9629100067997 y[1] (numeric) = 135.9629100068912 absolute error = 9.15179043659009e-11 relative error = 6.731093381373196e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 5.004999999999917 y[1] (analytic) = 150.1570831583755 y[1] (numeric) = 150.1570831584794 absolute error = 1.038245045492658e-10 relative error = 6.914392738953165e-11 % Correct digits = 12 h = 0.005 Finished! diff ( y , x , 1 ) = y - 1.0; Iterations = 781 Total Elapsed Time = 16 Seconds Elapsed Time(since restart) = 15 Seconds Time to Timeout = 9 Minutes 44 Seconds Percent Done = 100.3 %