##############ECHO OF PROBLEM################# ##############temp/nonlinear1postode.ode################# diff ( y , x , 1 ) = y * y ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=20; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=c(0.0); x_end=c(0.5); 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(1.0); array_given_rad_poles[1][2]=c(0.0); array_given_ord_poles[1][1]=c(0.0); 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 double exact_soln_y (double x) { return(c(1.0)/(c(1.0) - c(x))); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0 y[1] (closed_form) = 1 y[1] (numeric) = 1 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.01 y[1] (closed_form) = 1.01010101010101 y[1] (numeric) = 1.010101010101011 absolute error = 4.440892098500626e-16 relative error = 4.39648317751562e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.02000000000000001 y[1] (closed_form) = 1.020408163265306 y[1] (numeric) = 1.020408163265307 absolute error = 4.440892098500626e-16 relative error = 4.352074256530614e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.03000000000000002 y[1] (closed_form) = 1.030927835051547 y[1] (numeric) = 1.030927835051547 absolute error = 6.661338147750939e-16 relative error = 6.46149800331841e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.04000000000000003 y[1] (closed_form) = 1.041666666666667 y[1] (numeric) = 1.041666666666668 absolute error = 8.881784197001252e-16 relative error = 8.526512829121202e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.05000000000000004 y[1] (closed_form) = 1.052631578947368 y[1] (numeric) = 1.05263157894737 absolute error = 1.332267629550188e-15 relative error = 1.265654248072678e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.06000000000000005 y[1] (closed_form) = 1.063829787234043 y[1] (numeric) = 1.063829787234044 absolute error = 1.110223024625157e-15 relative error = 1.043609643147647e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.07000000000000005 y[1] (closed_form) = 1.075268817204301 y[1] (numeric) = 1.075268817204302 absolute error = 6.661338147750939e-16 relative error = 6.195044477408372e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.08000000000000006 y[1] (closed_form) = 1.086956521739131 y[1] (numeric) = 1.086956521739131 absolute error = 4.440892098500626e-16 relative error = 4.085620730620575e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.09000000000000007 y[1] (closed_form) = 1.098901098901099 y[1] (numeric) = 1.098901098901099 absolute error = 4.440892098500626e-16 relative error = 4.041211809635569e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1000000000000001 y[1] (closed_form) = 1.111111111111111 y[1] (numeric) = 1.111111111111112 absolute error = 4.440892098500626e-16 relative error = 3.996802888650564e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1100000000000001 y[1] (closed_form) = 1.123595505617978 y[1] (numeric) = 1.123595505617978 absolute error = 6.661338147750939e-16 relative error = 5.928590951498336e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1200000000000001 y[1] (closed_form) = 1.136363636363636 y[1] (numeric) = 1.136363636363637 absolute error = 4.440892098500626e-16 relative error = 3.90798504668055e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1300000000000001 y[1] (closed_form) = 1.149425287356322 y[1] (numeric) = 1.149425287356323 absolute error = 8.881784197001252e-16 relative error = 7.727152251391088e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1400000000000001 y[1] (closed_form) = 1.162790697674419 y[1] (numeric) = 1.16279069767442 absolute error = 8.881784197001252e-16 relative error = 7.638334409421077e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1500000000000001 y[1] (closed_form) = 1.176470588235294 y[1] (numeric) = 1.176470588235295 absolute error = 8.881784197001252e-16 relative error = 7.549516567451063e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1600000000000001 y[1] (closed_form) = 1.190476190476191 y[1] (numeric) = 1.190476190476191 absolute error = 4.440892098500626e-16 relative error = 3.730349362740525e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1700000000000001 y[1] (closed_form) = 1.204819277108434 y[1] (numeric) = 1.204819277108434 absolute error = 2.220446049250313e-16 relative error = 1.842970220877759e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1800000000000001 y[1] (closed_form) = 1.219512195121951 y[1] (numeric) = 1.219512195121952 absolute error = 4.440892098500626e-16 relative error = 3.641531520770513e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1900000000000001 y[1] (closed_form) = 1.234567901234568 y[1] (numeric) = 1.234567901234568 absolute error = 4.440892098500626e-16 relative error = 3.597122599785507e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2000000000000001 y[1] (closed_form) = 1.25 y[1] (numeric) = 1.25 absolute error = 2.220446049250313e-16 relative error = 1.77635683940025e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2100000000000002 y[1] (closed_form) = 1.265822784810127 y[1] (numeric) = 1.265822784810127 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2200000000000002 y[1] (closed_form) = 1.282051282051282 y[1] (numeric) = 1.282051282051282 absolute error = 2.220446049250313e-16 relative error = 1.731947918415244e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2300000000000002 y[1] (closed_form) = 1.298701298701299 y[1] (numeric) = 1.298701298701299 absolute error = 4.440892098500626e-16 relative error = 3.419486915845481e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2400000000000002 y[1] (closed_form) = 1.315789473684211 y[1] (numeric) = 1.31578947368421 absolute error = 4.440892098500626e-16 relative error = 3.375077994860475e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2500000000000002 y[1] (closed_form) = 1.333333333333334 y[1] (numeric) = 1.333333333333333 absolute error = 6.661338147750939e-16 relative error = 4.996003610813203e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2600000000000002 y[1] (closed_form) = 1.351351351351352 y[1] (numeric) = 1.351351351351351 absolute error = 4.440892098500626e-16 relative error = 3.286260152890462e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2700000000000002 y[1] (closed_form) = 1.369863013698631 y[1] (numeric) = 1.36986301369863 absolute error = 6.661338147750939e-16 relative error = 4.862776847858184e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2800000000000002 y[1] (closed_form) = 1.388888888888889 y[1] (numeric) = 1.388888888888888 absolute error = 1.110223024625157e-15 relative error = 7.993605777301125e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2900000000000002 y[1] (closed_form) = 1.408450704225353 y[1] (numeric) = 1.408450704225351 absolute error = 1.554312234475219e-15 relative error = 1.103561686477405e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3000000000000002 y[1] (closed_form) = 1.428571428571429 y[1] (numeric) = 1.428571428571427 absolute error = 1.77635683940025e-15 relative error = 1.243449787580175e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3100000000000002 y[1] (closed_form) = 1.449275362318841 y[1] (numeric) = 1.44927536231884 absolute error = 1.554312234475219e-15 relative error = 1.072475441787901e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3200000000000002 y[1] (closed_form) = 1.470588235294118 y[1] (numeric) = 1.470588235294117 absolute error = 1.332267629550188e-15 relative error = 9.059419880941274e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3300000000000002 y[1] (closed_form) = 1.492537313432837 y[1] (numeric) = 1.492537313432835 absolute error = 1.77635683940025e-15 relative error = 1.190159082398167e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3400000000000002 y[1] (closed_form) = 1.515151515151516 y[1] (numeric) = 1.515151515151514 absolute error = 1.332267629550188e-15 relative error = 8.792966355031236e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3500000000000003 y[1] (closed_form) = 1.538461538461539 y[1] (numeric) = 1.538461538461538 absolute error = 1.332267629550188e-15 relative error = 8.659739592076217e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3600000000000003 y[1] (closed_form) = 1.562500000000001 y[1] (numeric) = 1.562499999999999 absolute error = 1.77635683940025e-15 relative error = 1.13686837721616e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3700000000000003 y[1] (closed_form) = 1.587301587301588 y[1] (numeric) = 1.587301587301587 absolute error = 1.332267629550188e-15 relative error = 8.39328606616618e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3800000000000003 y[1] (closed_form) = 1.612903225806452 y[1] (numeric) = 1.612903225806451 absolute error = 1.332267629550188e-15 relative error = 8.260059303211161e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3900000000000003 y[1] (closed_form) = 1.639344262295083 y[1] (numeric) = 1.639344262295082 absolute error = 1.110223024625157e-15 relative error = 6.772360450213451e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4000000000000003 y[1] (closed_form) = 1.666666666666668 y[1] (numeric) = 1.666666666666666 absolute error = 1.332267629550188e-15 relative error = 7.993605777301122e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4100000000000003 y[1] (closed_form) = 1.694915254237289 y[1] (numeric) = 1.694915254237288 absolute error = 1.332267629550188e-15 relative error = 7.860379014346103e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4200000000000003 y[1] (closed_form) = 1.724137931034484 y[1] (numeric) = 1.724137931034483 absolute error = 1.110223024625157e-15 relative error = 6.439293542825904e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4300000000000003 y[1] (closed_form) = 1.754385964912282 y[1] (numeric) = 1.754385964912281 absolute error = 1.110223024625157e-15 relative error = 6.328271240363387e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4400000000000003 y[1] (closed_form) = 1.785714285714287 y[1] (numeric) = 1.785714285714286 absolute error = 1.332267629550188e-15 relative error = 7.460698725481047e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4500000000000003 y[1] (closed_form) = 1.818181818181819 y[1] (numeric) = 1.818181818181818 absolute error = 1.110223024625157e-15 relative error = 6.106226635438357e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4600000000000004 y[1] (closed_form) = 1.851851851851853 y[1] (numeric) = 1.851851851851852 absolute error = 1.332267629550188e-15 relative error = 7.194245199571009e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4700000000000004 y[1] (closed_form) = 1.88679245283019 y[1] (numeric) = 1.886792452830188 absolute error = 1.77635683940025e-15 relative error = 9.41469124882132e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4800000000000004 y[1] (closed_form) = 1.923076923076925 y[1] (numeric) = 1.923076923076923 absolute error = 1.332267629550188e-15 relative error = 6.927791673660971e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4900000000000004 y[1] (closed_form) = 1.960784313725492 y[1] (numeric) = 1.96078431372549 absolute error = 1.77635683940025e-15 relative error = 9.05941988094127e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 Finished! diff ( y , x , 1 ) = y * y ; Iterations = 500 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100.2 %