##############ECHO OF PROBLEM################# ##############temp/nonlinear2postode.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(0.2); 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(0.5); 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(2.0)/(c(1.0) - c(2.0)*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) = 2 y[1] (numeric) = 2 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) = 2.040816326530612 y[1] (numeric) = 2.040816326530613 absolute error = 4.440892098500626e-16 relative error = 2.176037128265307e-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) = 2.083333333333333 y[1] (numeric) = 2.083333333333333 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] = 0.03000000000000002 y[1] (closed_form) = 2.127659574468085 y[1] (numeric) = 2.127659574468086 absolute error = 4.440892098500626e-16 relative error = 2.087219286295294e-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) = 2.173913043478261 y[1] (numeric) = 2.173913043478262 absolute error = 8.881784197001252e-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] = 0.05000000000000004 y[1] (closed_form) = 2.222222222222222 y[1] (numeric) = 2.222222222222224 absolute error = 1.332267629550188e-15 relative error = 5.995204332975845e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.06000000000000005 y[1] (closed_form) = 2.272727272727273 y[1] (numeric) = 2.272727272727274 absolute error = 1.332267629550188e-15 relative error = 5.861977570020827e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.07000000000000005 y[1] (closed_form) = 2.325581395348837 y[1] (numeric) = 2.325581395348839 absolute error = 1.77635683940025e-15 relative error = 7.638334409421077e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.08000000000000006 y[1] (closed_form) = 2.380952380952381 y[1] (numeric) = 2.380952380952383 absolute error = 1.77635683940025e-15 relative error = 7.460698725481051e-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) = 2.439024390243903 y[1] (numeric) = 2.439024390243904 absolute error = 8.881784197001252e-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] = 0.1000000000000001 y[1] (closed_form) = 2.5 y[1] (numeric) = 2.500000000000002 absolute error = 1.332267629550188e-15 relative error = 5.329070518200751e-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) = 2.564102564102565 y[1] (numeric) = 2.564102564102566 absolute error = 8.881784197001252e-16 relative error = 3.463895836830488e-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) = 2.631578947368422 y[1] (numeric) = 2.631578947368423 absolute error = 8.881784197001252e-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] = 0.1300000000000001 y[1] (closed_form) = 2.702702702702704 y[1] (numeric) = 2.702702702702704 absolute error = 8.881784197001252e-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] = 0.1400000000000001 y[1] (closed_form) = 2.777777777777779 y[1] (numeric) = 2.77777777777778 absolute error = 1.77635683940025e-15 relative error = 6.3948846218409e-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) = 2.857142857142858 y[1] (numeric) = 2.85714285714286 absolute error = 1.77635683940025e-15 relative error = 6.217248937900874e-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) = 2.941176470588236 y[1] (numeric) = 2.941176470588238 absolute error = 1.77635683940025e-15 relative error = 6.039613253960849e-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) = 3.030303030303032 y[1] (numeric) = 3.030303030303033 absolute error = 1.77635683940025e-15 relative error = 5.861977570020824e-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) = 3.125000000000002 y[1] (numeric) = 3.125000000000003 absolute error = 1.332267629550188e-15 relative error = 4.263256414560599e-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) = 3.225806451612905 y[1] (numeric) = 3.225806451612906 absolute error = 1.332267629550188e-15 relative error = 4.13002965160558e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 Finished! diff ( y , x , 1 ) = y * y ; Iterations = 200 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100.5 %