##############ECHO OF PROBLEM################# ##############temp/expt_sin_linpostode.ode################# diff ( y , x , 1 ) = expt (sin(x) , (0.2 * x + 0.3)); ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=0.1; x_end=3.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_iter=1000000; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=10; glob_display_interval=0.1; glob_look_poles=true; glob_max_iter=10000000; glob_max_minutes=3; glob_subiter_method=3; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(0.0); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1e-10 range = 2.9 estimated_steps = 2900000 step_error = 3.448275862068966e-17 est_needed_step_err = 3.448275862068966e-17 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.1483916146355e-137 estimated_step_error = 1.1483916146355e-137 best_h = 2e-06 opt_iter = 2 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.331157807584952e-128 estimated_step_error = 4.331157807584952e-128 best_h = 4e-06 opt_iter = 3 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.906564052633966e-120 estimated_step_error = 2.906564052633966e-120 best_h = 8e-06 opt_iter = 4 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.95052621479496e-112 estimated_step_error = 1.95052621479496e-112 best_h = 1.6e-05 opt_iter = 5 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.308927800108432e-104 estimated_step_error = 1.308927800108432e-104 best_h = 3.2e-05 opt_iter = 6 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.783419120388358e-97 estimated_step_error = 8.783419120388358e-97 best_h = 6.4e-05 opt_iter = 7 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.893585062851224e-89 estimated_step_error = 5.893585062851224e-89 best_h = 0.000128 opt_iter = 8 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.953953854453335e-81 estimated_step_error = 3.953953854453335e-81 best_h = 0.000256 opt_iter = 9 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.651892431817196e-73 estimated_step_error = 2.651892431817196e-73 best_h = 0.000512 opt_iter = 10 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.777563355834718e-65 estimated_step_error = 1.777563355834718e-65 best_h = 0.001024 opt_iter = 11 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.190105358431556e-57 estimated_step_error = 1.190105358431556e-57 best_h = 0.002048 opt_iter = 12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.949386347041292e-50 estimated_step_error = 7.949386347041292e-50 best_h = 0.004096 opt_iter = 13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.285432161986111e-42 estimated_step_error = 5.285432161986111e-42 best_h = 0.008192 opt_iter = 14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.48274154068627e-34 estimated_step_error = 3.48274154068627e-34 best_h = 0.016384 opt_iter = 15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.256176356837282e-26 estimated_step_error = 2.256176356837282e-26 best_h = 0.032768 opt_iter = 16 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.419228170456367e-18 estimated_step_error = 1.419228170456367e-18 best_h = 0.065536 opt_iter = 17 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.624666625805802e-11 estimated_step_error = 8.624666625805802e-11 best_h = 0.032768 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 0 y[1] (numeric) = 0 absolute error = 0 relative error = -1 % Correct digits = -1 h = 0.032768 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09994 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 0.07421 Order of pole (six term test) = -0.823 TOP MAIN SOLVE Loop x[1] = 0.2038934150670758 y[1] (analytic) = 0 y[1] (numeric) = 0.05563554370086111 absolute error = 0.05563554370086111 relative error = -1 % Correct digits = -1 h = 0.007420958219076851 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2039 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 0.2671 Order of pole (six term test) = -0.6548 TOP MAIN SOLVE Loop x[1] = 0.3003658719150749 y[1] (analytic) = 0 y[1] (numeric) = 0.1148749103852524 absolute error = 0.1148749103852524 relative error = -1 % Correct digits = -1 h = 0.007420958219076851 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3004 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 0.41 Order of pole (six term test) = -0.6628 TOP MAIN SOLVE Loop x[1] = 0.4042592869821507 y[1] (analytic) = 0 y[1] (numeric) = 0.1848801240965931 absolute error = 0.1848801240965931 relative error = -1 % Correct digits = -1 h = 0.007420958219076851 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4043 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 0.5656 Order of pole (six term test) = -0.6751 TOP MAIN SOLVE Loop x[1] = 0.5007317438301497 y[1] (analytic) = 0 y[1] (numeric) = 0.2546970616588058 absolute error = 0.2546970616588058 relative error = -1 % Correct digits = -1 h = 0.007420958219076851 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5009 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 0.7104 Order of pole (six term test) = -0.6892 TOP MAIN SOLVE Loop x[1] = 0.6046251588972256 y[1] (analytic) = 0 y[1] (numeric) = 0.3344211159792485 absolute error = 0.3344211159792485 relative error = -1 % Correct digits = -1 h = 0.007420958219076851 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6049 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 0.8661 Order of pole (six term test) = -0.7065 TOP MAIN SOLVE Loop x[1] = 0.7010976157452246 y[1] (analytic) = 0 y[1] (numeric) = 0.4122472315132025 absolute error = 0.4122472315132025 relative error = -1 % Correct digits = -1 h = 0.007420958219076851 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7015 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 1.01 Order of pole (six term test) = -0.7243 TOP MAIN SOLVE Loop x[1] = 0.8049910308123004 y[1] (analytic) = 0 y[1] (numeric) = 0.4997770627320004 absolute error = 0.4997770627320004 relative error = -1 % Correct digits = -1 h = 0.007420958219076851 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8056 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 1.164 Order of pole (six term test) = -0.7448 TOP MAIN SOLVE Loop x[1] = 0.9014634876602994 y[1] (analytic) = 0 y[1] (numeric) = 0.5842025510433078 absolute error = 0.5842025510433078 relative error = -1 % Correct digits = -1 h = 0.007420958219076851 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9023 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 1.305 Order of pole (six term test) = -0.7642 TOP MAIN SOLVE Loop x[1] = 1.005356902727375 y[1] (analytic) = 0 y[1] (numeric) = 0.6781821009663229 absolute error = 0.6781821009663229 relative error = -1 % Correct digits = -1 h = 0.007420958219076851 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.006 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.101829359575376 y[1] (analytic) = 0 y[1] (numeric) = 0.7679775203386126 absolute error = 0.7679775203386126 relative error = -1 % Correct digits = -1 h = 0.007420958219076851 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.103 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.205722774642453 y[1] (analytic) = 0 y[1] (numeric) = 0.8670291791179445 absolute error = 0.8670291791179445 relative error = -1 % Correct digits = -1 h = 0.007420958219076851 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.207 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.302195231490453 y[1] (analytic) = 0 y[1] (numeric) = 0.9608115633046316 absolute error = 0.9608115633046316 relative error = -1 % Correct digits = -1 h = 0.007420958219076851 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.3 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.406088646557531 y[1] (analytic) = 0 y[1] (numeric) = 1.06329026102698 absolute error = 1.06329026102698 relative error = -1 % Correct digits = -1 h = 0.007420958219076851 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.321 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.502561103405531 y[1] (analytic) = 0 y[1] (numeric) = 1.159357142065749 absolute error = 1.159357142065749 relative error = -1 % Correct digits = -1 h = 0.007420958219076851 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.606454518472609 y[1] (analytic) = 0 y[1] (numeric) = 1.263215643420401 absolute error = 1.263215643420401 relative error = -1 % Correct digits = -1 h = 0.007420958219076851 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1243 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.702926975320609 y[1] (analytic) = 0 y[1] (numeric) = 1.359450690980829 absolute error = 1.359450690980829 relative error = -1 % Correct digits = -1 h = 0.007420958219076851 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.806820390387686 y[1] (analytic) = 0 y[1] (numeric) = 1.462166103073419 absolute error = 1.462166103073419 relative error = -1 % Correct digits = -1 h = 0.007420958219076851 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.903292847235687 y[1] (analytic) = 0 y[1] (numeric) = 1.555995773833957 absolute error = 1.555995773833957 relative error = -1 % Correct digits = -1 h = 0.007420958219076851 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.007186262302764 y[1] (analytic) = 0 y[1] (numeric) = 1.654550508437389 absolute error = 1.654550508437389 relative error = -1 % Correct digits = -1 h = 0.007420958219076851 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.068 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.103658719150762 y[1] (analytic) = 0 y[1] (numeric) = 1.742954072577747 absolute error = 1.742954072577747 relative error = -1 % Correct digits = -1 h = 0.007420958219076851 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.054 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.200131175998759 y[1] (analytic) = 0 y[1] (numeric) = 1.827552941841512 absolute error = 1.827552941841512 relative error = -1 % Correct digits = -1 h = 0.007420958219076851 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9539 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.304024591065834 y[1] (analytic) = 0 y[1] (numeric) = 1.913463736418661 absolute error = 1.913463736418661 relative error = -1 % Correct digits = -1 h = 0.007420958219076851 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.847 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.400497047913831 y[1] (analytic) = 0 y[1] (numeric) = 1.987518256154143 absolute error = 1.987518256154143 relative error = -1 % Correct digits = -1 h = 0.007420958219076851 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7482 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 0.9649 Order of pole (six term test) = -1.474 TOP MAIN SOLVE Loop x[1] = 2.504390462980906 y[1] (analytic) = 0 y[1] (numeric) = 2.060113266277539 absolute error = 2.060113266277539 relative error = -1 % Correct digits = -1 h = 0.007420958219076851 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6423 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 0.8769 Order of pole (six term test) = -1.485 TOP MAIN SOLVE Loop x[1] = 2.600862919828903 y[1] (analytic) = 0 y[1] (numeric) = 2.119986003286887 absolute error = 2.119986003286887 relative error = -1 % Correct digits = -1 h = 0.007420958219076851 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5443 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 0.777 Order of pole (six term test) = -1.498 TOP MAIN SOLVE Loop x[1] = 2.704756334895977 y[1] (analytic) = 0 y[1] (numeric) = 2.175397674994203 absolute error = 2.175397674994203 relative error = -1 % Correct digits = -1 h = 0.007420958219076851 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4391 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 0.664 Order of pole (six term test) = -1.521 TOP MAIN SOLVE Loop x[1] = 2.801228791743975 y[1] (analytic) = 0 y[1] (numeric) = 2.217626347062274 absolute error = 2.217626347062274 relative error = -1 % Correct digits = -1 h = 0.007420958219076851 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3417 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 0.5577 Order of pole (six term test) = -1.557 TOP MAIN SOLVE Loop x[1] = 2.905122206811049 y[1] (analytic) = 0 y[1] (numeric) = 2.252366715124135 absolute error = 2.252366715124135 relative error = -1 % Correct digits = -1 h = 0.007420958219076851 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2371 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 0.4407 Order of pole (six term test) = -1.64 Finished! diff ( y , x , 1 ) = expt (sin(x) , (0.2 * x + 0.3)); Iterations = 391 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100.3 %