##############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 */ /* # problem from Boyce DePrima - */ /* # _Elementary Differential Equations and Boundary Value Problems_ */ /* # page 23 */ /* # Singularity at x = 1 (which depends on init condition) */ /* # */ x_start=0.0; x_end=0.5; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_iter=1000000; glob_max_h=0.5; /* # Not Given = 0 */ /* # No Pole = 3 */ /* # Pole = 4 */ glob_type_given_pole=4; /* # Real Part */ array_given_rad_poles[1][1]=1.0; /* # Imag Part */ array_given_rad_poles[1][2]=0.0; /* # Order */ array_given_ord_poles[1][1]=0.0; /* # Not Used */ array_given_ord_poles[1][2]=0.0; /* 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(1.0/(1.0 - x)); } /* 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 = 0.5 estimated_steps = 500000 step_error = 2e-16 est_needed_step_err = 2e-16 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.00000050000025e-96 estimated_step_error = 1.00000050000025e-96 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 = 6.553606553606554e-92 estimated_step_error = 6.553606553606554e-92 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 = 4.294975885951771e-87 estimated_step_error = 4.294975885951771e-87 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 = 2.814761026150664e-82 estimated_step_error = 2.814761026150664e-82 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 = 1.844689164884273e-77 estimated_step_error = 1.844689164884273e-77 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 = 1.208945162737228e-72 estimated_step_error = 1.208945162737228e-72 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 = 7.923069789659443e-68 estimated_step_error = 7.923069789659443e-68 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 = 5.192629186801421e-63 estimated_step_error = 5.192629186801421e-63 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 = 3.403259286390906e-58 estimated_step_error = 3.403259286390906e-58 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 = 2.230645565080308e-53 estimated_step_error = 2.230645565080308e-53 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 = 1.462250309293101e-48 estimated_step_error = 1.462250309293101e-48 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 = 9.587915145236122e-44 estimated_step_error = 9.587915145236122e-44 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 = 6.28998356781367e-39 estimated_step_error = 6.28998356781367e-39 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 = 4.130680377433451e-34 estimated_step_error = 4.130680377433451e-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 = 2.718261180164227e-29 estimated_step_error = 2.718261180164227e-29 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 = 1.796269371485229e-24 estimated_step_error = 1.796269371485229e-24 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 = 1.19710695226547e-19 estimated_step_error = 1.19710695226547e-19 best_h = 0.131072 opt_iter = 18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.118466172287892e-15 estimated_step_error = 8.118466172287892e-15 best_h = 0.065536 START of Soultion TOP MAIN SOLVE Loop x[1] = 0 y[1] (analytic) = 1 y[1] (numeric) = 1 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.065536 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 1 Order of pole (three term test) = 18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.131072 y[1] (analytic) = 1.150843337998085 y[1] (numeric) = 1.150843337998085 absolute error = 2.220446049250313e-16 relative error = 1.929407744682976e-14 % Correct digits = 16 h = 0.065536 Radius of convergence (given) for eq 1 = 0.8689 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.8689 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 0.8689 Order of pole (three term test) = 18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.262144 y[1] (analytic) = 1.355277994622257 y[1] (numeric) = 1.355277994622257 absolute error = 4.440892098500626e-16 relative error = 3.276738880231278e-14 % Correct digits = 16 h = 0.065536 Radius of convergence (given) for eq 1 = 0.7379 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.7379 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 0.7379 Order of pole (three term test) = 18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.32768 y[1] (analytic) = 1.487386958591147 y[1] (numeric) = 1.487386958591147 absolute error = 4.440892098500626e-16 relative error = 2.985700575663941e-14 % Correct digits = 16 h = 0.065536 Radius of convergence (given) for eq 1 = 0.6723 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.6723 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 0.6723 Order of pole (three term test) = 18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4587519999999999 y[1] (analytic) = 1.847581884829135 y[1] (numeric) = 1.847581884829136 absolute error = 6.661338147750939e-16 relative error = 3.605435949793901e-14 % Correct digits = 16 h = 0.065536 Radius of convergence (given) for eq 1 = 0.5412 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.5412 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 0.5412 Order of pole (three term test) = 18 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = y * y; Iterations = 8 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 118 %