##############ECHO OF PROBLEM################# ##############temp/add_c_linpostode.ode################# diff ( y , x , 1 ) = 0.3 + ( 0.1 * x + 0.2 ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=0.1; x_end=1.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_display_interval=0.1; glob_look_poles=true; glob_type_given_pole=3; // END SECOND INPUT BLOCK // BEGIN OVERRIDE BLOCK glob_desired_digits_correct=16; glob_max_minutes=3.0; glob_subiter_method=3; glob_max_iter=100000000; // END OVERRIDE BLOCK ! // BEGIN USER DEF BLOCK double exact_soln_y (double x) { return(0.05 * x * x + 0.5 * x); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.9 estimated_steps = 900000.0000000001 step_error = 3.513641844631533e-21 est_needed_step_err = 3.513641844631533e-21 opt_iter = 1 NO POLE (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 min_size = 0.0505 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.9 estimated_steps = 900000.0000000001 step_error = 3.513641844631533e-21 est_needed_step_err = 3.513641844631533e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 2 NO POLE (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 min_size = 0.0505 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.9 estimated_steps = 450000.0000000001 step_error = 4.969039949999532e-21 est_needed_step_err = 4.969039949999532e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 3 NO POLE (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 min_size = 0.0505 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.9 estimated_steps = 225000 step_error = 7.027283689263065e-21 est_needed_step_err = 7.027283689263065e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 4 NO POLE (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 min_size = 0.0505 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.9 estimated_steps = 112500 step_error = 9.938079899999065e-21 est_needed_step_err = 9.938079899999065e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 5 NO POLE (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 min_size = 0.0505 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.9 estimated_steps = 56250.00000000001 step_error = 1.405456737852613e-20 est_needed_step_err = 1.405456737852613e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 6 NO POLE (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 min_size = 0.0505 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.9 estimated_steps = 28125 step_error = 1.987615979999813e-20 est_needed_step_err = 1.987615979999813e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 7 NO POLE (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 min_size = 0.0505 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.9 estimated_steps = 14062.5 step_error = 2.810913475705226e-20 est_needed_step_err = 2.810913475705226e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 8 NO POLE (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 min_size = 0.0505 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.9 estimated_steps = 7031.250000000001 step_error = 3.975231959999626e-20 est_needed_step_err = 3.975231959999626e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 9 NO POLE (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 min_size = 0.0505 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000256 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.9 estimated_steps = 3515.625 step_error = 5.621826951410452e-20 est_needed_step_err = 5.621826951410452e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 10 NO POLE (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 min_size = 0.0505 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000512 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.9 estimated_steps = 1757.8125 step_error = 7.950463919999252e-20 est_needed_step_err = 7.950463919999252e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 11 NO POLE (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 min_size = 0.0505 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.001024 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.9 estimated_steps = 878.9062500000001 step_error = 1.12436539028209e-19 est_needed_step_err = 1.12436539028209e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 12 NO POLE (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 min_size = 0.0505 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.002048 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.9 estimated_steps = 439.4531250000001 step_error = 1.59009278399985e-19 est_needed_step_err = 1.59009278399985e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 13 NO POLE (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 min_size = 0.0505 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.004096 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.9 estimated_steps = 219.7265625 step_error = 2.248730780564181e-19 est_needed_step_err = 2.248730780564181e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 14 NO POLE (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 min_size = 0.0505 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.008192 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.9 estimated_steps = 109.86328125 step_error = 3.180185567999701e-19 est_needed_step_err = 3.180185567999701e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 15 NO POLE (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 min_size = 0.0505 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.016384 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.9 estimated_steps = 54.93164062500001 step_error = 4.497461561128362e-19 est_needed_step_err = 4.497461561128362e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 16 NO POLE (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 min_size = 0.0505 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.032768 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.9 estimated_steps = 27.4658203125 step_error = 6.360371135999401e-19 est_needed_step_err = 6.360371135999401e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 17 NO POLE (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 min_size = 0.0505 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.065536 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.9 estimated_steps = 13.73291015625 step_error = 8.994923122256724e-19 est_needed_step_err = 8.994923122256724e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 18 SETTING H FOR MAX H SETTING H FOR DISPLAY INTERVAL NO POLE (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 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 0.0505 y[1] (numeric) = 0.0505 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.09 NO POLE (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] = 0.19 y[1] (closed_form) = 0.096805 y[1] (numeric) = 0.096805 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.09 NO POLE (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] = 0.28 y[1] (closed_form) = 0.14392 y[1] (numeric) = 0.14392 absolute error = 2.775557561562891e-17 relative error = 1.928541941052592e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.09 NO POLE (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] = 0.37 y[1] (closed_form) = 0.191845 y[1] (numeric) = 0.191845 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.09 NO POLE (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] = 0.46 y[1] (closed_form) = 0.24058 y[1] (numeric) = 0.24058 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.09 NO POLE (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] = 0.5499999999999999 y[1] (closed_form) = 0.290125 y[1] (numeric) = 0.290125 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.09 NO POLE (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] = 0.6399999999999999 y[1] (closed_form) = 0.3404799999999999 y[1] (numeric) = 0.3404799999999999 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.09 NO POLE (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] = 0.7299999999999999 y[1] (closed_form) = 0.3916449999999999 y[1] (numeric) = 0.391645 absolute error = 5.551115123125783e-17 relative error = 1.417384397381757e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.09 NO POLE (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] = 0.8199999999999998 y[1] (closed_form) = 0.4436199999999999 y[1] (numeric) = 0.44362 absolute error = 5.551115123125783e-17 relative error = 1.251322105208463e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.09 NO POLE (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] = 0.9099999999999998 y[1] (closed_form) = 0.4964049999999999 y[1] (numeric) = 0.496405 absolute error = 1.110223024625157e-16 relative error = 2.236526676051121e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.09 NO POLE (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] = 0.9999999999999998 y[1] (closed_form) = 0.5499999999999998 y[1] (numeric) = 0.5499999999999999 absolute error = 1.110223024625157e-16 relative error = 2.018587317500285e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.09 NO POLE (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 Finished! diff ( y , x , 1 ) = 0.3 + ( 0.1 * x + 0.2 ) ; Iterations = 11 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 120 %