##############ECHO OF PROBLEM################# ##############temp/expt_c_sin_newpostode.ode################# diff ( y , x , 1 ) = expt ( 2.0 , sin ( x ) ) * cos ( x ) * ln ( 2.0 ) ; ! /* BEGIN FIRST INPUT BLOCK */ /* # Comment 1 */ Digits=32; max_terms=30; /* # Comment 2 */ ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ /* # Comment 3 */ x_start=0.1; x_end=1.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_iter=1000000; /* # Comment 4 */ /* 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 */ /* # Comment 5 */ double exact_soln_y (double x) { /* # Comment 6 */ return(expt(2.0,sin(x))); /* # Comment 7 */ } /* 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 = 0.9 estimated_steps = 900000.0000000001 step_error = 1.111111111111111e-16 est_needed_step_err = 1.111111111111111e-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 = 2.517636384766835e-168 estimated_step_error = 2.517636384766835e-168 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 = 1.689557032224656e-160 estimated_step_error = 1.689557032224656e-160 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 = 1.133842336015974e-152 estimated_step_error = 1.133842336015974e-152 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 = 7.609084496039714e-145 estimated_step_error = 7.609084496039714e-145 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 = 5.106366654305628e-137 estimated_step_error = 5.106366654305628e-137 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 = 3.426819939899629e-129 estimated_step_error = 3.426819939899629e-129 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 = 2.299693606561296e-121 estimated_step_error = 2.299693606561296e-121 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 = 1.543289763369036e-113 estimated_step_error = 1.543289763369036e-113 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 = 1.035672830600492e-105 estimated_step_error = 1.035672830600492e-105 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 = 6.950129714308285e-98 estimated_step_error = 6.950129714308285e-98 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 = 4.663947690685019e-90 estimated_step_error = 4.663947690685019e-90 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 = 3.129646472987139e-82 estimated_step_error = 3.129646472987139e-82 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 = 2.09989957467806e-74 estimated_step_error = 2.09989957467806e-74 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 = 1.408720251788461e-66 estimated_step_error = 1.408720251788461e-66 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 = 9.447042414624482e-59 estimated_step_error = 9.447042414624482e-59 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 = 6.330708196557333e-51 estimated_step_error = 6.330708196557333e-51 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 = 4.236054799514908e-43 estimated_step_error = 4.236054799514908e-43 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 = 2.825559663661932e-35 estimated_step_error = 2.825559663661932e-35 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 1.071649715448469 y[1] (numeric) = 1.071649715448469 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.068 Order of pole (six term test) = 10.72 TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (analytic) = 1.147639341985178 y[1] (numeric) = 1.147639341985178 absolute error = 2.220446049250313e-16 relative error = 1.93479429296089e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.054 Order of pole (six term test) = 10.71 TOP MAIN SOLVE Loop x[1] = 0.3 y[1] (analytic) = 1.22732744693776 y[1] (numeric) = 1.22732744693776 absolute error = 2.220446049250313e-16 relative error = 1.809171671985688e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.065 Order of pole (six term test) = 11 TOP MAIN SOLVE Loop x[1] = 0.4 y[1] (analytic) = 1.309865193286304 y[1] (numeric) = 1.309865193286305 absolute error = 2.220446049250313e-16 relative error = 1.695171427282119e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.08 Order of pole (six term test) = 11.31 TOP MAIN SOLVE Loop x[1] = 0.5 y[1] (analytic) = 1.394188409090117 y[1] (numeric) = 1.394188409090117 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.074 Order of pole (six term test) = 11.3 TOP MAIN SOLVE Loop x[1] = 0.6 y[1] (analytic) = 1.479020934993095 y[1] (numeric) = 1.479020934993095 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.049 Order of pole (six term test) = 11.24 TOP MAIN SOLVE Loop x[1] = 0.7 y[1] (analytic) = 1.562891566160557 y[1] (numeric) = 1.562891566160557 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.021 Order of pole (six term test) = 11.48 TOP MAIN SOLVE Loop x[1] = 0.7999999999999999 y[1] (analytic) = 1.644166143193653 y[1] (numeric) = 1.644166143193653 absolute error = 2.220446049250313e-16 relative error = 1.350499801034271e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.016 Order of pole (six term test) = 11.75 TOP MAIN SOLVE Loop x[1] = 0.8999999999999999 y[1] (analytic) = 1.721095211168501 y[1] (numeric) = 1.721095211168501 absolute error = 2.220446049250313e-16 relative error = 1.290135510715173e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.032 Order of pole (six term test) = 11.69 TOP MAIN SOLVE Loop x[1] = 0.9999999999999999 y[1] (analytic) = 1.791876223827922 y[1] (numeric) = 1.791876223827922 absolute error = 2.220446049250313e-16 relative error = 1.239173788749121e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.046 Order of pole (six term test) = 11.6 Finished! diff ( y , x , 1 ) = expt ( 2.0 , sin ( x ) ) * cos ( x ) * ln ( 2.0 ) ; Iterations = 10 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 122.2 %