##############ECHO OF PROBLEM################# ##############temp/tanh_sqrt_newpostode.ode################# diff ( y , x , 1 ) = ( 1.0 - ( tanh ( sqrt ( 2.0 * x + 1.0 ) ) * tanh( sqrt ( 2.0 * x + 1.0 ) ) ) ) / sqrt ( 2.0 * x + 1.0 ) ; ! /* 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_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(tanh(sqrt(2.0*x + 1.0))); } /* 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 = 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 = 1.422395301078657e-153 estimated_step_error = 1.422395301078657e-153 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 = 9.54552577660257e-146 estimated_step_error = 9.54552577660257e-146 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 = 6.405883838716531e-138 estimated_step_error = 6.405883838716531e-138 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 = 4.298902353918124e-130 estimated_step_error = 4.298902353918124e-130 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 = 2.884926388918217e-122 estimated_step_error = 2.884926388918217e-122 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 = 1.936016973136703e-114 estimated_step_error = 1.936016973136703e-114 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 = 1.299206311769295e-106 estimated_step_error = 1.299206311769295e-106 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 = 8.718387300923809e-99 estimated_step_error = 8.718387300923809e-99 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 = 5.850221996271751e-91 estimated_step_error = 5.850221996271751e-91 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 = 3.925227648719572e-83 estimated_step_error = 3.925227648719572e-83 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 = 2.633116174839688e-75 estimated_step_error = 2.633116174839688e-75 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 = 1.765634026121936e-67 estimated_step_error = 1.765634026121936e-67 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 = 1.182995232736144e-59 estimated_step_error = 1.182995232736144e-59 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 = 7.913546536993005e-52 estimated_step_error = 7.913546536993005e-52 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 = 5.276933074348218e-44 estimated_step_error = 5.276933074348218e-44 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 = 3.496875179109302e-36 estimated_step_error = 3.496875179109302e-36 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 = 2.289502565761928e-28 estimated_step_error = 2.289502565761928e-28 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 = 1.466119370814806e-20 estimated_step_error = 1.466119370814806e-20 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 0.798856925051763 y[1] (numeric) = 0.798856925051763 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 Radius of convergence (three term test) for eq 1 = 0.5977 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 1.014 Order of pole (six term test) = 0.1232 TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (analytic) = 0.8284629839721465 y[1] (numeric) = 0.8284629839721465 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 Radius of convergence (three term test) for eq 1 = 0.6967 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 1.13 Order of pole (six term test) = 0.1268 TOP MAIN SOLVE Loop x[1] = 0.3 y[1] (analytic) = 0.8524123941670345 y[1] (numeric) = 0.8524123941670345 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 Radius of convergence (three term test) for eq 1 = 0.7953 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 1.234 Order of pole (six term test) = 0.1309 TOP MAIN SOLVE Loop x[1] = 0.4 y[1] (analytic) = 0.8720657803910121 y[1] (numeric) = 0.8720657803910121 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 Radius of convergence (three term test) for eq 1 = 0.8935 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 1.277 Order of pole (six term test) = 0.135 TOP MAIN SOLVE Loop x[1] = 0.5 y[1] (analytic) = 0.8883855615856606 y[1] (numeric) = 0.8883855615856605 absolute error = 1.110223024625157e-16 relative error = 1.249708541687173e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9912 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 1.363 Order of pole (six term test) = 0.1387 TOP MAIN SOLVE Loop x[1] = 0.6 y[1] (analytic) = 0.9020731932448007 y[1] (numeric) = 0.9020731932448007 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 Radius of convergence (three term test) for eq 1 = 1.088 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 1.445 Order of pole (six term test) = 0.1417 TOP MAIN SOLVE Loop x[1] = 0.7 y[1] (analytic) = 0.9136522959806183 y[1] (numeric) = 0.9136522959806183 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 Radius of convergence (three term test) for eq 1 = 1.185 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 1.519 Order of pole (six term test) = 0.1435 TOP MAIN SOLVE Loop x[1] = 0.7999999999999999 y[1] (analytic) = 0.9235214893514879 y[1] (numeric) = 0.9235214893514879 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 Radius of convergence (three term test) for eq 1 = 1.282 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 1.585 Order of pole (six term test) = 0.1437 TOP MAIN SOLVE Loop x[1] = 0.8999999999999999 y[1] (analytic) = 0.9319892786757529 y[1] (numeric) = 0.9319892786757529 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 Radius of convergence (three term test) for eq 1 = 1.378 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 1.639 Order of pole (six term test) = 0.1419 TOP MAIN SOLVE Loop x[1] = 0.9999999999999999 y[1] (analytic) = 0.9392978193411512 y[1] (numeric) = 0.9392978193411512 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 Radius of convergence (three term test) for eq 1 = 1.475 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 1.677 Order of pole (six term test) = 0.137 Finished! diff ( y , x , 1 ) = ( 1.0 - ( tanh ( sqrt ( 2.0 * x + 1.0 ) ) * tanh( sqrt ( 2.0 * x + 1.0 ) ) ) ) / sqrt ( 2.0 * x + 1.0 ) ; 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 %