##############ECHO OF PROBLEM################# ##############temp/tan_sqrt_newpostode.ode################# diff ( y , x , 1 ) = ( 1.0 + ( tan ( sqrt ( 2.0 * x + 1.0 ) ) * tan( 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=-0.4; x_end=0.1; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_iter=1000000; glob_max_h=0.001; /* 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(tan(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 = 0.5 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 = 9.616832167432261e-134 estimated_step_error = 9.616832167432261e-134 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 = 6.453716339796431e-126 estimated_step_error = 6.453716339796431e-126 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 = 4.330974811693662e-118 estimated_step_error = 4.330974811693662e-118 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 = 2.906413089708119e-110 estimated_step_error = 2.906413089708119e-110 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 = 1.950387117517977e-102 estimated_step_error = 1.950387117517977e-102 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 = 1.308783744182861e-94 estimated_step_error = 1.308783744182861e-94 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 = 8.78177199837587e-87 estimated_step_error = 8.78177199837587e-87 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 = 5.891567125938798e-79 estimated_step_error = 5.891567125938798e-79 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 = 3.951376463442679e-71 estimated_step_error = 3.951376463442679e-71 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 = 2.648525502260272e-63 estimated_step_error = 2.648525502260272e-63 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 = 1.773118278595071e-55 estimated_step_error = 1.773118278595071e-55 best_h = 0.001 START of Soultion TOP MAIN SOLVE Loop x[1] = -0.4 y[1] (analytic) = 0.4796230858878048 y[1] (numeric) = 0.4796230858878048 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.2999999999999999 y[1] (analytic) = 0.7328823955249676 y[1] (numeric) = 0.7328823955249673 absolute error = 3.33066907387547e-16 relative error = 4.544616017812371e-14 % Correct digits = 16 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2001 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.1999999999999998 y[1] (analytic) = 0.9786270403695344 y[1] (numeric) = 0.9786270403695341 absolute error = 3.33066907387547e-16 relative error = 3.403410018813493e-14 % Correct digits = 16 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3001 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.09999999999999976 y[1] (analytic) = 1.245836224584262 y[1] (numeric) = 1.245836224584262 absolute error = 2.220446049250313e-16 relative error = 1.782293695940074e-14 % Correct digits = 16 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3717 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.261280134836397e-16 y[1] (analytic) = 1.557407724654903 y[1] (numeric) = 1.557407724654903 absolute error = 2.220446049250313e-16 relative error = 1.425732012304183e-14 % Correct digits = 16 h = 0.001 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 Finished! diff ( y , x , 1 ) = ( 1.0 + ( tan ( sqrt ( 2.0 * x + 1.0 ) ) * tan( sqrt ( 2.0 * x + 1.0 ) ) ) ) / sqrt ( 2.0 * x + 1.0 ) ; Iterations = 500 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100.2 %