##############ECHO OF PROBLEM################# ##############temp/div_sin_lin_newpostode.ode################# diff( y , x , 1 ) = cos ( x ) / ( 2.0 * x + 1.0 ) - 2.0 * sin ( x ) / ( 2.0 * x + 1.0 ) / ( 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; 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(sin(x)/(2*x+1)); } /* 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 = 4.504046601192705e-152 estimated_step_error = 4.504046601192705e-152 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 = 3.022612082540084e-144 estimated_step_error = 3.022612082540084e-144 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 = 2.028437376207862e-136 estimated_step_error = 2.028437376207862e-136 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 = 1.361256910671959e-128 estimated_step_error = 1.361256910671959e-128 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 = 9.135181843500689e-121 estimated_step_error = 9.135181843500689e-121 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 = 6.130438048725264e-113 estimated_step_error = 6.130438048725264e-113 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 = 4.11396169297458e-105 estimated_step_error = 4.11396169297458e-105 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 = 2.760691181218542e-97 estimated_step_error = 2.760691181218542e-97 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 = 1.852478230655873e-89 estimated_step_error = 1.852478230655873e-89 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 = 1.242921813138978e-81 estimated_step_error = 1.242921813138978e-81 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 = 8.337682853441601e-74 estimated_step_error = 8.337682853441601e-74 best_h = 0.001 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 0.0831945138723568 y[1] (numeric) = 0.0831945138723568 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 = 0.6 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2000000000000001 y[1] (analytic) = 0.1419066648536152 y[1] (numeric) = 0.1419066648536153 absolute error = 8.326672684688674e-17 relative error = 5.867710789537695e-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 = 0.7 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3000000000000002 y[1] (analytic) = 0.1847001291633373 y[1] (numeric) = 0.1847001291633375 absolute error = 1.942890293094024e-16 relative error = 1.051916044615135e-13 % Correct digits = 15 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 = 0.8 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4000000000000002 y[1] (analytic) = 0.2163435235048059 y[1] (numeric) = 0.2163435235048062 absolute error = 2.775557561562891e-16 relative error = 1.282939982024114e-13 % Correct digits = 15 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 = 0.9 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5000000000000003 y[1] (analytic) = 0.2397127693021015 y[1] (numeric) = 0.2397127693021019 absolute error = 3.608224830031759e-16 relative error = 1.505228461769778e-13 % Correct digits = 15 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 = 1 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6000000000000004 y[1] (analytic) = 0.2566556697250161 y[1] (numeric) = 0.2566556697250167 absolute error = 6.661338147750939e-16 relative error = 2.59543775319204e-13 % Correct digits = 15 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 = 1.1 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7000000000000005 y[1] (analytic) = 0.2684240363490379 y[1] (numeric) = 0.2684240363490387 absolute error = 7.216449660063518e-16 relative error = 2.688451361591107e-13 % Correct digits = 15 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 = 1.2 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8000000000000006 y[1] (analytic) = 0.2759061888075087 y[1] (numeric) = 0.2759061888075095 absolute error = 7.771561172376096e-16 relative error = 2.816740431218843e-13 % Correct digits = 15 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 = 1.3 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9000000000000007 y[1] (analytic) = 0.2797596105812441 y[1] (numeric) = 0.279759610581245 absolute error = 9.436895709313831e-16 relative error = 3.373215915516615e-13 % Correct digits = 15 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 = 1.4 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff( y , x , 1 ) = cos ( x ) / ( 2.0 * x + 1.0 ) - 2.0 * sin ( x ) / ( 2.0 * x + 1.0 ) / ( 2.0 * x + 1.0 ) ; Iterations = 900 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100.1 %