##############ECHO OF PROBLEM################# ##############temp/expt_lin_sin_newpostode.ode################# diff ( y , x , 1 ) = expt ( 2.0 * x + 1.0 , sin ( x ) ) * ( cos ( x ) * ln ( 2.0* x + 1.0 )+ ( 2.0 * sin ( x ) ) / ( 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=0.00001; /* 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(expt(2.0*x+1.0,sin(x))); } /* 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 = 1.031890051472423e-152 estimated_step_error = 1.031890051472423e-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 = 1.668123813664462e-144 estimated_step_error = 1.668123813664462e-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 = 1.119457130919725e-136 estimated_step_error = 1.119457130919725e-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 = 7.512525334680391e-129 estimated_step_error = 7.512525334680391e-129 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 = 5.041537794430858e-121 estimated_step_error = 5.041537794430858e-121 best_h = 1e-05 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 1.01836844605944 y[1] (numeric) = 1.01836844605944 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6007 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2000000000000653 y[1] (analytic) = 1.069131582795966 y[1] (numeric) = 1.0691315827977 absolute error = 1.733724275254644e-12 relative error = 1.621619174994954e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6999 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3000000000001653 y[1] (analytic) = 1.149004102833311 y[1] (numeric) = 1.149004102834961 absolute error = 1.650235503802833e-12 relative error = 1.436231167263497e-10 % Correct digits = 12 h = 1e-05 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] = 0.4000000000002653 y[1] (analytic) = 1.257209910215132 y[1] (numeric) = 1.257209910216679 absolute error = 1.547872940932393e-12 relative error = 1.231196897475557e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8995 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5000000000003653 y[1] (analytic) = 1.394188409090671 y[1] (numeric) = 1.394188409092077 absolute error = 1.405986438385298e-12 relative error = 1.008462291909544e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9821 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6000099999999101 y[1] (analytic) = 1.560815052986506 y[1] (numeric) = 1.560815052988667 absolute error = 2.161382184340255e-12 relative error = 1.384777895500564e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.01 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.700009999999455 y[1] (analytic) = 1.757697140993933 y[1] (numeric) = 1.757697140996992 absolute error = 3.058886477447231e-12 relative error = 1.740280737850839e-10 % Correct digits = 12 h = 1e-05 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 TOP MAIN SOLVE Loop x[1] = 0.8000099999989999 y[1] (analytic) = 1.984672930923937 y[1] (numeric) = 1.984672930928027 absolute error = 4.090061622719077e-12 relative error = 2.060824007316412e-10 % Correct digits = 12 h = 1e-05 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 TOP MAIN SOLVE Loop x[1] = 0.9000099999985448 y[1] (analytic) = 2.240144990209862 y[1] (numeric) = 2.240144990215109 absolute error = 5.24646992516864e-12 relative error = 2.342022479838297e-10 % Correct digits = 12 h = 1e-05 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 ) = expt ( 2.0 * x + 1.0 , sin ( x ) ) * ( cos ( x ) * ln ( 2.0* x + 1.0 )+ ( 2.0 * sin ( x ) ) / ( 2.0 * x + 1.0 ) ); Iterations = 90001 Total Elapsed Time = 4.0 Seconds Elapsed Time(since restart) = 4.0 Seconds Time to Timeout = 2 Minutes 56.0 Seconds Percent Done = 100 %