##############ECHO OF PROBLEM################# ##############temp/lin_arctanpostode.ode################# diff ( y , x , 1 ) = arctan (0.1 * x + 0.2 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=-1.0; x_end=-0.6; /* # */ /* # Trouble further */ /* # */ array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_iter=100; 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(10.0 * (0.1 * x + 0.2) * arctan(0.1 * x + 0.2) - 5.0 * ln(1.0 + expt((0.1 * x + 0.2) , 2))); } /* 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 = 0.4 estimated_steps = 400000.0000000001 step_error = 2.5e-16 est_needed_step_err = 2.5e-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 = 9.686664026714664e-185 estimated_step_error = 9.686664026714664e-185 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 = 6.500610408548449e-177 estimated_step_error = 6.500610408548449e-177 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 = 4.362486094492734e-169 estimated_step_error = 4.362486094492734e-169 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 = 2.927615257792038e-161 estimated_step_error = 2.927615257792038e-161 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 = 1.964689875470976e-153 estimated_step_error = 1.964689875470976e-153 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 = 1.318481772838249e-145 estimated_step_error = 1.318481772838249e-145 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 = 8.848191011791856e-138 estimated_step_error = 8.848191011791856e-138 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 = 5.937933375903845e-130 estimated_step_error = 5.937933375903845e-130 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 = 3.984896951977733e-122 estimated_step_error = 3.984896951977733e-122 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 = 2.674242319674759e-114 estimated_step_error = 2.674242319674759e-114 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 = 1.794684836698651e-106 estimated_step_error = 1.794684836698651e-106 best_h = 0.001 START of Soultion TOP MAIN SOLVE Loop x[1] = -1 y[1] (analytic) = 0.04991699822532158 y[1] (numeric) = 0.04991699822532158 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 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 10.07 Order of pole (six term test) = -0.948 TOP MAIN SOLVE Loop x[1] = -0.8999999999999999 y[1] (analytic) = 0.06037857838774653 y[1] (numeric) = 0.06037857842234334 absolute error = 3.459681152673255e-11 relative error = 5.729981137441581e-08 % Correct digits = 10 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 Radius of convergence (six term test) for eq 1 = 10.09 Order of pole (six term test) = -0.9529 TOP MAIN SOLVE Loop x[1] = -0.7999999999999998 y[1] (analytic) = 0.07182818771788424 y[1] (numeric) = 0.07182818779029003 absolute error = 7.240578969724965e-11 relative error = 1.00804143885175e-07 % Correct digits = 9 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 Radius of convergence (six term test) for eq 1 = 10.1 Order of pole (six term test) = -0.9578 TOP MAIN SOLVE Loop x[1] = -0.6999999999999997 y[1] (analytic) = 0.08426358618781293 y[1] (numeric) = 0.08426358630121693 absolute error = 1.13403994528305e-10 relative error = 1.34582444990582e-07 % Correct digits = 9 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 Radius of convergence (six term test) for eq 1 = 10.11 Order of pole (six term test) = -0.9628 Finished! diff ( y , x , 1 ) = arctan (0.1 * x + 0.2 ) ; Iterations = 400 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100.3 %