##############ECHO OF PROBLEM################# ##############temp/sinpostode.ode################# diff ( y , x , 1 ) = sin ( x ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=16; max_terms=40; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=0.0; x_end=1.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=false; glob_type_given_pole=3; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=16; glob_max_minutes=3.0; glob_subiter_method=3; glob_max_iter=100000000; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(2.0 - cos(x)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 1000000 step_error = 2.5e-21 est_needed_step_err = 2.5e-21 opt_iter = 1 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 1000000 step_error = 2.5e-21 est_needed_step_err = 2.5e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.688220266286633e-258 estimated_step_error = 2.688220266286633e-258 Double H and LOOP opt_iter = 2 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 500000 step_error = 3.535533905932738e-21 est_needed_step_err = 3.535533905932738e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.847330900503279e-247 estimated_step_error = 1.847330900503279e-247 Double H and LOOP opt_iter = 3 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 250000 step_error = 5e-21 est_needed_step_err = 5e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.269476128408287e-236 estimated_step_error = 1.269476128408287e-236 Double H and LOOP opt_iter = 4 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 125000 step_error = 7.071067811865475e-21 est_needed_step_err = 7.071067811865475e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.723773527305992e-226 estimated_step_error = 8.723773527305992e-226 Double H and LOOP opt_iter = 5 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 62500 step_error = 9.999999999999999e-21 est_needed_step_err = 9.999999999999999e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.994931519598163e-215 estimated_step_error = 5.994931519598163e-215 Double H and LOOP opt_iter = 6 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 31250 step_error = 1.414213562373095e-20 est_needed_step_err = 1.414213562373095e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.119685570948828e-204 estimated_step_error = 4.119685570948828e-204 Double H and LOOP opt_iter = 7 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 15625 step_error = 2e-20 est_needed_step_err = 2e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.831026367522982e-193 estimated_step_error = 2.831026367522982e-193 Double H and LOOP opt_iter = 8 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 7812.5 step_error = 2.82842712474619e-20 est_needed_step_err = 2.82842712474619e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.945466506015731e-182 estimated_step_error = 1.945466506015731e-182 Double H and LOOP opt_iter = 9 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000256 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 3906.25 step_error = 4e-20 est_needed_step_err = 4e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.336914402996468e-171 estimated_step_error = 1.336914402996468e-171 Double H and LOOP opt_iter = 10 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000512 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 1953.125 step_error = 5.65685424949238e-20 est_needed_step_err = 5.65685424949238e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.187205821152739e-161 estimated_step_error = 9.187205821152739e-161 Double H and LOOP opt_iter = 11 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.001024 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 976.5625 step_error = 8e-20 est_needed_step_err = 8e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.31339976607266e-150 estimated_step_error = 6.31339976607266e-150 Double H and LOOP opt_iter = 12 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.002048 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 488.28125 step_error = 1.131370849898476e-19 est_needed_step_err = 1.131370849898476e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.338535281070264e-139 estimated_step_error = 4.338535281070264e-139 Double H and LOOP opt_iter = 13 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.004096 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 244.140625 step_error = 1.6e-19 est_needed_step_err = 1.6e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.981418736487726e-128 estimated_step_error = 2.981418736487726e-128 Double H and LOOP opt_iter = 14 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.008192 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 122.0703125 step_error = 2.262741699796952e-19 est_needed_step_err = 2.262741699796952e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.048815336687678e-117 estimated_step_error = 2.048815336687678e-117 Double H and LOOP opt_iter = 15 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.016384 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 61.03515625 step_error = 3.2e-19 est_needed_step_err = 3.2e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.407935128257766e-106 estimated_step_error = 1.407935128257766e-106 Double H and LOOP opt_iter = 16 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.032768 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 30.517578125 step_error = 4.525483399593904e-19 est_needed_step_err = 4.525483399593904e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.675255143800629e-96 estimated_step_error = 9.675255143800629e-96 Double H and LOOP opt_iter = 17 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.065536 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 15.2587890625 step_error = 6.4e-19 est_needed_step_err = 6.4e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.648780899506596e-85 estimated_step_error = 6.648780899506596e-85 Double H and LOOP opt_iter = 18 SETTING H FOR MAX H SETTING H FOR DISPLAY INTERVAL START of Soultion TOP MAIN SOLVE Loop x[1] = 0 y[1] (closed_form) = 1 y[1] (numeric) = 1 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.1 NO POLE (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] = 0.1 y[1] (closed_form) = 1.004995834721974 y[1] (numeric) = 1.004995834721974 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.1 SETTING H FOR POLE NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09933 Order of pole (three term test) = 32.01 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1993346653975308 y[1] (closed_form) = 1.019801457511377 y[1] (numeric) = 1.019801457511376 absolute error = 2.220446049250313e-16 relative error = 2.177331707947223e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753067 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1941 Order of pole (three term test) = 32.04 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3086027973348146 y[1] (closed_form) = 1.047241131073968 y[1] (numeric) = 1.047241131073968 absolute error = 2.220446049250313e-16 relative error = 2.12028155060449e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753067 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2894 Order of pole (three term test) = 32.09 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4079374627323454 y[1] (closed_form) = 1.082058981914906 y[1] (numeric) = 1.082058981914905 absolute error = 2.220446049250313e-16 relative error = 2.052056390974935e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753067 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3642 Order of pole (three term test) = 32.16 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5072721281298761 y[1] (closed_form) = 1.125927056194683 y[1] (numeric) = 1.125927056194683 absolute error = 4.440892098500626e-16 relative error = 3.944209417535086e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753067 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4246 Order of pole (three term test) = 32.24 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6066067935274063 y[1] (closed_form) = 1.178412846958887 y[1] (numeric) = 1.178412846958886 absolute error = 4.440892098500626e-16 relative error = 3.768536731385077e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753067 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4684 Order of pole (three term test) = 32.32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7059414589249365 y[1] (closed_form) = 1.238998882905525 y[1] (numeric) = 1.238998882905524 absolute error = 2.220446049250313e-16 relative error = 1.792129177746503e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753067 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4937 Order of pole (three term test) = 32.42 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8052761243224668 y[1] (closed_form) = 1.307087830271547 y[1] (numeric) = 1.307087830271547 absolute error = 2.220446049250313e-16 relative error = 1.698773408967489e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753067 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4996 Order of pole (three term test) = 32.52 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.904610789719997 y[1] (closed_form) = 1.382008382104505 y[1] (numeric) = 1.382008382104505 absolute error = 2.220446049250313e-16 relative error = 1.606680594707426e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753067 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4859 Order of pole (three term test) = 32.62 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = sin ( x ) ; Iterations = 92 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 101.4 %