##############ECHO OF PROBLEM################# ##############temp/sin_backpostode.ode################# diff ( y , x , 1 ) = sin ( x ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=40; ! // 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_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 = -0.9 estimated_steps = 900000.0000000001 step_error = 2.635231383473649e-21 est_needed_step_err = 2.635231383473649e-21 opt_iter = 1 min_size = 1.004995834721974 glob_desired_digits_correct = 16 estimated_h = -1e-06 estimated_answer = 1.004995834721974 desired_abs_gbl_error = 1.004995834721974e-16 range = -0.9 estimated_steps = 900000.0000000001 step_error = 2.648396563919643e-21 est_needed_step_err = 2.648396563919643e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.674790358513323e-258 estimated_step_error = 2.674790358513323e-258 Double H and LOOP opt_iter = 2 min_size = 1.004995834721974 glob_desired_digits_correct = 16 estimated_h = -2e-06 estimated_answer = 1.004995834721974 desired_abs_gbl_error = 1.004995834721974e-16 range = -0.9 estimated_steps = 450000.0000000001 step_error = 3.745398339237463e-21 est_needed_step_err = 3.745398339237463e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.838101935663098e-247 estimated_step_error = 1.838101935663098e-247 Double H and LOOP opt_iter = 3 min_size = 1.004995834721974 glob_desired_digits_correct = 16 estimated_h = -4e-06 estimated_answer = 1.004995834721974 desired_abs_gbl_error = 1.004995834721974e-16 range = -0.9 estimated_steps = 225000 step_error = 5.296793127839286e-21 est_needed_step_err = 5.296793127839286e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.263134028636665e-236 estimated_step_error = 1.263134028636665e-236 Double H and LOOP opt_iter = 4 min_size = 1.004995834721974 glob_desired_digits_correct = 16 estimated_h = -8e-06 estimated_answer = 1.004995834721974 desired_abs_gbl_error = 1.004995834721974e-16 range = -0.9 estimated_steps = 112500 step_error = 7.490796678474927e-21 est_needed_step_err = 7.490796678474927e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.68019090245767e-226 estimated_step_error = 8.68019090245767e-226 Double H and LOOP opt_iter = 5 min_size = 1.004995834721974 glob_desired_digits_correct = 16 estimated_h = -1.6e-05 estimated_answer = 1.004995834721974 desired_abs_gbl_error = 1.004995834721974e-16 range = -0.9 estimated_steps = 56250.00000000001 step_error = 1.059358625567857e-20 est_needed_step_err = 1.059358625567857e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.964981703152477e-215 estimated_step_error = 5.964981703152477e-215 Double H and LOOP opt_iter = 6 min_size = 1.004995834721974 glob_desired_digits_correct = 16 estimated_h = -3.2e-05 estimated_answer = 1.004995834721974 desired_abs_gbl_error = 1.004995834721974e-16 range = -0.9 estimated_steps = 28125 step_error = 1.498159335694985e-20 est_needed_step_err = 1.498159335694985e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.099104124878063e-204 estimated_step_error = 4.099104124878063e-204 Double H and LOOP opt_iter = 7 min_size = 1.004995834721974 glob_desired_digits_correct = 16 estimated_h = -6.4e-05 estimated_answer = 1.004995834721974 desired_abs_gbl_error = 1.004995834721974e-16 range = -0.9 estimated_steps = 14062.5 step_error = 2.118717251135714e-20 est_needed_step_err = 2.118717251135714e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.816882783259633e-193 estimated_step_error = 2.816882783259633e-193 Double H and LOOP opt_iter = 8 min_size = 1.004995834721974 glob_desired_digits_correct = 16 estimated_h = -0.000128 estimated_answer = 1.004995834721974 desired_abs_gbl_error = 1.004995834721974e-16 range = -0.9 estimated_steps = 7031.250000000001 step_error = 2.996318671389971e-20 est_needed_step_err = 2.996318671389971e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.935746940941988e-182 estimated_step_error = 1.935746940941988e-182 Double H and LOOP opt_iter = 9 SETTING H FOR POLE ACCURACY START of Soultion TOP MAIN SOLVE Loop x[1] = -0.100128 y[1] (closed_form) = 1.005008621550344 y[1] (numeric) = 1.005008621550344 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = -0.000128 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] = -0.2000959999999943 y[1] (closed_form) = 1.019952498930631 y[1] (numeric) = 1.019952498930631 absolute error = 2.220446049250313e-16 relative error = 2.177009274038094e-14 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 16 h = -0.000128 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] = -0.3000639999999968 y[1] (closed_form) = 1.044682426124135 y[1] (numeric) = 1.044682426124135 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 16 h = -0.000128 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] = -0.40003200000001 y[1] (closed_form) = 1.078951467855654 y[1] (numeric) = 1.078951467855651 absolute error = 2.886579864025407e-15 relative error = 2.675356538290177e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = -0.000128 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] = -0.5001280000000233 y[1] (closed_form) = 1.122478811767569 y[1] (numeric) = 1.122478811767562 absolute error = 6.883382752675971e-15 relative error = 6.132305287648771e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = -0.000128 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] = -0.6000960000000366 y[1] (closed_form) = 1.174718594570852 y[1] (numeric) = 1.174718594570838 absolute error = 1.376676550535194e-14 relative error = 1.171920285332779e-12 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 14 h = -0.000128 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] = -0.7000640000000499 y[1] (closed_form) = 1.235199044213896 y[1] (numeric) = 1.235199044213874 absolute error = 2.176037128265307e-14 relative error = 1.761689452771702e-12 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 14 h = -0.000128 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] = -0.8000320000000631 y[1] (closed_form) = 1.303316246404499 y[1] (numeric) = 1.303316246404468 absolute error = 3.108624468950438e-14 relative error = 2.385165133578518e-12 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 14 h = -0.000128 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] = -0.9001280000000764 y[1] (closed_form) = 1.378490302665783 y[1] (numeric) = 1.378490302665742 absolute error = 4.04121180963557e-14 relative error = 2.931621500579658e-12 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 14 h = -0.000128 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 Finished! diff ( y , x , 1 ) = sin ( x ) ; Iterations = 7032 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Expected Time Remaining = 0.0 Seconds Optimized Time Remaining = 0.0 Seconds Expected Total Time = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 0 %