##############ECHO OF PROBLEM################# ##############temp/add_c_sinpostode.ode################# diff ( y , x , 1 ) = 1.0 + 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_max_h=0.001; 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) + 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 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 min_size = 1.104995834721974 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 1.104995834721974 desired_abs_gbl_error = 1.104995834721974e-16 range = 0.9 estimated_steps = 900000.0000000001 step_error = 2.911919702267009e-21 est_needed_step_err = 2.911919702267009e-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 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 min_size = 1.104995834721974 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 1.104995834721974 desired_abs_gbl_error = 1.104995834721974e-16 range = 0.9 estimated_steps = 450000.0000000001 step_error = 4.118076335487429e-21 est_needed_step_err = 4.118076335487429e-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 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 min_size = 1.104995834721974 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 1.104995834721974 desired_abs_gbl_error = 1.104995834721974e-16 range = 0.9 estimated_steps = 225000 step_error = 5.823839404534018e-21 est_needed_step_err = 5.823839404534018e-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 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 min_size = 1.104995834721974 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 1.104995834721974 desired_abs_gbl_error = 1.104995834721974e-16 range = 0.9 estimated_steps = 112500 step_error = 8.236152670974858e-21 est_needed_step_err = 8.236152670974858e-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 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 min_size = 1.104995834721974 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 1.104995834721974 desired_abs_gbl_error = 1.104995834721974e-16 range = 0.9 estimated_steps = 56250.00000000001 step_error = 1.164767880906804e-20 est_needed_step_err = 1.164767880906804e-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 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 min_size = 1.104995834721974 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 1.104995834721974 desired_abs_gbl_error = 1.104995834721974e-16 range = 0.9 estimated_steps = 28125 step_error = 1.647230534194972e-20 est_needed_step_err = 1.647230534194972e-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 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 min_size = 1.104995834721974 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 1.104995834721974 desired_abs_gbl_error = 1.104995834721974e-16 range = 0.9 estimated_steps = 14062.5 step_error = 2.329535761813607e-20 est_needed_step_err = 2.329535761813607e-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 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 min_size = 1.104995834721974 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 1.104995834721974 desired_abs_gbl_error = 1.104995834721974e-16 range = 0.9 estimated_steps = 7031.250000000001 step_error = 3.294461068389943e-20 est_needed_step_err = 3.294461068389943e-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 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 SETTING H FOR POLE ACCURACY START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 1.104995834721974 y[1] (numeric) = 1.104995834721974 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] = 0.1901119999999951 y[1] (closed_form) = 1.208128923238048 y[1] (numeric) = 1.208128923238053 absolute error = 5.551115123125783e-15 relative error = 4.594803597820993e-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] = 0.2800959999999941 y[1] (closed_form) = 1.319067096259986 y[1] (numeric) = 1.319067096259994 absolute error = 7.771561172376096e-15 relative error = 5.891710281009338e-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] = 0.3700800000000061 y[1] (closed_form) = 1.437781586611948 y[1] (numeric) = 1.437781586611937 absolute error = 1.06581410364015e-14 relative error = 7.412906894653464e-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] = 0.460064000000018 y[1] (closed_form) = 1.564039916988443 y[1] (numeric) = 1.564039916988414 absolute error = 2.886579864025407e-14 relative error = 1.845592195360022e-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] = 0.55004800000003 y[1] (closed_form) = 1.697548567909627 y[1] (numeric) = 1.697548567909583 absolute error = 4.463096558993129e-14 relative error = 2.629142189721863e-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] = 0.6400320000000419 y[1] (closed_form) = 1.837955352780568 y[1] (numeric) = 1.837955352780508 absolute error = 5.972999872483342e-14 relative error = 3.249806837498547e-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] = 0.7300160000000538 y[1] (closed_form) = 1.984852267664761 y[1] (numeric) = 1.984852267664683 absolute error = 7.793765632868599e-14 relative error = 3.926622529967029e-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] = 0.8200000000000658 y[1] (closed_form) = 2.1377787927125 y[1] (numeric) = 2.137778792712402 absolute error = 9.769962616701378e-14 relative error = 4.57014666344634e-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] = 0.9101120000000777 y[1] (closed_form) = 2.296454678779401 y[1] (numeric) = 2.29645467877928 absolute error = 1.216804434989172e-13 relative error = 5.298621593681616e-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 ) = 1.0 + sin ( x ) ; Iterations = 7032 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100 %