##############ECHO OF PROBLEM################# ##############temp/h3sinpostode.ode################# diff ( y , x , 3 ) = 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=1.5; array_y_init[0 + 1] = exact_soln_y(x_start); array_y_init[1 + 1] = exact_soln_yp(x_start); array_y_init[2 + 1] = exact_soln_ypp(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(1.0 + cos(x)); } double exact_soln_yp (double x) { return(-sin(x)); } double exact_soln_ypp (double x) { return(-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 = 1.4 estimated_steps = 1400000 step_error = 2.112885636821292e-21 est_needed_step_err = 2.112885636821292e-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 = 1.995004165278026 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 1.995004165278026 desired_abs_gbl_error = 1.995004165278026e-16 range = 1.4 estimated_steps = 1400000 step_error = 4.21521564621459e-21 est_needed_step_err = 4.21521564621459e-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 = 1.995004165278026 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 1.995004165278026 desired_abs_gbl_error = 1.995004165278026e-16 range = 1.4 estimated_steps = 700000 step_error = 5.961215135203943e-21 est_needed_step_err = 5.961215135203943e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.838101935663099e-247 estimated_step_error = 1.838101935663099e-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 = 1.995004165278026 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 1.995004165278026 desired_abs_gbl_error = 1.995004165278026e-16 range = 1.4 estimated_steps = 350000 step_error = 8.430431292429179e-21 est_needed_step_err = 8.430431292429179e-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 = 1.995004165278026 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 1.995004165278026 desired_abs_gbl_error = 1.995004165278026e-16 range = 1.4 estimated_steps = 175000 step_error = 1.192243027040789e-20 est_needed_step_err = 1.192243027040789e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.680190902457671e-226 estimated_step_error = 8.680190902457671e-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 = 1.995004165278026 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 1.995004165278026 desired_abs_gbl_error = 1.995004165278026e-16 range = 1.4 estimated_steps = 87500 step_error = 1.686086258485836e-20 est_needed_step_err = 1.686086258485836e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.964981703152478e-215 estimated_step_error = 5.964981703152478e-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 = 1.995004165278026 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 1.995004165278026 desired_abs_gbl_error = 1.995004165278026e-16 range = 1.4 estimated_steps = 43750 step_error = 2.384486054081577e-20 est_needed_step_err = 2.384486054081577e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.099104124878064e-204 estimated_step_error = 4.099104124878064e-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 = 1.995004165278026 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 1.995004165278026 desired_abs_gbl_error = 1.995004165278026e-16 range = 1.4 estimated_steps = 21875 step_error = 3.372172516971672e-20 est_needed_step_err = 3.372172516971672e-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 = 1.995004165278026 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 1.995004165278026 desired_abs_gbl_error = 1.995004165278026e-16 range = 1.4 estimated_steps = 10937.5 step_error = 4.768972108163154e-20 est_needed_step_err = 4.768972108163154e-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) = 1.995004165278026 y[1] (numeric) = 1.995004165278026 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) = 1.980047501069369 y[1] (numeric) = 1.980047501069369 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] = 0.3000639999999968 y[1] (closed_form) = 1.955317573875865 y[1] (numeric) = 1.955317573875863 absolute error = 1.110223024625157e-15 relative error = 5.677967811768055e-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] = 0.40003200000001 y[1] (closed_form) = 1.921048532144346 y[1] (numeric) = 1.921048532144348 absolute error = 1.77635683940025e-15 relative error = 9.246808759263435e-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] = 0.5000000000000233 y[1] (closed_form) = 1.877582561890362 y[1] (numeric) = 1.877582561890368 absolute error = 6.217248937900877e-15 relative error = 3.311305219857449e-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) = 1.825281405429148 y[1] (numeric) = 1.825281405429165 absolute error = 1.620925615952729e-14 relative error = 8.880414883597781e-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] = 0.7000640000000499 y[1] (closed_form) = 1.764800955786104 y[1] (numeric) = 1.764800955786132 absolute error = 2.797762022055394e-14 relative error = 1.585313070509514e-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) = 1.696683753595501 y[1] (numeric) = 1.696683753595541 absolute error = 4.019007349143067e-14 relative error = 2.368742755169459e-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] = 0.9000000000000764 y[1] (closed_form) = 1.621609968270604 y[1] (numeric) = 1.621609968270658 absolute error = 5.373479439185758e-14 relative error = 3.313669466965847e-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] = 1.00009600000009 y[1] (closed_form) = 1.540221522163934 y[1] (numeric) = 1.540221522164003 absolute error = 6.94999613415348e-14 relative error = 4.512335423276702e-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] = 1.100064000000016 y[1] (closed_form) = 1.453539083225593 y[1] (numeric) = 1.453539083225604 absolute error = 1.088018564132653e-14 relative error = 7.485306564431677e-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] = 1.200031999999943 y[1] (closed_form) = 1.362327929040454 y[1] (numeric) = 1.362327929040397 absolute error = 5.684341886080801e-14 relative error = 4.172520995062127e-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] = 1.299999999999869 y[1] (closed_form) = 1.267498828624713 y[1] (numeric) = 1.267498828624586 absolute error = 1.27453603226968e-13 relative error = 1.005552039564882e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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] = 1.400095999999796 y[1] (closed_form) = 1.1698725389433 y[1] (numeric) = 1.1698725389431 absolute error = 2.002842336423782e-13 relative error = 1.712017565804965e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 , 3 ) = sin ( x ) ; Iterations = 10938 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100 %