##############ECHO OF PROBLEM################# ##############temp/divpostode.ode################# diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=0.0; x_end=1.5; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_iter=10000000; glob_display_interval=0.1; glob_max_minutes=10; glob_max_h=0.001; /* # Not Given = 0 */ /* # No Pole = 3 */ /* # Pole = 4 */ glob_type_given_pole=4; /* # Real Part */ array_given_rad_poles[1][1]=1.570796327; /* # Imag Part */ array_given_rad_poles[1][2]=0.0; /* # Order */ array_given_ord_poles[1][1]=0.0; /* # Not Used */ array_given_ord_poles[1][2]=0.0; /* 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(2.0 - ln(fabs(cos(x)))); } /* 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 = 1.5 estimated_steps = 1500000 step_error = 6.666666666666667e-17 est_needed_step_err = 6.666666666666667e-17 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.122655795896327e-163 estimated_step_error = 6.122655795896327e-163 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 = 4.108844751257343e-155 estimated_step_error = 4.108844751257343e-155 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 = 2.757399036095542e-147 estimated_step_error = 2.757399036095542e-147 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 = 1.850459169079025e-139 estimated_step_error = 1.850459169079025e-139 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 = 1.241822127175205e-131 estimated_step_error = 1.241822127175205e-131 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 = 8.333727225081321e-124 estimated_step_error = 8.333727225081321e-124 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 = 5.592669671227225e-116 estimated_step_error = 5.592669671227225e-116 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 = 3.753177087972187e-108 estimated_step_error = 3.753177087972187e-108 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 = 2.518714519293995e-100 estimated_step_error = 2.518714519293995e-100 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 = 1.690280732567496e-92 estimated_step_error = 1.690280732567496e-92 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 = 1.134328281966585e-84 estimated_step_error = 1.134328281966585e-84 best_h = 0.001 START of Soultion TOP MAIN SOLVE Loop x[1] = 0 y[1] (analytic) = 2 y[1] (numeric) = 2 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.571 Order of pole (given) = 0 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] = 0.1000000000000001 y[1] (analytic) = 2.005008355623235 y[1] (numeric) = 2.005008355623235 absolute error = 8.881784197001252e-16 relative error = 4.429799093899758e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.471 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.253 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 0.1711 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2000000000000001 y[1] (analytic) = 2.020134773052408 y[1] (numeric) = 2.020134773052408 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.371 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.419 Order of pole (ratio test) = 0 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3000000000000002 y[1] (analytic) = 2.045691655926058 y[1] (numeric) = 2.045691655926058 absolute error = 4.440892098500626e-16 relative error = 2.170851157180036e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.271 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.318 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 1.161 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4000000000000003 y[1] (analytic) = 2.082229019075056 y[1] (numeric) = 2.082229019075056 absolute error = 4.440892098500626e-16 relative error = 2.132758720495265e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.171 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.214 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 1.159 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5000000000000003 y[1] (analytic) = 2.130584240443723 y[1] (numeric) = 2.130584240443721 absolute error = 1.77635683940025e-15 relative error = 8.337416590626335e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.071 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.11 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 1.07 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6000000000000004 y[1] (analytic) = 2.191965169419438 y[1] (numeric) = 2.191965169419437 absolute error = 4.440892098500626e-16 relative error = 2.025986617149048e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.9708 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.007 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 0.9707 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7000000000000005 y[1] (analytic) = 2.268085757567932 y[1] (numeric) = 2.268085757567932 absolute error = 4.440892098500626e-16 relative error = 1.957991263638371e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.8708 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.903 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 0.8708 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8000000000000006 y[1] (analytic) = 2.361390746811344 y[1] (numeric) = 2.361390746811343 absolute error = 1.77635683940025e-15 relative error = 7.522502753087e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.7708 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.7993 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 0.7708 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9000000000000007 y[1] (analytic) = 2.475442443585815 y[1] (numeric) = 2.475442443585812 absolute error = 3.552713678800501e-15 relative error = 1.435183309555846e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.6708 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.6956 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 0.6708 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.000000000000001 y[1] (analytic) = 2.615626470386015 y[1] (numeric) = 2.615626470386013 absolute error = 1.77635683940025e-15 relative error = 6.791324600481256e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.5708 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.5919 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 0.5708 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.10099999999999 y[1] (analytic) = 2.792515270239914 y[1] (numeric) = 2.792515270239929 absolute error = 1.509903313490213e-14 relative error = 5.406965288897032e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.4698 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.4872 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 0.4698 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.200999999999979 y[1] (analytic) = 3.017699249287779 y[1] (numeric) = 3.017699249287819 absolute error = 3.996802888650564e-14 relative error = 1.324453684241021e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 0.3698 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.3835 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 0.3698 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.300999999999968 y[1] (analytic) = 3.322249198474641 y[1] (numeric) = 3.322249198474714 absolute error = 7.283063041541027e-14 relative error = 2.192208532967645e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 0.2698 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.2798 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 0.2698 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.400999999999957 y[1] (analytic) = 3.777965396306683 y[1] (numeric) = 3.777965396306809 absolute error = 1.252331571777177e-13 relative error = 3.31483071020568e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 0.1698 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.1761 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 0.1698 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ; Iterations = 1501 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100.1 %