##############ECHO OF PROBLEM################# ##############temp/tanpostode.ode################# diff ( y , x , 1 ) = tan ( x ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=20; ! /* 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); glob_look_poles=true; glob_max_iter=10000; glob_max_h=0.5; /* # 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(-ln(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 = 1.4 estimated_steps = 1400000 step_error = 7.142857142857143e-17 est_needed_step_err = 7.142857142857143e-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 = 1.472759789521329e-100 estimated_step_error = 1.472759789521329e-100 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 = 9.651880976585251e-96 estimated_step_error = 9.651880976585251e-96 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 = 6.32545988873263e-91 estimated_step_error = 6.32545988873263e-91 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 = 4.145457550185764e-86 estimated_step_error = 4.145457550185764e-86 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 = 2.716772509442037e-81 estimated_step_error = 2.716772509442037e-81 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 = 1.780471174431388e-76 estimated_step_error = 1.780471174431388e-76 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 = 1.166858951060327e-71 estimated_step_error = 1.166858951060327e-71 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 = 7.647249538401255e-67 estimated_step_error = 7.647249538401255e-67 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 = 5.011862317086469e-62 estimated_step_error = 5.011862317086469e-62 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 = 3.284784962328325e-57 estimated_step_error = 3.284784962328325e-57 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 = 2.152993154639358e-52 estimated_step_error = 2.152993154639358e-52 best_h = 0.002048 opt_iter = 12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.41134820597272e-47 estimated_step_error = 1.41134820597272e-47 best_h = 0.004096 opt_iter = 13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.254170252679238e-43 estimated_step_error = 9.254170252679238e-43 best_h = 0.008192 opt_iter = 14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.071065531500803e-38 estimated_step_error = 6.071065531500803e-38 best_h = 0.016384 opt_iter = 15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.986968797991624e-33 estimated_step_error = 3.986968797991624e-33 best_h = 0.032768 opt_iter = 16 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.623798877420881e-28 estimated_step_error = 2.623798877420881e-28 best_h = 0.065536 opt_iter = 17 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.734093222285235e-23 estimated_step_error = 1.734093222285235e-23 best_h = 0.131072 opt_iter = 18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.156260417858527e-18 estimated_step_error = 1.156260417858527e-18 best_h = 0.262144 opt_iter = 19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.856144663557703e-14 estimated_step_error = 7.856144663557703e-14 best_h = 0.131072 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 0.005008355623235254 y[1] (numeric) = 0.005008355623235254 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 1.471 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1072 Order of pole (three term test) = 18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (analytic) = 0.02013477305240835 y[1] (numeric) = 0.02013477305240829 absolute error = 5.898059818321144e-17 relative error = 2.929290438471402e-13 % Correct digits = 15 h = 0.1 Radius of convergence (given) for eq 1 = 1.371 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.157 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] = 0.3 y[1] (analytic) = 0.04569165592605806 y[1] (numeric) = 0.04569165592605796 absolute error = 9.71445146547012e-17 relative error = 2.126088728583361e-13 % Correct digits = 15 h = 0.1 Radius of convergence (given) for eq 1 = 1.271 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.297 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] = 0.4 y[1] (analytic) = 0.08222901907505541 y[1] (numeric) = 0.08222901907505538 absolute error = 2.775557561562891e-17 relative error = 3.375399089984853e-14 % Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 1.171 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.239 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] = 0.5 y[1] (analytic) = 0.1305842404437227 y[1] (numeric) = 0.1305842404437227 absolute error = 2.775557561562891e-17 relative error = 2.125491982900541e-14 % Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 1.071 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.134 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 0.8377 Order of pole (three term test) = 18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6 y[1] (analytic) = 0.1919651694194377 y[1] (numeric) = 0.1919651694194377 absolute error = 2.775557561562891e-17 relative error = 1.445865190001415e-14 % Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 0.9708 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.028 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 0.8776 Order of pole (three term test) = 18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7 y[1] (analytic) = 0.268085757567931 y[1] (numeric) = 0.2680857575679311 absolute error = 5.551115123125783e-17 relative error = 2.070649024209789e-14 % Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 0.8708 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.922 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 0.8384 Order of pole (three term test) = 18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7999999999999999 y[1] (analytic) = 0.3613907468113436 y[1] (numeric) = 0.3613907468113436 absolute error = 5.551115123125783e-17 relative error = 1.53604240620572e-14 % Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 0.7708 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.8161 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 0.7607 Order of pole (three term test) = 18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8999999999999999 y[1] (analytic) = 0.4754424435858142 y[1] (numeric) = 0.4754424435858142 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 0.6708 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.7103 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 0.668 Order of pole (three term test) = 18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9999999999999999 y[1] (analytic) = 0.6156264703860141 y[1] (numeric) = 0.6156264703860141 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 0.5708 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.6044 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 0.5701 Order of pole (three term test) = 18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (analytic) = 0.7905480772542314 y[1] (numeric) = 0.7905480772542312 absolute error = 2.220446049250313e-16 relative error = 2.808742583958297e-14 % Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 0.4708 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.4985 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 0.4707 Order of pole (three term test) = 18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.2 y[1] (analytic) = 1.01512328314066 y[1] (numeric) = 1.015123283140648 absolute error = 1.13242748511766e-14 relative error = 1.115556606695175e-12 % Correct digits = 14 h = 0.1 Radius of convergence (given) for eq 1 = 0.3708 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.3926 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 0.3708 Order of pole (three term test) = 18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.3 y[1] (analytic) = 1.318640091629169 y[1] (numeric) = 1.31864009162807 absolute error = 1.09889874977398e-12 relative error = 8.333576058773549e-11 % Correct digits = 13 h = 0.1 Radius of convergence (given) for eq 1 = 0.2708 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.2867 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 0.2708 Order of pole (three term test) = 18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.4 y[1] (analytic) = 1.7721501376697 y[1] (numeric) = 1.772150137179981 absolute error = 4.897191541175516e-10 relative error = 2.763417972934906e-08 % Correct digits = 10 h = 0.1 Radius of convergence (given) for eq 1 = 0.1708 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.1808 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 0.1708 Order of pole (three term test) = 18 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = tan ( x ) ; Iterations = 14 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 107.1 %