##############ECHO OF PROBLEM################# ##############temp/mult_sin_sinpostode.ode################# diff ( y , x , 1 ) = sin ( x ) * sin ( x ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=0.1; x_end=0.2; 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(-(sin(x) * cos(x))/2.0 + x/2.0); } // 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 = 0.1 estimated_steps = 100000 step_error = 1.05409255338946e-20 est_needed_step_err = 1.05409255338946e-20 opt_iter = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09735 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0003326673012346917 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.1 estimated_steps = 100000 step_error = 1.05409255338946e-20 est_needed_step_err = 1.05409255338946e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.264789130434852e-177 estimated_step_error = 8.264789130434852e-177 Double H and LOOP opt_iter = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09735 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0003326673012346917 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.1 estimated_steps = 50000.00000000001 step_error = 1.49071198499986e-20 est_needed_step_err = 1.49071198499986e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.54640711081085e-169 estimated_step_error = 5.54640711081085e-169 Double H and LOOP opt_iter = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09735 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0003326673012346917 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.1 estimated_steps = 25000 step_error = 2.108185106778919e-20 est_needed_step_err = 2.108185106778919e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.722132165016696e-161 estimated_step_error = 3.722132165016696e-161 Double H and LOOP opt_iter = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09735 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0003326673012346917 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.1 estimated_steps = 12500 step_error = 2.98142396999972e-20 est_needed_step_err = 2.98142396999972e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.497882438065287e-153 estimated_step_error = 2.497882438065287e-153 Double H and LOOP opt_iter = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09735 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0003326673012346917 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.1 estimated_steps = 6250.000000000001 step_error = 4.216370213557839e-20 est_needed_step_err = 4.216370213557839e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.676302978444555e-145 estimated_step_error = 1.676302978444555e-145 Double H and LOOP opt_iter = 6 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09735 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0003326673012346917 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.1 estimated_steps = 3125 step_error = 5.962847939999439e-20 est_needed_step_err = 5.962847939999439e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.124951174639119e-137 estimated_step_error = 1.124951174639119e-137 Double H and LOOP opt_iter = 7 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09735 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0003326673012346917 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.1 estimated_steps = 1562.5 step_error = 8.432740427115678e-20 est_needed_step_err = 8.432740427115678e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.549463677467823e-130 estimated_step_error = 7.549463677467823e-130 Double H and LOOP opt_iter = 8 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09735 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0003326673012346917 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.1 estimated_steps = 781.2500000000001 step_error = 1.192569587999888e-19 est_needed_step_err = 1.192569587999888e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.066418554253187e-122 estimated_step_error = 5.066418554253187e-122 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 = 0.09735 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0003326673012346917 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000256 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.1 estimated_steps = 390.6250000000001 step_error = 1.686548085423136e-19 est_needed_step_err = 1.686548085423136e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.400095450684846e-114 estimated_step_error = 3.400095450684846e-114 Double H and LOOP opt_iter = 10 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09735 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0003326673012346917 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000512 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.1 estimated_steps = 195.3125 step_error = 2.385139175999776e-19 est_needed_step_err = 2.385139175999776e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.281872152706583e-106 estimated_step_error = 2.281872152706583e-106 Double H and LOOP opt_iter = 11 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09735 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0003326673012346917 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.001024 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.1 estimated_steps = 97.65625000000001 step_error = 3.373096170846271e-19 est_needed_step_err = 3.373096170846271e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.531481717098863e-98 estimated_step_error = 1.531481717098863e-98 Double H and LOOP opt_iter = 12 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09735 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0003326673012346917 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.002048 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.1 estimated_steps = 48.82812500000001 step_error = 4.770278351999551e-19 est_needed_step_err = 4.770278351999551e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.02795223067176e-90 estimated_step_error = 1.02795223067176e-90 Double H and LOOP opt_iter = 13 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09735 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0003326673012346917 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.004096 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.1 estimated_steps = 24.4140625 step_error = 6.746192341692542e-19 est_needed_step_err = 6.746192341692542e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.901050895634196e-83 estimated_step_error = 6.901050895634196e-83 Double H and LOOP opt_iter = 14 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09735 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0003326673012346917 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.008192 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.1 estimated_steps = 12.20703125 step_error = 9.540556703999103e-19 est_needed_step_err = 9.540556703999103e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.634679859924864e-75 estimated_step_error = 4.634679859924864e-75 Double H and LOOP opt_iter = 15 SETTING H FOR DISPLAY INTERVAL SETTING H FOR POLE NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05942 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 0.0003326673012346917 y[1] (numeric) = 0.0003326673012346917 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.005942052342356119 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09735 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1118841046847122 y[1] (closed_form) = 0.0004656896105969255 y[1] (numeric) = 0.0004656896105969226 absolute error = 2.927345865710862e-18 relative error = 6.286045037505907e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.005942052342356119 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1082 Order of pole (three term test) = 22.95 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1237682093694245 y[1] (closed_form) = 0.0006300505828308947 y[1] (numeric) = 0.0006300505828308899 absolute error = 4.77048955893622e-18 relative error = 7.571597723950708e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.005942052342356119 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1188 Order of pole (three term test) = 22.94 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1297102617117806 y[1] (closed_form) = 0.0007250037547591043 y[1] (numeric) = 0.0007250037547590992 absolute error = 5.095750210681871e-18 relative error = 7.028584579365422e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.005942052342356119 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.124 Order of pole (three term test) = 22.93 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1415943663964928 y[1] (closed_form) = 0.0009424863558749469 y[1] (numeric) = 0.000942486355874944 absolute error = 2.927345865710862e-18 relative error = 3.105982221878737e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.005942052342356119 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1341 Order of pole (three term test) = 22.92 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1534784710812051 y[1] (closed_form) = 0.001199429957794609 y[1] (numeric) = 0.001199429957794599 absolute error = 1.019150042136374e-17 relative error = 8.496953369501328e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.005942052342356119 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.144 Order of pole (three term test) = 22.91 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1594205234235612 y[1] (closed_form) = 0.001343704155969613 y[1] (numeric) = 0.001343704155969617 absolute error = 3.903127820947816e-18 relative error = 2.904752362049018e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.005942052342356119 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1488 Order of pole (three term test) = 22.9 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1713046281082734 y[1] (closed_form) = 0.001665853405258544 y[1] (numeric) = 0.00166585340525855 absolute error = 5.637851296924623e-18 relative error = 3.384362200856213e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.005942052342356119 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1582 Order of pole (three term test) = 22.89 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1831887327929857 y[1] (closed_form) = 0.002035446705427171 y[1] (numeric) = 0.002035446705427169 absolute error = 2.168404344971009e-18 relative error = 1.06532111068756e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.005942052342356119 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1672 Order of pole (three term test) = 22.87 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1950728374776979 y[1] (closed_form) = 0.002455631945174203 y[1] (numeric) = 0.002455631945174201 absolute error = 1.734723475976807e-18 relative error = 7.064264982323097e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.005942052342356119 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1759 Order of pole (three term test) = 22.86 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = sin ( x ) * sin ( x ) ; Iterations = 17 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 107 %