##############ECHO OF PROBLEM################# ##############temp/mtest3postode.ode################# diff ( y2 , x , 1 ) = m1 * y1 + 1.0 ; diff ( y1 , x , 1 ) = y2 - 1.0 ; ! // BEGIN FIRST INPUT BLOCK Digits=16; max_terms=40; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=0.1; x_end=0.5; array_y1_init[0 + 1] = exact_soln_y1(x_start); array_y2_init[0 + 1] = exact_soln_y2(x_start); 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_y1 (double x) { return(1.0 + cos(x)); } double exact_soln_y2 (double x) { return(1.0 - sin(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 = 0.4 estimated_steps = 400000.0000000001 step_error = 3.952847075210474e-21 est_needed_step_err = 3.952847075210474e-21 opt_iter = 1 min_size = 0.9001665833531718 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.4 estimated_steps = 400000.0000000001 step_error = 3.952847075210474e-21 est_needed_step_err = 3.952847075210474e-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 min_size = 0.9001665833531718 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.4 estimated_steps = 200000 step_error = 5.590169943749474e-21 est_needed_step_err = 5.590169943749474e-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 min_size = 0.9001665833531718 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.4 estimated_steps = 100000 step_error = 7.905694150420948e-21 est_needed_step_err = 7.905694150420948e-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 min_size = 0.9001665833531718 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.4 estimated_steps = 50000.00000000001 step_error = 1.118033988749895e-20 est_needed_step_err = 1.118033988749895e-20 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 min_size = 0.9001665833531718 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.4 estimated_steps = 25000 step_error = 1.58113883008419e-20 est_needed_step_err = 1.58113883008419e-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 min_size = 0.9001665833531718 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.4 estimated_steps = 12500 step_error = 2.23606797749979e-20 est_needed_step_err = 2.23606797749979e-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 min_size = 0.9001665833531718 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.4 estimated_steps = 6250.000000000001 step_error = 3.162277660168379e-20 est_needed_step_err = 3.162277660168379e-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 min_size = 0.9001665833531718 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.4 estimated_steps = 3125 step_error = 4.472135954999579e-20 est_needed_step_err = 4.472135954999579e-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 min_size = 0.9001665833531718 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000256 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.4 estimated_steps = 1562.5 step_error = 6.324555320336758e-20 est_needed_step_err = 6.324555320336758e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.330234937872e-171 estimated_step_error = 1.330234937872e-171 Double H and LOOP opt_iter = 10 min_size = 0.9001665833531718 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000512 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.4 estimated_steps = 781.2500000000001 step_error = 8.944271909999158e-20 est_needed_step_err = 8.944271909999158e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.141301713349235e-161 estimated_step_error = 9.141301713349235e-161 Double H and LOOP opt_iter = 11 min_size = 0.9001665833531718 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.001024 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.4 estimated_steps = 390.6250000000001 step_error = 1.264911064067352e-19 est_needed_step_err = 1.264911064067352e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.281850342480742e-150 estimated_step_error = 6.281850342480742e-150 Double H and LOOP opt_iter = 12 min_size = 0.9001665833531718 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.002048 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.4 estimated_steps = 195.3125 step_error = 1.788854381999832e-19 est_needed_step_err = 1.788854381999832e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.316848688683022e-139 estimated_step_error = 4.316848688683022e-139 Double H and LOOP opt_iter = 13 min_size = 0.9001665833531718 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.004096 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.4 estimated_steps = 97.65625000000001 step_error = 2.529822128134703e-19 est_needed_step_err = 2.529822128134703e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.96650758617814e-128 estimated_step_error = 2.96650758617814e-128 Double H and LOOP opt_iter = 14 min_size = 0.9001665833531718 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.008192 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.4 estimated_steps = 48.82812500000001 step_error = 3.577708763999663e-19 est_needed_step_err = 3.577708763999663e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.038557150732884e-117 estimated_step_error = 2.038557150732884e-117 Double H and LOOP opt_iter = 15 min_size = 0.9001665833531718 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.016384 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.4 estimated_steps = 24.4140625 step_error = 5.059644256269407e-19 est_needed_step_err = 5.059644256269407e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.400870196540969e-106 estimated_step_error = 1.400870196540969e-106 Double H and LOOP opt_iter = 16 min_size = 0.9001665833531718 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.032768 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.4 estimated_steps = 12.20703125 step_error = 7.155417527999327e-19 est_needed_step_err = 7.155417527999327e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.626491451141893e-96 estimated_step_error = 9.626491451141893e-96 Double H and LOOP opt_iter = 17 SETTING H FOR DISPLAY INTERVAL START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y2[1] (closed_form) = 0.9001665833531718 y2[1] (numeric) = 0.9001665833531718 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.04 y1[1] (closed_form) = 1.995004165278026 y1[1] (numeric) = 1.995004165278026 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.04 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 = 0.09933 Order of pole (three term test) = 32.99 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.09933 Order of pole (three term test) = 32.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.1397338661590122 y2[1] (closed_form) = 0.8607204202808578 y2[1] (numeric) = 0.8607204202808576 absolute error = 2.220446049250313e-16 relative error = 2.579752956861148e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753057 y1[1] (closed_form) = 1.990253098290159 y1[1] (numeric) = 1.990253098290159 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753057 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1379 Order of pole (three term test) = 32.98 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1379 Order of pole (three term test) = 32.02 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.1794677323180244 y2[1] (closed_form) = 0.8214941201115696 y2[1] (numeric) = 0.8214941201115694 absolute error = 2.220446049250313e-16 relative error = 2.702936022169882e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753057 y1[1] (closed_form) = 1.983938845073848 y1[1] (numeric) = 1.983938845073848 absolute error = 2.220446049250313e-16 relative error = 1.11921093473406e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753057 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1756 Order of pole (three term test) = 32.97 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1756 Order of pole (three term test) = 32.03 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2192015984770366 y2[1] (closed_form) = 0.7825496044008404 y2[1] (numeric) = 0.7825496044008401 absolute error = 3.33066907387547e-16 relative error = 4.256176292396951e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753057 y1[1] (closed_form) = 1.976071373135064 y1[1] (numeric) = 1.976071373135064 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753057 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2122 Order of pole (three term test) = 32.95 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2122 Order of pole (three term test) = 32.05 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2688689311758019 y2[1] (closed_form) = 0.7343588249102597 y2[1] (numeric) = 0.7343588249102594 absolute error = 3.33066907387547e-16 relative error = 4.535479061319219e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753057 y1[1] (closed_form) = 1.964071971430008 y1[1] (numeric) = 1.964071971430008 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753057 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2561 Order of pole (three term test) = 32.93 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2561 Order of pole (three term test) = 32.07 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3086027973348142 y2[1] (closed_form) = 0.6962722638895356 y2[1] (numeric) = 0.6962722638895353 absolute error = 2.220446049250313e-16 relative error = 3.189048543807268e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753057 y1[1] (closed_form) = 1.952758868926032 y1[1] (numeric) = 1.952758868926032 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753057 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2894 Order of pole (three term test) = 32.91 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2894 Order of pole (three term test) = 32.09 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3483366634938265 y2[1] (closed_form) = 0.6586651590958148 y2[1] (numeric) = 0.6586651590958146 absolute error = 2.220446049250313e-16 relative error = 3.371130260325959e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753057 y1[1] (closed_form) = 1.939941767549945 y1[1] (numeric) = 1.939941767549945 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753057 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3208 Order of pole (three term test) = 32.88 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3208 Order of pole (three term test) = 32.12 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3880705296528388 y2[1] (closed_form) = 0.6215968760674698 y2[1] (numeric) = 0.6215968760674697 absolute error = 1.110223024625157e-16 relative error = 1.786082053128996e-14 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 16 h = 0.009933466539753057 y1[1] (closed_form) = 1.925640900024465 y1[1] (numeric) = 1.925640900024465 absolute error = 2.220446049250313e-16 relative error = 1.15309456151565e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753057 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3503 Order of pole (three term test) = 32.86 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3503 Order of pole (three term test) = 32.14 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4278043958118511 y2[1] (closed_form) = 0.5851259297736962 y2[1] (numeric) = 0.585125929773696 absolute error = 1.110223024625157e-16 relative error = 1.897408691244545e-14 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 16 h = 0.009933466539753057 y1[1] (closed_form) = 1.909878841304632 y1[1] (numeric) = 1.909878841304632 absolute error = 2.220446049250313e-16 relative error = 1.162610947474309e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753057 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3775 Order of pole (three term test) = 32.83 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3775 Order of pole (three term test) = 32.17 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4675382619708635 y2[1] (closed_form) = 0.5493098922443951 y2[1] (numeric) = 0.5493098922443951 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 16 h = 0.009933466539753057 y1[1] (closed_form) = 1.892680472941601 y1[1] (numeric) = 1.892680472941602 absolute error = 4.440892098500626e-16 relative error = 2.346350671436155e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753057 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4023 Order of pole (three term test) = 32.8 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4023 Order of pole (three term test) = 32.2 NO COMPLEX POLE (six term test) for Equation 2 Finished! diff ( y2 , x , 1 ) = m1 * y1 + 1.0 ; diff ( y1 , x , 1 ) = y2 - 1.0 ; Iterations = 41 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 104.3 %