##############ECHO OF PROBLEM################# ##############temp/mtest8postode.ode################# diff ( y2 , x , 4 ) = y1 - 1.0 ; diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=40; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=0.1; x_end=1.4; array_y1_init[0 + 1] = exact_soln_y1(x_start); array_y2_init[0 + 1] = exact_soln_y2(x_start); array_y2_init[1 + 1] = exact_soln_y2p(x_start); array_y2_init[2 + 1] = exact_soln_y2pp(x_start); array_y2_init[3 + 1] = exact_soln_y2ppp(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_y1 (double x) { return(1.0 + sin(x)); } double exact_soln_y2 (double x) { return(1.0 + sin(x)); } double exact_soln_y2p (double x) { return( cos(x)); } double exact_soln_y2pp (double x) { return( -sin(x)); } double exact_soln_y2ppp (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 = 1.3 estimated_steps = 1300000 step_error = 2.192645048267574e-21 est_needed_step_err = 2.192645048267574e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size = 1.099833416646828 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 1.099833416646828 desired_abs_gbl_error = 1.099833416646828e-16 range = 1.3 estimated_steps = 1300000 step_error = 2.411544294929875e-21 est_needed_step_err = 2.411544294929875e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.683742500284562e-259 estimated_step_error = 2.683742500284562e-259 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size = 1.099833416646828 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 1.099833416646828 desired_abs_gbl_error = 1.099833416646828e-16 range = 1.3 estimated_steps = 649999.9999999999 step_error = 3.410438648153292e-21 est_needed_step_err = 3.410438648153292e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.844254051529349e-248 estimated_step_error = 1.844254051529349e-248 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size = 1.099833416646828 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 1.099833416646828 desired_abs_gbl_error = 1.099833416646828e-16 range = 1.3 estimated_steps = 324999.9999999999 step_error = 4.82308858985975e-21 est_needed_step_err = 4.82308858985975e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.267362075281025e-237 estimated_step_error = 1.267362075281025e-237 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size = 1.099833416646828 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 1.099833416646828 desired_abs_gbl_error = 1.099833416646828e-16 range = 1.3 estimated_steps = 162500 step_error = 6.820877296306584e-21 est_needed_step_err = 6.820877296306584e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.709250556831444e-227 estimated_step_error = 8.709250556831444e-227 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size = 1.099833416646828 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 1.099833416646828 desired_abs_gbl_error = 1.099833416646828e-16 range = 1.3 estimated_steps = 81249.99999999999 step_error = 9.646177179719499e-21 est_needed_step_err = 9.646177179719499e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.984957858910743e-216 estimated_step_error = 5.984957858910743e-216 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size = 1.099833416646828 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 1.099833416646828 desired_abs_gbl_error = 1.099833416646828e-16 range = 1.3 estimated_steps = 40624.99999999999 step_error = 1.364175459261317e-20 est_needed_step_err = 1.364175459261317e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.112840586441793e-205 estimated_step_error = 4.112840586441793e-205 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size = 1.099833416646828 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 1.099833416646828 desired_abs_gbl_error = 1.099833416646828e-16 range = 1.3 estimated_steps = 20312.5 step_error = 1.9292354359439e-20 est_needed_step_err = 1.9292354359439e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.82633471110443e-194 estimated_step_error = 2.82633471110443e-194 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size = 1.099833416646828 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 1.099833416646828 desired_abs_gbl_error = 1.099833416646828e-16 range = 1.3 estimated_steps = 10156.25 step_error = 2.728350918522633e-20 est_needed_step_err = 2.728350918522633e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.942259165876972e-183 estimated_step_error = 1.942259165876972e-183 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) = 32.99 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) = 32.99 NO COMPLEX POLE (six term test) for Equation 2 SETTING H FOR POLE ACCURACY START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y2[1] (closed_form) = 1.099833416646828 y2[1] (numeric) = 1.099833416646828 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.000128 y1[1] (closed_form) = 1.099833416646828 y1[1] (numeric) = 1.099833416646828 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2000959999999943 y2[1] (closed_form) = 1.198763416270916 y2[1] (numeric) = 1.198763416270922 absolute error = 6.661338147750939e-15 relative error = 5.556841372814721e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.000128 y1[1] (closed_form) = 1.198763416270916 y1[1] (numeric) = 1.198763416270922 absolute error = 6.883382752675971e-15 relative error = 5.742069418575212e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3000639999999968 y2[1] (closed_form) = 1.295581347591373 y2[1] (numeric) = 1.295581347591376 absolute error = 3.108624468950438e-15 relative error = 2.399405081533251e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.000128 y1[1] (closed_form) = 1.295581347591373 y1[1] (numeric) = 1.295581347591377 absolute error = 3.33066907387547e-15 relative error = 2.570791158785626e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.40003200000001 y2[1] (closed_form) = 1.389447816061081 y2[1] (numeric) = 1.389447816061072 absolute error = 8.659739592076221e-15 relative error = 6.232504374741869e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.000128 y1[1] (closed_form) = 1.389447816061081 y1[1] (numeric) = 1.389447816061072 absolute error = 8.43769498715119e-15 relative error = 6.072696570261309e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5000000000000233 y2[1] (closed_form) = 1.479425538604223 y2[1] (numeric) = 1.479425538604205 absolute error = 1.865174681370263e-14 relative error = 1.26074251978236e-12 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 14 h = 0.000128 y1[1] (closed_form) = 1.479425538604223 y1[1] (numeric) = 1.479425538604205 absolute error = 1.798561299892754e-14 relative error = 1.215716001218704e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6000960000000366 y2[1] (closed_form) = 1.564721703012103 y2[1] (numeric) = 1.564721703012073 absolute error = 2.953193245502916e-14 relative error = 1.887360058864138e-12 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 14 h = 0.000128 y1[1] (closed_form) = 1.564721703012103 y1[1] (numeric) = 1.564721703012074 absolute error = 2.886579864025407e-14 relative error = 1.844788027461187e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7000640000000499 y2[1] (closed_form) = 1.644266635818324 y2[1] (numeric) = 1.644266635818288 absolute error = 3.663735981263017e-14 relative error = 2.228188483213756e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y1[1] (closed_form) = 1.644266635818324 y1[1] (numeric) = 1.644266635818288 absolute error = 3.574918139293004e-14 relative error = 2.174171792711604e-12 % Desired digits = 16 Estimated correct digits = 11 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8000320000000631 y2[1] (closed_form) = 1.717378385146976 y2[1] (numeric) = 1.717378385146931 absolute error = 4.463096558993129e-14 relative error = 2.598784634529549e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y1[1] (closed_form) = 1.717378385146976 y1[1] (numeric) = 1.717378385146932 absolute error = 4.329869796038111e-14 relative error = 2.521208973797323e-12 % Desired digits = 16 Estimated correct digits = 11 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9000000000000764 y2[1] (closed_form) = 1.783326909627531 y2[1] (numeric) = 1.783326909627479 absolute error = 5.151434834260726e-14 relative error = 2.888665452447339e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y1[1] (closed_form) = 1.783326909627531 y1[1] (numeric) = 1.783326909627483 absolute error = 4.818367926873179e-14 relative error = 2.701898289573589e-12 % Desired digits = 16 Estimated correct digits = 11 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.00009600000009 y2[1] (closed_form) = 1.84152284995173 y2[1] (numeric) = 1.841522849951676 absolute error = 5.46229728115577e-14 relative error = 2.966184905769129e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y1[1] (closed_form) = 1.84152284995173 y1[1] (numeric) = 1.841522849951681 absolute error = 4.907185768843192e-14 relative error = 2.664743350304786e-12 % Desired digits = 16 Estimated correct digits = 11 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.100064000000016 y2[1] (closed_form) = 1.891236388388001 y2[1] (numeric) = 1.891236388387984 absolute error = 1.731947918415244e-14 relative error = 9.157754837254759e-13 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (closed_form) = 1.891236388388001 y1[1] (numeric) = 1.891236388387993 absolute error = 7.993605777301127e-15 relative error = 4.226656078732966e-13 % Desired digits = 16 Estimated correct digits = 11 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.200031999999943 y2[1] (closed_form) = 1.932050680938143 y2[1] (numeric) = 1.932050680938148 absolute error = 5.551115123125783e-15 relative error = 2.873172623210037e-13 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (closed_form) = 1.932050680938143 y1[1] (numeric) = 1.932050680938162 absolute error = 1.909583602355269e-14 relative error = 9.883713823842528e-13 % Desired digits = 16 Estimated correct digits = 11 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.299999999999869 y2[1] (closed_form) = 1.963558185417158 y2[1] (numeric) = 1.963558185417174 absolute error = 1.620925615952729e-14 relative error = 8.25504244280066e-13 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (closed_form) = 1.963558185417158 y1[1] (numeric) = 1.963558185417194 absolute error = 3.61932706027801e-14 relative error = 1.843249202981517e-12 % Desired digits = 16 Estimated correct digits = 11 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 Finished! diff ( y2 , x , 4 ) = y1 - 1.0 ; diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ; Iterations = 10157 Total Elapsed Time = 5.0 Seconds Elapsed Time(since restart) = 5.0 Seconds Time to Timeout = 2 Minutes 55.0 Seconds Percent Done = 100 %