##############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=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=0.1; x_end=1.4; /* # */ /* # Trouble about Pi/2 */ /* # */ 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_max_iter=20; /* 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_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 = 10 desired_abs_gbl_error = 1e-10 range = 1.3 estimated_steps = 1300000 step_error = 7.692307692307694e-17 est_needed_step_err = 7.692307692307694e-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 = 2.475466125514874e-184 estimated_step_error = 2.475466125514874e-184 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 = 1.661257502151858e-176 estimated_step_error = 1.661257502151858e-176 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 = 1.114851449339245e-168 estimated_step_error = 1.114851449339245e-168 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 = 7.481646952857931e-161 estimated_step_error = 7.481646952857931e-161 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 = 5.020855692025195e-153 estimated_step_error = 5.020855692025195e-153 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 = 3.369449168190198e-145 estimated_step_error = 3.369449168190198e-145 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 = 2.261212414751385e-137 estimated_step_error = 2.261212414751385e-137 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 = 1.517491888835743e-129 estimated_step_error = 1.517491888835743e-129 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 = 1.01839562596518e-121 estimated_step_error = 1.01839562596518e-121 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 = 6.834660257908669e-114 estimated_step_error = 6.834660257908669e-114 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 = 4.587096248204525e-106 estimated_step_error = 4.587096248204525e-106 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 = 3.078929868524917e-98 estimated_step_error = 3.078929868524917e-98 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 = 2.067015579248804e-90 estimated_step_error = 2.067015579248804e-90 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 = 1.388198528557742e-82 estimated_step_error = 1.388198528557742e-82 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 = 9.330106382801208e-75 estimated_step_error = 9.330106382801208e-75 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 = 6.280203627412161e-67 estimated_step_error = 6.280203627412161e-67 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 = 4.239904976716618e-59 estimated_step_error = 4.239904976716618e-59 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 = 2.879345661003233e-51 estimated_step_error = 2.879345661003233e-51 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y2[1] (analytic) = 1.099833416646828 y2[1] (numeric) = 1.099833416646828 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 y1[1] (analytic) = 1.099833416646828 y1[1] (numeric) = 1.099833416646828 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (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) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (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] = 0.2 y2[1] (analytic) = 1.198669330795061 y2[1] (numeric) = 1.198669330795061 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 y1[1] (analytic) = 1.198669330795061 y1[1] (numeric) = 1.198669330795061 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1947 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (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] = 0.3 y2[1] (analytic) = 1.29552020666134 y2[1] (numeric) = 1.29552020666134 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 y1[1] (analytic) = 1.29552020666134 y1[1] (numeric) = 1.29552020666134 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2823 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (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] = 0.4 y2[1] (analytic) = 1.389418342308651 y2[1] (numeric) = 1.389418342308651 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 y1[1] (analytic) = 1.389418342308651 y1[1] (numeric) = 1.389418342308651 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3587 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (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] = 0.5 y2[1] (analytic) = 1.479425538604203 y2[1] (numeric) = 1.479425538604203 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 y1[1] (analytic) = 1.479425538604203 y1[1] (numeric) = 1.479425538604203 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4207 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (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] = 0.6 y2[1] (analytic) = 1.564642473395035 y2[1] (numeric) = 1.564642473395035 absolute error = 2.220446049250313e-16 relative error = 1.419139571503696e-14 % Correct digits = 16 h = 0.1 y1[1] (analytic) = 1.564642473395035 y1[1] (numeric) = 1.564642473395035 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.466 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (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] = 0.7 y2[1] (analytic) = 1.644217687237691 y2[1] (numeric) = 1.644217687237691 absolute error = 2.220446049250313e-16 relative error = 1.350457464656455e-14 % Correct digits = 16 h = 0.1 y1[1] (analytic) = 1.644217687237691 y1[1] (numeric) = 1.644217687237691 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4927 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (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] = 0.7999999999999999 y2[1] (analytic) = 1.717356090899523 y2[1] (numeric) = 1.717356090899523 absolute error = 2.220446049250313e-16 relative error = 1.292944463304218e-14 % Correct digits = 16 h = 0.1 y1[1] (analytic) = 1.717356090899523 y1[1] (numeric) = 1.717356090899523 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4998 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (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] = 0.8999999999999999 y2[1] (analytic) = 1.783326909627483 y2[1] (numeric) = 1.783326909627484 absolute error = 2.220446049250313e-16 relative error = 1.245114419158369e-14 % Correct digits = 16 h = 0.1 y1[1] (analytic) = 1.783326909627483 y1[1] (numeric) = 1.783326909627483 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4869 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (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] = 0.9999999999999999 y2[1] (analytic) = 1.841470984807896 y2[1] (numeric) = 1.841470984807897 absolute error = 4.440892098500626e-16 relative error = 2.411600364674713e-14 % Correct digits = 16 h = 0.1 y1[1] (analytic) = 1.841470984807896 y1[1] (numeric) = 1.841470984807897 absolute error = 2.220446049250313e-16 relative error = 1.205800182337357e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4546 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (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] = 1.1 y2[1] (analytic) = 1.891207360061435 y2[1] (numeric) = 1.891207360061436 absolute error = 2.220446049250313e-16 relative error = 1.174089153913922e-14 % Correct digits = 16 h = 0.1 y1[1] (analytic) = 1.891207360061435 y1[1] (numeric) = 1.891207360061435 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4042 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (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] = 1.2 y2[1] (analytic) = 1.932039085967226 y2[1] (numeric) = 1.932039085967227 absolute error = 4.440892098500626e-16 relative error = 2.298551893052105e-14 % Correct digits = 16 h = 0.1 y1[1] (analytic) = 1.932039085967226 y1[1] (numeric) = 1.932039085967227 absolute error = 2.220446049250313e-16 relative error = 1.149275946526052e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3377 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (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] = 1.3 y2[1] (analytic) = 1.963558185417193 y2[1] (numeric) = 1.963558185417193 absolute error = 2.220446049250313e-16 relative error = 1.130827731890481e-14 % Correct digits = 16 h = 0.1 y1[1] (analytic) = 1.963558185417193 y1[1] (numeric) = 1.963558185417193 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2578 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (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 = 13 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 107.7 %