##############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=5.1; 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_h=0.00001; glob_look_poles=true; glob_max_iter=20; // END SECOND INPUT BLOCK // BEGIN OVERRIDE BLOCK glob_desired_digits_correct=10; glob_display_interval=0.001; glob_look_poles=true; glob_max_iter=10000000; glob_max_minutes=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 opt_iter = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1e-10 range = 5 estimated_steps = 5000 step_error = 2e-14 est_needed_step_err = 2e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 value3 = 48033.96449572552 value3 = 1998856345722948 max_value3 = 1998856345722948 value3 = 1998856345722948 best_h = 0 opt_iter = 2 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1e-10 range = 5 estimated_steps = 10000 step_error = 1e-14 est_needed_step_err = 1e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 value3 = 0.0003619608527353955 value3 = 29785280.61096293 max_value3 = 29785280.61096293 value3 = 29785280.61096293 best_h = 0 opt_iter = 3 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1e-10 range = 5 estimated_steps = 20000 step_error = 5e-15 est_needed_step_err = 5e-15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 value3 = 2.712019666856976e-12 value3 = 0.4438352675879439 max_value3 = 0.4438352675879439 value3 = 0.4438352675879439 best_h = 0 opt_iter = 4 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1e-10 range = 5 estimated_steps = 40000 step_error = 2.5e-15 est_needed_step_err = 2.5e-15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 value3 = 2.026278324076019e-20 value3 = 6.61366086584246e-09 max_value3 = 6.61366086584246e-09 value3 = 6.61366086584246e-09 best_h = 0 opt_iter = 5 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1e-10 range = 5 estimated_steps = 80000 step_error = 1.25e-15 est_needed_step_err = 1.25e-15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 value3 = 1.511810801877739e-28 value3 = 9.855122664336056e-17 max_value3 = 9.855122664336056e-17 value3 = 9.855122664336056e-17 best_h = 6.25e-05 START of Soultion x[1] = 0.1 y2[1] (analytic) = 1.099833416646828 y2[1] (numeric) = 1.099833416646828 absolute error = 0 relative error = 0 % Correct digits = 16 h = 6.25e-05 y1[1] (analytic) = 1.099833416646828 y1[1] (numeric) = 1.099833416646828 absolute error = 0 relative error = 0 % Correct digits = 16 h = 6.25e-05 x[1] = 0.1 y2[1] (analytic) = 1.099833416646828 y2[1] (numeric) = 1.099833416646828 absolute error = 0 relative error = 0 % Correct digits = 16 h = 6.25e-05 y1[1] (analytic) = 1.099833416646828 y1[1] (numeric) = 1.099833416646828 absolute error = 0 relative error = 0 % Correct digits = 16 h = 6.25e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1010624999999999 y2[1] (analytic) = 1.100890552022245 y2[1] (numeric) = 1.100890552022245 absolute error = 0 relative error = 0 % Correct digits = 16 h = 6.25e-05 y1[1] (analytic) = 1.100890552022245 y1[1] (numeric) = 1.100890594432981 absolute error = 4.241073603417078e-08 relative error = 3.852402580462312e-06 % Correct digits = 7 h = 6.25e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1020624999999998 y2[1] (analytic) = 1.101885398941817 y2[1] (numeric) = 1.101885398941817 absolute error = 4.440892098500626e-16 relative error = 4.030266761648159e-14 % Correct digits = 15 h = 6.25e-05 y1[1] (analytic) = 1.101885398941817 y1[1] (numeric) = 1.101885559280534 absolute error = 1.603387167481429e-07 relative error = 1.4551306052528e-05 % Correct digits = 6 h = 6.25e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1030624999999997 y2[1] (analytic) = 1.102880143975998 y2[1] (numeric) = 1.102880143975999 absolute error = 6.661338147750939e-16 relative error = 6.039947481270376e-14 % Correct digits = 15 h = 6.25e-05 y1[1] (analytic) = 1.102880143975998 y1[1] (numeric) = 1.102880498652341 absolute error = 3.546763431838684e-07 relative error = 3.215910134216609e-05 % Correct digits = 6 h = 6.25e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1040624999999996 y2[1] (analytic) = 1.103874786130044 y2[1] (numeric) = 1.103874786130044 absolute error = 6.661338147750939e-16 relative error = 6.034505209693404e-14 % Correct digits = 15 h = 6.25e-05 y1[1] (analytic) = 1.103874786130044 y1[1] (numeric) = 1.103875412299668 absolute error = 6.261696248177628e-07 relative error = 5.672469673965323e-05 % Correct digits = 6 h = 6.25e-05 TOP MAIN SOLVE Loop NO POLE NO POLE Finished! Maximum Time Reached before Solution Completed! diff ( y2 , x , 4 ) = y1 - 1.0; diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ; Iterations = 70 Total Elapsed Time = 3 Minutes 4 Seconds Elapsed Time(since restart) = 2 Minutes 51 Seconds Expected Time Remaining = 2 Days 9 Hours 32 Minutes 19 Seconds Optimized Time Remaining = 2 Days 5 Hours 28 Minutes 25 Seconds Expected Total Time = 2 Days 5 Hours 31 Minutes 29 Seconds Time to Timeout Unknown Percent Done = 0.08875 %