##############ECHO OF PROBLEM################# ##############temp/div_c_lin_backpostode.ode################# diff ( y , x , 1 ) = 2.0 / ( 0.2 * x + 0.3 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=3.1; x_end=2.5; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_display_interval=0.1; glob_type_given_pole=1; array_given_rad_poles[1][1]=-1.5; array_given_rad_poles[1][2]=0.0; array_given_ord_poles[1][1]=1.0; array_given_ord_poles[1][2]=0.0; /* 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(10.0* ln(0.2* x + 0.3)); } /* 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 = -0.6000000000000001 estimated_steps = 600000.0000000001 step_error = 4.303314829119351e-21 est_needed_step_err = 4.303314829119351e-21 opt_iter = 1 min_size = 0.8338160893905089 min_size = 1 glob_desired_digits_correct = 16 estimated_h = -1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = -0.6000000000000001 estimated_steps = 600000.0000000001 step_error = 4.303314829119351e-21 est_needed_step_err = 4.303314829119351e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 2 min_size = 0.8338160893905089 min_size = 1 glob_desired_digits_correct = 16 estimated_h = -2e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = -0.6000000000000001 estimated_steps = 300000.0000000001 step_error = 6.085806194501846e-21 est_needed_step_err = 6.085806194501846e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 3 min_size = 0.8338160893905089 min_size = 1 glob_desired_digits_correct = 16 estimated_h = -4e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = -0.6000000000000001 estimated_steps = 150000 step_error = 8.606629658238703e-21 est_needed_step_err = 8.606629658238703e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 4 min_size = 0.8338160893905089 min_size = 1 glob_desired_digits_correct = 16 estimated_h = -8e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = -0.6000000000000001 estimated_steps = 75000.00000000001 step_error = 1.217161238900369e-20 est_needed_step_err = 1.217161238900369e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 5 min_size = 0.8338160893905089 min_size = 1 glob_desired_digits_correct = 16 estimated_h = -1.6e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = -0.6000000000000001 estimated_steps = 37500.00000000001 step_error = 1.721325931647741e-20 est_needed_step_err = 1.721325931647741e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 6 min_size = 0.8338160893905089 min_size = 1 glob_desired_digits_correct = 16 estimated_h = -3.2e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = -0.6000000000000001 estimated_steps = 18750 step_error = 2.434322477800738e-20 est_needed_step_err = 2.434322477800738e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 7 min_size = 0.8338160893905089 min_size = 1 glob_desired_digits_correct = 16 estimated_h = -6.4e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = -0.6000000000000001 estimated_steps = 9375.000000000002 step_error = 3.442651863295481e-20 est_needed_step_err = 3.442651863295481e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 8 min_size = 0.8338160893905089 min_size = 1 glob_desired_digits_correct = 16 estimated_h = -0.000128 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = -0.6000000000000001 estimated_steps = 4687.500000000001 step_error = 4.868644955601476e-20 est_needed_step_err = 4.868644955601476e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 9 min_size = 0.8338160893905089 min_size = 1 glob_desired_digits_correct = 16 estimated_h = -0.000256 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = -0.6000000000000001 estimated_steps = 2343.75 step_error = 6.885303726590962e-20 est_needed_step_err = 6.885303726590962e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 10 min_size = 0.8338160893905089 min_size = 1 glob_desired_digits_correct = 16 estimated_h = -0.000512 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = -0.6000000000000001 estimated_steps = 1171.875 step_error = 9.737289911202953e-20 est_needed_step_err = 9.737289911202953e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 11 min_size = 0.8338160893905089 min_size = 1 glob_desired_digits_correct = 16 estimated_h = -0.001024 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = -0.6000000000000001 estimated_steps = 585.9375000000001 step_error = 1.377060745318192e-19 est_needed_step_err = 1.377060745318192e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 12 min_size = 0.8338160893905089 min_size = 1 glob_desired_digits_correct = 16 estimated_h = -0.002048 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = -0.6000000000000001 estimated_steps = 292.9687500000001 step_error = 1.947457982240591e-19 est_needed_step_err = 1.947457982240591e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 13 min_size = 0.8338160893905089 min_size = 1 glob_desired_digits_correct = 16 estimated_h = -0.004096 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = -0.6000000000000001 estimated_steps = 146.484375 step_error = 2.754121490636385e-19 est_needed_step_err = 2.754121490636385e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 14 min_size = 0.8338160893905089 min_size = 1 glob_desired_digits_correct = 16 estimated_h = -0.008192 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = -0.6000000000000001 estimated_steps = 73.24218750000001 step_error = 3.894915964481181e-19 est_needed_step_err = 3.894915964481181e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 15 min_size = 0.8338160893905089 min_size = 1 glob_desired_digits_correct = 16 estimated_h = -0.016384 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = -0.6000000000000001 estimated_steps = 36.62109375000001 step_error = 5.50824298127277e-19 est_needed_step_err = 5.50824298127277e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 16 min_size = 0.8338160893905089 min_size = 1 glob_desired_digits_correct = 16 estimated_h = -0.032768 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = -0.6000000000000001 estimated_steps = 18.310546875 step_error = 7.789831928962362e-19 est_needed_step_err = 7.789831928962362e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 17 min_size = 0.8338160893905089 min_size = 1 glob_desired_digits_correct = 16 estimated_h = -0.065536 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = -0.6000000000000001 estimated_steps = 9.155273437500002 step_error = 1.101648596254554e-18 est_needed_step_err = 1.101648596254554e-18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 18 SETTING H FOR MAX H SETTING H FOR DISPLAY INTERVAL START of Soultion TOP MAIN SOLVE Loop x[1] = 3 y[1] (closed_form) = -1.053605156578262 y[1] (numeric) = -1.053605156399005 absolute error = 1.792563875113728e-10 relative error = 1.701362093685404e-08 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 10 h = -0.1 Radius of convergence (given) for eq 1 = 4.5 Order of pole (given) = 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 TOP MAIN SOLVE Loop x[1] = 2.9 y[1] (closed_form) = -1.27833371509885 y[1] (numeric) = -1.27833371471498 absolute error = 3.838702689051843e-10 relative error = 3.002895600508358e-08 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 10 h = -0.1 Radius of convergence (given) for eq 1 = 4.4 Order of pole (given) = 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 TOP MAIN SOLVE Loop x[1] = 2.8 y[1] (closed_form) = -1.508228897345838 y[1] (numeric) = -1.508228896727717 absolute error = 6.181204437183396e-10 relative error = 4.098319855866044e-08 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 10 h = -0.1 Radius of convergence (given) for eq 1 = 4.3 Order of pole (given) = 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 TOP MAIN SOLVE Loop x[1] = 2.7 y[1] (closed_form) = -1.743533871447779 y[1] (numeric) = -1.743533870560638 absolute error = 8.871414713951253e-10 relative error = 5.088180309674565e-08 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 10 h = -0.1 Radius of convergence (given) for eq 1 = 4.2 Order of pole (given) = 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 TOP MAIN SOLVE Loop x[1] = 2.6 y[1] (closed_form) = -1.984509387238385 y[1] (numeric) = -1.984509386041278 absolute error = 1.197106191952457e-09 relative error = 6.032252604349398e-08 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 10 h = -0.1 Radius of convergence (given) for eq 1 = 4.1 Order of pole (given) = 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 Finished! diff ( y , x , 1 ) = 2.0 / ( 0.2 * x + 0.3 ) ; Iterations = 6 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Expected Time Remaining = 0.0 Seconds Optimized Time Remaining = 0.0 Seconds Expected Total Time = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 0 %