##############ECHO OF PROBLEM################# ##############temp/div_c_linpostode.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=2.5; x_end=3.1; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; 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 Radius of convergence (given) for eq 1 = 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 min_size = 2.231435513142097 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 2.231435513142097 desired_abs_gbl_error = 2.231435513142097e-16 range = 0.6000000000000001 estimated_steps = 600000.0000000001 step_error = 9.602569533927934e-21 est_needed_step_err = 9.602569533927934e-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 Radius of convergence (given) for eq 1 = 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 min_size = 2.231435513142097 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 2.231435513142097 desired_abs_gbl_error = 2.231435513142097e-16 range = 0.6000000000000001 estimated_steps = 300000.0000000001 step_error = 1.358008406851158e-20 est_needed_step_err = 1.358008406851158e-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 = 3 Radius of convergence (given) for eq 1 = 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 min_size = 2.231435513142097 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 2.231435513142097 desired_abs_gbl_error = 2.231435513142097e-16 range = 0.6000000000000001 estimated_steps = 150000 step_error = 1.920513906785587e-20 est_needed_step_err = 1.920513906785587e-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 = 4 Radius of convergence (given) for eq 1 = 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 min_size = 2.231435513142097 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 2.231435513142097 desired_abs_gbl_error = 2.231435513142097e-16 range = 0.6000000000000001 estimated_steps = 75000.00000000001 step_error = 2.716016813702316e-20 est_needed_step_err = 2.716016813702316e-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 Radius of convergence (given) for eq 1 = 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 min_size = 2.231435513142097 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 2.231435513142097 desired_abs_gbl_error = 2.231435513142097e-16 range = 0.6000000000000001 estimated_steps = 37500.00000000001 step_error = 3.841027813571174e-20 est_needed_step_err = 3.841027813571174e-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 Radius of convergence (given) for eq 1 = 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 min_size = 2.231435513142097 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 2.231435513142097 desired_abs_gbl_error = 2.231435513142097e-16 range = 0.6000000000000001 estimated_steps = 18750 step_error = 5.432033627404632e-20 est_needed_step_err = 5.432033627404632e-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 Radius of convergence (given) for eq 1 = 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 min_size = 2.231435513142097 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 2.231435513142097 desired_abs_gbl_error = 2.231435513142097e-16 range = 0.6000000000000001 estimated_steps = 9375.000000000002 step_error = 7.682055627142348e-20 est_needed_step_err = 7.682055627142348e-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 Radius of convergence (given) for eq 1 = 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 min_size = 2.231435513142097 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 2.231435513142097 desired_abs_gbl_error = 2.231435513142097e-16 range = 0.6000000000000001 estimated_steps = 4687.500000000001 step_error = 1.086406725480926e-19 est_needed_step_err = 1.086406725480926e-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 = 9 Radius of convergence (given) for eq 1 = 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 min_size = 2.231435513142097 glob_desired_digits_correct = 16 estimated_h = 0.000256 estimated_answer = 2.231435513142097 desired_abs_gbl_error = 2.231435513142097e-16 range = 0.6000000000000001 estimated_steps = 2343.75 step_error = 1.53641112542847e-19 est_needed_step_err = 1.53641112542847e-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 = 10 Radius of convergence (given) for eq 1 = 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 min_size = 2.231435513142097 glob_desired_digits_correct = 16 estimated_h = 0.000512 estimated_answer = 2.231435513142097 desired_abs_gbl_error = 2.231435513142097e-16 range = 0.6000000000000001 estimated_steps = 1171.875 step_error = 2.172813450961853e-19 est_needed_step_err = 2.172813450961853e-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 = 11 Radius of convergence (given) for eq 1 = 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 min_size = 2.231435513142097 glob_desired_digits_correct = 16 estimated_h = 0.001024 estimated_answer = 2.231435513142097 desired_abs_gbl_error = 2.231435513142097e-16 range = 0.6000000000000001 estimated_steps = 585.9375000000001 step_error = 3.072822250856939e-19 est_needed_step_err = 3.072822250856939e-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 Radius of convergence (given) for eq 1 = 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 min_size = 2.231435513142097 glob_desired_digits_correct = 16 estimated_h = 0.002048 estimated_answer = 2.231435513142097 desired_abs_gbl_error = 2.231435513142097e-16 range = 0.6000000000000001 estimated_steps = 292.9687500000001 step_error = 4.345626901923705e-19 est_needed_step_err = 4.345626901923705e-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 Radius of convergence (given) for eq 1 = 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 min_size = 2.231435513142097 glob_desired_digits_correct = 16 estimated_h = 0.004096 estimated_answer = 2.231435513142097 desired_abs_gbl_error = 2.231435513142097e-16 range = 0.6000000000000001 estimated_steps = 146.484375 step_error = 6.145644501713878e-19 est_needed_step_err = 6.145644501713878e-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 Radius of convergence (given) for eq 1 = 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 min_size = 2.231435513142097 glob_desired_digits_correct = 16 estimated_h = 0.008192 estimated_answer = 2.231435513142097 desired_abs_gbl_error = 2.231435513142097e-16 range = 0.6000000000000001 estimated_steps = 73.24218750000001 step_error = 8.69125380384741e-19 est_needed_step_err = 8.69125380384741e-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 Radius of convergence (given) for eq 1 = 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 min_size = 2.231435513142097 glob_desired_digits_correct = 16 estimated_h = 0.016384 estimated_answer = 2.231435513142097 desired_abs_gbl_error = 2.231435513142097e-16 range = 0.6000000000000001 estimated_steps = 36.62109375000001 step_error = 1.229128900342776e-18 est_needed_step_err = 1.229128900342776e-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 = 16 Radius of convergence (given) for eq 1 = 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 min_size = 2.231435513142097 glob_desired_digits_correct = 16 estimated_h = 0.032768 estimated_answer = 2.231435513142097 desired_abs_gbl_error = 2.231435513142097e-16 range = 0.6000000000000001 estimated_steps = 18.310546875 step_error = 1.738250760769482e-18 est_needed_step_err = 1.738250760769482e-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 = 17 SETTING H FOR DISPLAY INTERVAL Radius of convergence (given) for eq 1 = 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 START of Soultion TOP MAIN SOLVE Loop x[1] = 2.5 y[1] (closed_form) = -2.231435513142097 y[1] (numeric) = -2.231435513142097 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.06000000000000001 Radius of convergence (given) for eq 1 = 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] = 2.56 y[1] (closed_form) = -2.08254938820459 y[1] (numeric) = -2.082549388185847 absolute error = 1.874322919093174e-11 relative error = 9.000136706045024e-10 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 12 h = 0.06000000000000001 Radius of convergence (given) for eq 1 = 4.06 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] = 2.62 y[1] (closed_form) = -1.935847490726653 y[1] (numeric) = -1.935847490690765 absolute error = 3.588773722640326e-11 relative error = 1.853851473234196e-09 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 11 h = 0.06000000000000001 Radius of convergence (given) for eq 1 = 4.12 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] = 2.68 y[1] (closed_form) = -1.791266658974353 y[1] (numeric) = -1.791266658922762 absolute error = 5.15909537313064e-11 relative error = 2.880138111923908e-09 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 11 h = 0.06000000000000001 Radius of convergence (given) for eq 1 = 4.18 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] = 2.74 y[1] (closed_form) = -1.648746431902339 y[1] (numeric) = -1.648746431836347 absolute error = 6.599187862832423e-11 relative error = 4.002548684953464e-09 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 11 h = 0.06000000000000001 Radius of convergence (given) for eq 1 = 4.24 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) = -1.508228897345835 y[1] (numeric) = -1.508228897266621 absolute error = 7.921463485160984e-11 relative error = 5.252162651903229e-09 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 11 h = 0.06000000000000001 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] = 2.86 y[1] (closed_form) = -1.369658550731573 y[1] (numeric) = -1.369658550640203 absolute error = 9.137024470362576e-11 relative error = 6.671023566773073e-09 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 11 h = 0.06000000000000001 Radius of convergence (given) for eq 1 = 4.36 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] = 2.92 y[1] (closed_form) = -1.232982163444935 y[1] (numeric) = -1.232982163342377 absolute error = 1.025577400781685e-10 relative error = 8.317860802756762e-09 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 11 h = 0.06000000000000001 Radius of convergence (given) for eq 1 = 4.42 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] = 2.98 y[1] (closed_form) = -1.098148660072064 y[1] (numeric) = -1.098148659959198 absolute error = 1.12866382906418e-10 relative error = 1.027787830647732e-08 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 10 h = 0.06000000000000001 Radius of convergence (given) for eq 1 = 4.48 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] = 3.04 y[1] (closed_form) = -0.965109003808436 y[1] (numeric) = -0.9651090036860609 absolute error = 1.223751100454251e-10 relative error = 1.267992626351202e-08 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 10 h = 0.06000000000000001 Radius of convergence (given) for eq 1 = 4.54 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 = 10 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 110 %