##############ECHO OF PROBLEM################# ##############temp/sing5postode.ode################# diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=20; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=-1.0; x_end=-0.7; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_iter=100; glob_max_h=0.5; /* # Not Given = 0 */ /* # No Pole = 3 */ /* # Pole = 4 */ glob_type_given_pole=4; /* # Real Part */ array_given_rad_poles[1][1]=0.0; /* # Imag Part */ array_given_rad_poles[1][2]=0.0; /* # Order */ array_given_ord_poles[1][1]=4.0; /* # Not Used */ array_given_ord_poles[1][2]=0.0; /* 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_y (double x) { return(1.0/x/x/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 = 0.3 estimated_steps = 300000.0000000001 step_error = 3.333333333333333e-16 est_needed_step_err = 3.333333333333333e-16 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.562503088236751e-96 estimated_step_error = 6.562503088236751e-96 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 = 4.300804047815587e-91 estimated_step_error = 4.300804047815587e-91 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 = 2.818577593557857e-86 estimated_step_error = 2.818577593557857e-86 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 = 1.84718648877761e-81 estimated_step_error = 1.84718648877761e-81 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 = 1.210576694767835e-76 estimated_step_error = 1.210576694767835e-76 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 = 7.933695163342623e-72 estimated_step_error = 7.933695163342623e-72 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 = 5.199504761864128e-67 estimated_step_error = 5.199504761864128e-67 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 = 3.407650074260134e-62 estimated_step_error = 3.407650074260134e-62 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 = 2.233372088676544e-57 estimated_step_error = 2.233372088676544e-57 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 = 1.463839103043679e-52 estimated_step_error = 1.463839103043679e-52 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 = 9.595728513874726e-48 estimated_step_error = 9.595728513874726e-48 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 = 6.291689965187279e-43 estimated_step_error = 6.291689965187279e-43 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 = 4.127303536344029e-38 estimated_step_error = 4.127303536344029e-38 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 = 2.710103506895254e-33 estimated_step_error = 2.710103506895254e-33 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 = 1.782993138358322e-28 estimated_step_error = 1.782993138358322e-28 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 = 1.177649712997481e-23 estimated_step_error = 1.177649712997481e-23 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 = 7.84046077726719e-19 estimated_step_error = 7.84046077726719e-19 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 = 5.306168743950719e-14 estimated_step_error = 5.306168743950719e-14 best_h = 0.065536 START of Soultion TOP MAIN SOLVE Loop x[1] = -1 y[1] (analytic) = -1 y[1] (numeric) = -1 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.065536 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1 Order of pole (three term test) = 18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8689279999999999 y[1] (analytic) = -1.524223397812678 y[1] (numeric) = -1.524220673854956 absolute error = 2.72395772227263e-06 relative error = 0.0001787111867054146 % Correct digits = 6 h = 0.065536 Radius of convergence (given) for eq 1 = 0.8689 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8689 Order of pole (three term test) = 18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7378559999999998 y[1] (analytic) = -2.489345404397779 y[1] (numeric) = -2.489332158156209 absolute error = 1.324624156939791e-05 relative error = 0.0005321174613212198 % Correct digits = 6 h = 0.065536 Radius of convergence (given) for eq 1 = 0.7379 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7379 Order of pole (three term test) = 18 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ; Iterations = 5 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 131.1 %