##############ECHO OF PROBLEM################# ##############temp/sing2postode.ode################# diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=20; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=-2.0; x_end=-1.5; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_iter=100; /* # 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]=1.0; /* # Order */ array_given_ord_poles[1][1]=1.0; /* # 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(arctan(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 = 0.5 estimated_steps = 500000 step_error = 2e-16 est_needed_step_err = 2e-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 = 1.450574160593344e-103 estimated_step_error = 1.450574160593344e-103 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 = 9.506485024763502e-99 estimated_step_error = 9.506485024763502e-99 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 = 6.230172917146513e-94 estimated_step_error = 6.230172917146513e-94 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 = 4.083009912693051e-89 estimated_step_error = 4.083009912693051e-89 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 = 2.675846343644817e-84 estimated_step_error = 2.675846343644817e-84 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 = 1.753649170490209e-79 estimated_step_error = 1.753649170490209e-79 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 = 1.149280054178545e-74 estimated_step_error = 1.149280054178545e-74 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 = 7.532033619367402e-70 estimated_step_error = 7.532033619367402e-70 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 = 4.936340170324363e-65 estimated_step_error = 4.936340170324363e-65 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 = 3.23527208230291e-60 estimated_step_error = 3.23527208230291e-60 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 = 2.120519852904889e-55 estimated_step_error = 2.120519852904889e-55 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 = 1.390034209407698e-50 estimated_step_error = 1.390034209407698e-50 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 = 9.11406022249457e-46 estimated_step_error = 9.11406022249457e-46 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 = 5.978675072587399e-41 estimated_step_error = 5.978675072587399e-41 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 = 3.925652381455763e-36 estimated_step_error = 3.925652381455763e-36 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 = 2.582548449662719e-31 estimated_step_error = 2.582548449662719e-31 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 = 1.705504046989834e-26 estimated_step_error = 1.705504046989834e-26 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 = 1.135071642510307e-21 estimated_step_error = 1.135071642510307e-21 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = -2 y[1] (analytic) = -1.10714871779409 y[1] (numeric) = -1.10714871779409 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 2.236 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.236 Order of pole (six term test) = -1.084e-13 TOP MAIN SOLVE Loop x[1] = -1.9 y[1] (analytic) = -1.086318397757873 y[1] (numeric) = -1.086318397757873 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 2.147 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.147 Order of pole (six term test) = -5.329e-15 TOP MAIN SOLVE Loop x[1] = -1.8 y[1] (analytic) = -1.06369782240256 y[1] (numeric) = -1.06369782240256 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 2.059 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.059 Order of pole (six term test) = 8.171e-14 TOP MAIN SOLVE Loop x[1] = -1.7 y[1] (analytic) = -1.039072259536091 y[1] (numeric) = -1.039072259536091 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 1.972 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.972 Order of pole (six term test) = 1.101e-13 TOP MAIN SOLVE Loop x[1] = -1.6 y[1] (analytic) = -1.012197011451334 y[1] (numeric) = -1.012197011451334 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 1.887 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.887 Order of pole (six term test) = 1.297e-13 Finished! diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ; 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 = 120 %