##############ECHO OF PROBLEM################# ##############temp/sing2postode.ode################# diff ( y , x , 1 ) = 1.0 / ( x * x + 1.0 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=16; max_terms=20; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(-2.0); x_end=c(-1.5); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_h=c(0.001); glob_min_h=c(0.001); glob_type_given_pole=2; array_given_rad_poles[1][1]=c(0.0); array_given_rad_poles[1][2]=c(1.0); array_given_ord_poles[1][1]=c(1.0); array_given_ord_poles[1][2]=c(0.0); /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=8; glob_max_minutes=(5.0); glob_subiter_method=3; glob_max_iter=1000; glob_upper_ratio_limit=c(1.1); glob_lower_ratio_limit=c(0.9); /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(arctan(c(x))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 8 estimated_h = 0.001 estimated_answer = 1 desired_abs_gbl_error = 1e-08 range = 0.5 estimated_steps = 500 step_error = 2.23606797749979e-11 est_needed_step_err = 2.23606797749979e-11 opt_iter = 1 SETTING H FOR MIN H SETTING H FOR DISPLAY INTERVAL START of Soultion TOP MAIN SOLVE Loop x[1] = -2 y[1] (closed_form) = -1.10714871779409 y[1] (numeric) = -1.10714871779409 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.05 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) = -1.155e-14 TOP MAIN SOLVE Loop x[1] = -1.95 y[1] (closed_form) = -1.096944990300136 y[1] (numeric) = -1.096944990300136 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 2.191 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 = 2.191 Order of pole (six term test) = -2.141e-13 TOP MAIN SOLVE Loop x[1] = -1.9 y[1] (closed_form) = -1.086318397757873 y[1] (numeric) = -1.086318397757873 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.05 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) = -1.332e-14 TOP MAIN SOLVE Loop x[1] = -1.85 y[1] (closed_form) = -1.075244653309068 y[1] (numeric) = -1.075244653309068 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 2.103 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 = 2.103 Order of pole (six term test) = -3.642e-14 TOP MAIN SOLVE Loop x[1] = -1.8 y[1] (closed_form) = -1.06369782240256 y[1] (numeric) = -1.06369782240256 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 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) = -6.661e-14 TOP MAIN SOLVE Loop x[1] = -1.75 y[1] (closed_form) = -1.051650212548374 y[1] (numeric) = -1.051650212548374 absolute error = 2.220446049250313e-16 relative error = 2.111392193674071e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 2.016 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 = 2.016 Order of pole (six term test) = -2.132e-14 TOP MAIN SOLVE Loop x[1] = -1.7 y[1] (closed_form) = -1.039072259536091 y[1] (numeric) = -1.039072259536091 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 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) = 1.155e-14 TOP MAIN SOLVE Loop x[1] = -1.65 y[1] (closed_form) = -1.025932411343353 y[1] (numeric) = -1.025932411343353 absolute error = 2.220446049250313e-16 relative error = 2.164320012409851e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 1.929 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 = 1.929 Order of pole (six term test) = 1.599e-14 TOP MAIN SOLVE Loop x[1] = -1.6 y[1] (closed_form) = -1.012197011451334 y[1] (numeric) = -1.012197011451334 absolute error = 2.220446049250313e-16 relative error = 2.193689592173896e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 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) = 7.105e-15 TOP MAIN SOLVE Loop x[1] = -1.55 y[1] (closed_form) = -0.9978301839061904 y[1] (numeric) = -0.9978301839061906 absolute error = 2.220446049250313e-16 relative error = 2.225274485642404e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 1.845 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 = 1.845 Order of pole (six term test) = -8.882e-15 Finished! diff ( y , x , 1 ) = 1.0 / ( x * x + 1.0 ) ; Iterations = 10 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 5 Minutes 0.0 Seconds Percent Done = 110 %