##############ECHO OF PROBLEM################# ##############temp/sing4postode.ode################# diff ( y , x , 1 ) = m1 * 2.0 * x / ( x * x + 1.0 ) / ( x * x + 1.0 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(-2.0); x_end=c(-1.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_h=c(0.1); 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(c(1.0) / (c(x) * c( x) + c(1.0))); } /* 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 = 1 estimated_steps = 1000 step_error = 1.05409255338946e-11 est_needed_step_err = 1.05409255338946e-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) = 0.2 y[1] (numeric) = 0.2 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 = 2.236 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 TOP MAIN SOLVE Loop x[1] = -1.95 y[1] (closed_form) = 0.2082248828735034 y[1] (numeric) = 0.2082248828735034 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 = 2.191 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) = 1 TOP MAIN SOLVE Loop x[1] = -1.9 y[1] (closed_form) = 0.2169197396963124 y[1] (numeric) = 0.2169197396963124 absolute error = 2.775557561562891e-17 relative error = 1.279532035880493e-14 % Desired digits = 8 Estimated correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = -1.85 y[1] (closed_form) = 0.2261164499717355 y[1] (numeric) = 0.2261164499717354 absolute error = 2.775557561562891e-17 relative error = 1.227490331601189e-14 % Desired digits = 8 Estimated correct digits = 13 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) = 1 TOP MAIN SOLVE Loop x[1] = -1.8 y[1] (closed_form) = 0.2358490566037736 y[1] (numeric) = 0.2358490566037736 absolute error = 2.775557561562891e-17 relative error = 1.176836406102666e-14 % 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) = 1 TOP MAIN SOLVE Loop x[1] = -1.75 y[1] (closed_form) = 0.2461538461538462 y[1] (numeric) = 0.2461538461538462 absolute error = 2.775557561562891e-17 relative error = 1.127570259384924e-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) = 1 TOP MAIN SOLVE Loop x[1] = -1.7 y[1] (closed_form) = 0.2570694087403599 y[1] (numeric) = 0.2570694087403599 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 TOP MAIN SOLVE Loop x[1] = -1.65 y[1] (closed_form) = 0.2686366689053057 y[1] (numeric) = 0.2686366689053056 absolute error = 5.551115123125783e-17 relative error = 2.066402604583572e-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 TOP MAIN SOLVE Loop x[1] = -1.6 y[1] (closed_form) = 0.2808988764044945 y[1] (numeric) = 0.2808988764044945 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 = 1.887 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 TOP MAIN SOLVE Loop x[1] = -1.55 y[1] (closed_form) = 0.2939015429831007 y[1] (numeric) = 0.2939015429831007 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 = 1.845 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) = 1 TOP MAIN SOLVE Loop x[1] = -1.5 y[1] (closed_form) = 0.3076923076923078 y[1] (numeric) = 0.3076923076923078 absolute error = 5.551115123125783e-17 relative error = 1.804112415015879e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 1.803 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 = 1.803 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.45 y[1] (closed_form) = 0.3223207091055602 y[1] (numeric) = 0.3223207091055601 absolute error = 5.551115123125783e-17 relative error = 1.722233466949773e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 1.761 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 = 1.761 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.399999999999999 y[1] (closed_form) = 0.3378378378378381 y[1] (numeric) = 0.3378378378378379 absolute error = 1.110223024625157e-16 relative error = 3.286260152890461e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 1.72 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 = 1.72 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.349999999999999 y[1] (closed_form) = 0.3542958370239151 y[1] (numeric) = 0.3542958370239151 absolute error = 5.551115123125783e-17 relative error = 1.566802243502251e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 1.68 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 = 1.68 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.299999999999999 y[1] (closed_form) = 0.371747211895911 y[1] (numeric) = 0.3717472118959109 absolute error = 5.551115123125783e-17 relative error = 1.493249968120835e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 1.64 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 = 1.64 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.249999999999999 y[1] (closed_form) = 0.3902439024390247 y[1] (numeric) = 0.3902439024390245 absolute error = 1.665334536937735e-16 relative error = 4.267419750902942e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 1.601 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 = 1.601 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.199999999999999 y[1] (closed_form) = 0.4098360655737707 y[1] (numeric) = 0.4098360655737706 absolute error = 1.110223024625157e-16 relative error = 2.70894418008538e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 1.562 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 = 1.562 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.149999999999999 y[1] (closed_form) = 0.4305705059203448 y[1] (numeric) = 0.4305705059203446 absolute error = 2.775557561562891e-16 relative error = 6.446232436729809e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 1.524 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 = 1.524 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.099999999999999 y[1] (closed_form) = 0.4524886877828058 y[1] (numeric) = 0.4524886877828055 absolute error = 2.775557561562891e-16 relative error = 6.133982211053985e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 1.487 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 = 1.487 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.049999999999999 y[1] (closed_form) = 0.4756242568370991 y[1] (numeric) = 0.4756242568370989 absolute error = 2.220446049250313e-16 relative error = 4.668487818548779e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 1.45 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 = 1.45 Order of pole (six term test) = 1 Finished! diff ( y , x , 1 ) = m1 * 2.0 * x / ( x * x + 1.0 ) / ( x * x + 1.0 ) ; Iterations = 20 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 5 Minutes 0.0 Seconds Percent Done = 105 %