##############ECHO OF PROBLEM################# ##############temp/tanh_sqrtpostode.ode################# diff ( y , x , 1 ) = tanh ( sqrt ( 2.0 * x + 3.0 ) ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=c(0.1); x_end=c(5.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_h=0.1; glob_type_given_pole=1; array_given_rad_poles[1][1]=c(-1.5); array_given_rad_poles[1][2]=c(0.0); array_given_ord_poles[1][1]=c(0.5); array_given_ord_poles[1][2]=c(0.0); // END SECOND INPUT BLOCK // BEGIN OVERRIDE BLOCK glob_desired_digits_correct=8; glob_max_minutes=(3.0); glob_subiter_method=3; glob_max_iter=100000; glob_upper_ratio_limit=c(1.000001); glob_lower_ratio_limit=c(0.999999); glob_look_poles=true; glob_h=c(0.001); glob_display_interval=c(0.01); // END OVERRIDE BLOCK ! // BEGIN USER DEF BLOCK double exact_soln_y (double x) { return(c(0.0)); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 0 y[1] (numeric) = 0 absolute error = 0 relative error = -1 % Desired digits = 8 Estimated correct digits = -16 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.6 Order of pole (given) = 0.5 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] = 0.11 y[1] (closed_form) = 0 y[1] (numeric) = 0.009459044391666397 absolute error = 0.009459044391666397 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.61 Order of pole (given) = 0.5 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] = 0.12 y[1] (closed_form) = 0 y[1] (numeric) = 0.0189239250703097 absolute error = 0.0189239250703097 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.62 Order of pole (given) = 0.5 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] = 0.13 y[1] (closed_form) = 0 y[1] (numeric) = 0.0283945630182302 absolute error = 0.0283945630182302 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.63 Order of pole (given) = 0.5 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] = 0.14 y[1] (closed_form) = 0 y[1] (numeric) = 0.03787088054398797 absolute error = 0.03787088054398797 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.64 Order of pole (given) = 0.5 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] = 0.15 y[1] (closed_form) = 0 y[1] (numeric) = 0.04735280125525821 absolute error = 0.04735280125525821 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.65 Order of pole (given) = 0.5 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] = 0.1600000000000001 y[1] (closed_form) = 0 y[1] (numeric) = 0.05684025003235239 absolute error = 0.05684025003235239 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.66 Order of pole (given) = 0.5 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] = 0.1700000000000001 y[1] (closed_form) = 0 y[1] (numeric) = 0.06633315300238578 absolute error = 0.06633315300238578 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.67 Order of pole (given) = 0.5 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] = 0.1800000000000001 y[1] (closed_form) = 0 y[1] (numeric) = 0.07583143751407287 absolute error = 0.07583143751407287 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.68 Order of pole (given) = 0.5 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] = 0.1900000000000001 y[1] (closed_form) = 0 y[1] (numeric) = 0.08533503211313286 absolute error = 0.08533503211313286 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.69 Order of pole (given) = 0.5 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] = 0.2000000000000001 y[1] (closed_form) = 0 y[1] (numeric) = 0.09484386651828737 absolute error = 0.09484386651828737 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.7 Order of pole (given) = 0.5 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] = 0.2100000000000001 y[1] (closed_form) = 0 y[1] (numeric) = 0.1043578715978342 absolute error = 0.1043578715978342 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.71 Order of pole (given) = 0.5 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] = 0.2200000000000001 y[1] (closed_form) = 0 y[1] (numeric) = 0.1138769793467804 absolute error = 0.1138769793467804 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.72 Order of pole (given) = 0.5 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] = 0.2300000000000001 y[1] (closed_form) = 0 y[1] (numeric) = 0.1234011228645188 absolute error = 0.1234011228645188 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.73 Order of pole (given) = 0.5 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] = 0.2400000000000001 y[1] (closed_form) = 0 y[1] (numeric) = 0.132930236333034 absolute error = 0.132930236333034 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.74 Order of pole (given) = 0.5 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] = 0.2500000000000001 y[1] (closed_form) = 0 y[1] (numeric) = 0.1424642549956209 absolute error = 0.1424642549956209 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.75 Order of pole (given) = 0.5 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] = 0.2600000000000001 y[1] (closed_form) = 0 y[1] (numeric) = 0.1520031151361038 absolute error = 0.1520031151361038 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.76 Order of pole (given) = 0.5 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] = 0.2700000000000001 y[1] (closed_form) = 0 y[1] (numeric) = 0.161546754058541 absolute error = 0.161546754058541 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.77 Order of pole (given) = 0.5 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] = 0.2800000000000001 y[1] (closed_form) = 0 y[1] (numeric) = 0.1710951100674021 absolute error = 0.1710951100674021 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.78 Order of pole (given) = 0.5 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] = 0.2900000000000001 y[1] (closed_form) = 0 y[1] (numeric) = 0.1806481224482039 absolute error = 0.1806481224482039 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.79 Order of pole (given) = 0.5 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] = 0.3000000000000002 y[1] (closed_form) = 0 y[1] (numeric) = 0.1902057314485947 absolute error = 0.1902057314485947 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.8 Order of pole (given) = 0.5 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] = 0.3100000000000002 y[1] (closed_form) = 0 y[1] (numeric) = 0.1997678782598726 absolute error = 0.1997678782598726 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.81 Order of pole (given) = 0.5 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] = 0.3200000000000002 y[1] (closed_form) = 0 y[1] (numeric) = 0.2093345049989275 absolute error = 0.2093345049989275 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.82 Order of pole (given) = 0.5 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] = 0.3300000000000002 y[1] (closed_form) = 0 y[1] (numeric) = 0.2189055546905941 absolute error = 0.2189055546905941 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.83 Order of pole (given) = 0.5 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] = 0.3400000000000002 y[1] (closed_form) = 0 y[1] (numeric) = 0.228480971250407 absolute error = 0.228480971250407 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.84 Order of pole (given) = 0.5 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] = 0.3500000000000002 y[1] (closed_form) = 0 y[1] (numeric) = 0.2380606994677444 absolute error = 0.2380606994677444 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.85 Order of pole (given) = 0.5 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] = 0.3600000000000002 y[1] (closed_form) = 0 y[1] (numeric) = 0.2476446849893533 absolute error = 0.2476446849893533 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.86 Order of pole (given) = 0.5 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] = 0.3700000000000002 y[1] (closed_form) = 0 y[1] (numeric) = 0.2572328743032428 absolute error = 0.2572328743032428 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.87 Order of pole (given) = 0.5 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] = 0.3800000000000002 y[1] (closed_form) = 0 y[1] (numeric) = 0.2668252147229385 absolute error = 0.2668252147229385 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.88 Order of pole (given) = 0.5 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] = 0.3900000000000002 y[1] (closed_form) = 0 y[1] (numeric) = 0.2764216543720871 absolute error = 0.2764216543720871 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.89 Order of pole (given) = 0.5 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] = 0.4000000000000002 y[1] (closed_form) = 0 y[1] (numeric) = 0.2860221421694024 absolute error = 0.2860221421694024 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.9 Order of pole (given) = 0.5 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] = 0.4100000000000003 y[1] (closed_form) = 0 y[1] (numeric) = 0.2956266278139443 absolute error = 0.2956266278139443 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.91 Order of pole (given) = 0.5 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] = 0.4200000000000003 y[1] (closed_form) = 0 y[1] (numeric) = 0.3052350617707214 absolute error = 0.3052350617707214 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.92 Order of pole (given) = 0.5 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] = 0.4300000000000003 y[1] (closed_form) = 0 y[1] (numeric) = 0.3148473952566094 absolute error = 0.3148473952566094 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.93 Order of pole (given) = 0.5 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] = 0.4400000000000003 y[1] (closed_form) = 0 y[1] (numeric) = 0.3244635802265766 absolute error = 0.3244635802265766 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.94 Order of pole (given) = 0.5 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] = 0.4500000000000003 y[1] (closed_form) = 0 y[1] (numeric) = 0.3340835693602101 absolute error = 0.3340835693602101 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.95 Order of pole (given) = 0.5 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] = 0.4600000000000003 y[1] (closed_form) = 0 y[1] (numeric) = 0.3437073160485332 absolute error = 0.3437073160485332 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.96 Order of pole (given) = 0.5 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] = 0.4700000000000003 y[1] (closed_form) = 0 y[1] (numeric) = 0.3533347743811078 absolute error = 0.3533347743811078 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.97 Order of pole (given) = 0.5 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] = 0.4800000000000003 y[1] (closed_form) = 0 y[1] (numeric) = 0.362965899133414 absolute error = 0.362965899133414 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.98 Order of pole (given) = 0.5 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] = 0.4900000000000003 y[1] (closed_form) = 0 y[1] (numeric) = 0.3726006457545009 absolute error = 0.3726006457545009 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.99 Order of pole (given) = 0.5 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] = 0.5000000000000003 y[1] (closed_form) = 0 y[1] (numeric) = 0.3822389703549 absolute error = 0.3822389703549 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 0.5 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] = 0.5100000000000003 y[1] (closed_form) = 0 y[1] (numeric) = 0.3918808296947969 absolute error = 0.3918808296947969 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.01 Order of pole (given) = 0.5 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] = 0.5200000000000004 y[1] (closed_form) = 0 y[1] (numeric) = 0.4015261811724533 absolute error = 0.4015261811724533 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.02 Order of pole (given) = 0.5 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] = 0.5300000000000004 y[1] (closed_form) = 0 y[1] (numeric) = 0.4111749828128731 absolute error = 0.4111749828128731 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.03 Order of pole (given) = 0.5 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] = 0.5400000000000004 y[1] (closed_form) = 0 y[1] (numeric) = 0.4208271932567079 absolute error = 0.4208271932567079 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.04 Order of pole (given) = 0.5 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] = 0.5500000000000004 y[1] (closed_form) = 0 y[1] (numeric) = 0.4304827717493944 absolute error = 0.4304827717493944 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.05 Order of pole (given) = 0.5 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] = 0.5600000000000004 y[1] (closed_form) = 0 y[1] (numeric) = 0.440141678130519 absolute error = 0.440141678130519 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.06 Order of pole (given) = 0.5 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] = 0.5700000000000004 y[1] (closed_form) = 0 y[1] (numeric) = 0.4498038728234046 absolute error = 0.4498038728234046 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.07 Order of pole (given) = 0.5 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] = 0.5800000000000004 y[1] (closed_form) = 0 y[1] (numeric) = 0.4594693168249118 absolute error = 0.4594693168249118 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.08 Order of pole (given) = 0.5 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] = 0.5900000000000004 y[1] (closed_form) = 0 y[1] (numeric) = 0.4691379716954528 absolute error = 0.4691379716954528 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.09 Order of pole (given) = 0.5 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] = 0.6000000000000004 y[1] (closed_form) = 0 y[1] (numeric) = 0.4788097995492097 absolute error = 0.4788097995492097 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.1 Order of pole (given) = 0.5 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] = 0.6100000000000004 y[1] (closed_form) = 0 y[1] (numeric) = 0.4884847630445539 absolute error = 0.4884847630445539 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.11 Order of pole (given) = 0.5 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] = 0.6200000000000004 y[1] (closed_form) = 0 y[1] (numeric) = 0.4981628253746626 absolute error = 0.4981628253746626 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.12 Order of pole (given) = 0.5 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] = 0.6300000000000004 y[1] (closed_form) = 0 y[1] (numeric) = 0.5078439502583247 absolute error = 0.5078439502583247 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.13 Order of pole (given) = 0.5 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] = 0.6400000000000005 y[1] (closed_form) = 0 y[1] (numeric) = 0.5175281019309348 absolute error = 0.5175281019309348 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.14 Order of pole (given) = 0.5 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] = 0.6500000000000005 y[1] (closed_form) = 0 y[1] (numeric) = 0.5272152451356701 absolute error = 0.5272152451356701 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.15 Order of pole (given) = 0.5 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] = 0.6600000000000005 y[1] (closed_form) = 0 y[1] (numeric) = 0.5369053451148431 absolute error = 0.5369053451148431 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.16 Order of pole (given) = 0.5 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] = 0.6700000000000005 y[1] (closed_form) = 0 y[1] (numeric) = 0.546598367601431 absolute error = 0.546598367601431 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.17 Order of pole (given) = 0.5 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] = 0.6800000000000005 y[1] (closed_form) = 0 y[1] (numeric) = 0.5562942788107733 absolute error = 0.5562942788107733 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.18 Order of pole (given) = 0.5 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] = 0.6900000000000005 y[1] (closed_form) = 0 y[1] (numeric) = 0.565993045432435 absolute error = 0.565993045432435 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.19 Order of pole (given) = 0.5 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] = 0.7000000000000005 y[1] (closed_form) = 0 y[1] (numeric) = 0.5756946346222322 absolute error = 0.5756946346222322 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.2 Order of pole (given) = 0.5 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] = 0.7100000000000005 y[1] (closed_form) = 0 y[1] (numeric) = 0.5853990139944175 absolute error = 0.5853990139944175 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.21 Order of pole (given) = 0.5 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] = 0.7200000000000005 y[1] (closed_form) = 0 y[1] (numeric) = 0.5951061516140168 absolute error = 0.5951061516140168 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.22 Order of pole (given) = 0.5 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] = 0.7300000000000005 y[1] (closed_form) = 0 y[1] (numeric) = 0.6048160159893199 absolute error = 0.6048160159893199 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.23 Order of pole (given) = 0.5 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] = 0.7400000000000005 y[1] (closed_form) = 0 y[1] (numeric) = 0.6145285760645177 absolute error = 0.6145285760645177 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.24 Order of pole (given) = 0.5 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] = 0.7500000000000006 y[1] (closed_form) = 0 y[1] (numeric) = 0.624243801212483 absolute error = 0.624243801212483 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.25 Order of pole (given) = 0.5 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] = 0.7600000000000006 y[1] (closed_form) = 0 y[1] (numeric) = 0.6339616612276933 absolute error = 0.6339616612276933 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.26 Order of pole (given) = 0.5 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] = 0.7700000000000006 y[1] (closed_form) = 0 y[1] (numeric) = 0.6436821263192913 absolute error = 0.6436821263192913 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.27 Order of pole (given) = 0.5 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] = 0.7800000000000006 y[1] (closed_form) = 0 y[1] (numeric) = 0.6534051671042787 absolute error = 0.6534051671042787 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.28 Order of pole (given) = 0.5 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] = 0.7900000000000006 y[1] (closed_form) = 0 y[1] (numeric) = 0.6631307546008425 absolute error = 0.6631307546008425 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.29 Order of pole (given) = 0.5 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] = 0.8000000000000006 y[1] (closed_form) = 0 y[1] (numeric) = 0.6728588602218111 absolute error = 0.6728588602218111 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.3 Order of pole (given) = 0.5 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] = 0.8100000000000006 y[1] (closed_form) = 0 y[1] (numeric) = 0.6825894557682327 absolute error = 0.6825894557682327 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.31 Order of pole (given) = 0.5 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] = 0.8200000000000006 y[1] (closed_form) = 0 y[1] (numeric) = 0.6923225134230814 absolute error = 0.6923225134230814 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.32 Order of pole (given) = 0.5 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] = 0.8300000000000006 y[1] (closed_form) = 0 y[1] (numeric) = 0.7020580057450787 absolute error = 0.7020580057450787 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.33 Order of pole (given) = 0.5 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] = 0.8400000000000006 y[1] (closed_form) = 0 y[1] (numeric) = 0.711795905662637 absolute error = 0.711795905662637 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.34 Order of pole (given) = 0.5 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] = 0.8500000000000006 y[1] (closed_form) = 0 y[1] (numeric) = 0.721536186467914 absolute error = 0.721536186467914 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.35 Order of pole (given) = 0.5 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] = 0.8600000000000007 y[1] (closed_form) = 0 y[1] (numeric) = 0.7312788218109821 absolute error = 0.7312788218109821 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.36 Order of pole (given) = 0.5 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] = 0.8700000000000007 y[1] (closed_form) = 0 y[1] (numeric) = 0.7410237856941079 absolute error = 0.7410237856941079 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.37 Order of pole (given) = 0.5 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] = 0.8800000000000007 y[1] (closed_form) = 0 y[1] (numeric) = 0.7507710524661368 absolute error = 0.7507710524661368 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.38 Order of pole (given) = 0.5 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] = 0.8900000000000007 y[1] (closed_form) = 0 y[1] (numeric) = 0.7605205968169856 absolute error = 0.7605205968169856 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.39 Order of pole (given) = 0.5 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] = 0.9000000000000007 y[1] (closed_form) = 0 y[1] (numeric) = 0.7702723937722362 absolute error = 0.7702723937722362 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.4 Order of pole (given) = 0.5 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] = 0.9100000000000007 y[1] (closed_form) = 0 y[1] (numeric) = 0.7800264186878312 absolute error = 0.7800264186878312 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.41 Order of pole (given) = 0.5 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] = 0.9200000000000007 y[1] (closed_form) = 0 y[1] (numeric) = 0.789782647244867 absolute error = 0.789782647244867 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.42 Order of pole (given) = 0.5 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] = 0.9300000000000007 y[1] (closed_form) = 0 y[1] (numeric) = 0.7995410554444836 absolute error = 0.7995410554444836 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.43 Order of pole (given) = 0.5 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] = 0.9400000000000007 y[1] (closed_form) = 0 y[1] (numeric) = 0.8093016196028496 absolute error = 0.8093016196028496 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.44 Order of pole (given) = 0.5 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] = 0.9500000000000007 y[1] (closed_form) = 0 y[1] (numeric) = 0.8190643163462376 absolute error = 0.8190643163462376 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.45 Order of pole (given) = 0.5 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] = 0.9600000000000007 y[1] (closed_form) = 0 y[1] (numeric) = 0.8288291226061921 absolute error = 0.8288291226061921 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.46 Order of pole (given) = 0.5 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] = 0.9700000000000008 y[1] (closed_form) = 0 y[1] (numeric) = 0.8385960156147848 absolute error = 0.8385960156147848 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.47 Order of pole (given) = 0.5 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] = 0.9800000000000008 y[1] (closed_form) = 0 y[1] (numeric) = 0.848364972899956 absolute error = 0.848364972899956 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.48 Order of pole (given) = 0.5 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] = 0.9900000000000008 y[1] (closed_form) = 0 y[1] (numeric) = 0.8581359722809418 absolute error = 0.8581359722809418 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.49 Order of pole (given) = 0.5 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] = 1.000000000000001 y[1] (closed_form) = 0 y[1] (numeric) = 0.8679089918637827 absolute error = 0.8679089918637827 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.5 Order of pole (given) = 0.5 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] = 1.01 y[1] (closed_form) = 0 y[1] (numeric) = 0.8776840100369152 absolute error = 0.8776840100369152 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.51 Order of pole (given) = 0.5 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] = 1.019999999999998 y[1] (closed_form) = 0 y[1] (numeric) = 0.8874610054668418 absolute error = 0.8874610054668418 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.52 Order of pole (given) = 0.5 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] = 1.029999999999997 y[1] (closed_form) = 0 y[1] (numeric) = 0.8972399570938794 absolute error = 0.8972399570938794 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.53 Order of pole (given) = 0.5 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] = 1.039999999999996 y[1] (closed_form) = 0 y[1] (numeric) = 0.907020844127983 absolute error = 0.907020844127983 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.54 Order of pole (given) = 0.5 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] = 1.049999999999995 y[1] (closed_form) = 0 y[1] (numeric) = 0.9168036460446453 absolute error = 0.9168036460446453 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.55 Order of pole (given) = 0.5 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] = 1.059999999999994 y[1] (closed_form) = 0 y[1] (numeric) = 0.9265883425808681 absolute error = 0.9265883425808681 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.56 Order of pole (given) = 0.5 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] = 1.069999999999993 y[1] (closed_form) = 0 y[1] (numeric) = 0.9363749137312066 absolute error = 0.9363749137312066 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.57 Order of pole (given) = 0.5 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] = 1.079999999999992 y[1] (closed_form) = 0 y[1] (numeric) = 0.946163339743883 absolute error = 0.946163339743883 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.58 Order of pole (given) = 0.5 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] = 1.089999999999991 y[1] (closed_form) = 0 y[1] (numeric) = 0.9559536011169688 absolute error = 0.9559536011169688 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.59 Order of pole (given) = 0.5 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] = 1.09999999999999 y[1] (closed_form) = 0 y[1] (numeric) = 0.9657456785946346 absolute error = 0.9657456785946346 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.6 Order of pole (given) = 0.5 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] = 1.109999999999989 y[1] (closed_form) = 0 y[1] (numeric) = 0.9755395531634654 absolute error = 0.9755395531634654 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.61 Order of pole (given) = 0.5 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] = 1.119999999999987 y[1] (closed_form) = 0 y[1] (numeric) = 0.9853352060488419 absolute error = 0.9853352060488419 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.62 Order of pole (given) = 0.5 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] = 1.129999999999986 y[1] (closed_form) = 0 y[1] (numeric) = 0.9951326187113831 absolute error = 0.9951326187113831 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.63 Order of pole (given) = 0.5 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] = 1.139999999999985 y[1] (closed_form) = 0 y[1] (numeric) = 1.004931772843452 absolute error = 1.004931772843452 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.64 Order of pole (given) = 0.5 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] = 1.149999999999984 y[1] (closed_form) = 0 y[1] (numeric) = 1.014732650365721 absolute error = 1.014732650365721 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.65 Order of pole (given) = 0.5 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] = 1.159999999999983 y[1] (closed_form) = 0 y[1] (numeric) = 1.024535233423801 absolute error = 1.024535233423801 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.66 Order of pole (given) = 0.5 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] = 1.169999999999982 y[1] (closed_form) = 0 y[1] (numeric) = 1.034339504384919 absolute error = 1.034339504384919 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.67 Order of pole (given) = 0.5 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] = 1.179999999999981 y[1] (closed_form) = 0 y[1] (numeric) = 1.044145445834667 absolute error = 1.044145445834667 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.68 Order of pole (given) = 0.5 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] = 1.18999999999998 y[1] (closed_form) = 0 y[1] (numeric) = 1.053953040573794 absolute error = 1.053953040573794 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.69 Order of pole (given) = 0.5 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] = 1.199999999999979 y[1] (closed_form) = 0 y[1] (numeric) = 1.063762271615058 absolute error = 1.063762271615058 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.7 Order of pole (given) = 0.5 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] = 1.209999999999978 y[1] (closed_form) = 0 y[1] (numeric) = 1.073573122180139 absolute error = 1.073573122180139 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.71 Order of pole (given) = 0.5 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] = 1.219999999999976 y[1] (closed_form) = 0 y[1] (numeric) = 1.083385575696588 absolute error = 1.083385575696588 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.72 Order of pole (given) = 0.5 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] = 1.229999999999975 y[1] (closed_form) = 0 y[1] (numeric) = 1.093199615794843 absolute error = 1.093199615794843 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.73 Order of pole (given) = 0.5 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] = 1.239999999999974 y[1] (closed_form) = 0 y[1] (numeric) = 1.10301522630529 absolute error = 1.10301522630529 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.74 Order of pole (given) = 0.5 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] = 1.249999999999973 y[1] (closed_form) = 0 y[1] (numeric) = 1.112832391255374 absolute error = 1.112832391255374 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.75 Order of pole (given) = 0.5 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] = 1.259999999999972 y[1] (closed_form) = 0 y[1] (numeric) = 1.122651094866757 absolute error = 1.122651094866757 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.76 Order of pole (given) = 0.5 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] = 1.269999999999971 y[1] (closed_form) = 0 y[1] (numeric) = 1.132471321552528 absolute error = 1.132471321552528 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.77 Order of pole (given) = 0.5 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] = 1.27999999999997 y[1] (closed_form) = 0 y[1] (numeric) = 1.142293055914454 absolute error = 1.142293055914454 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.78 Order of pole (given) = 0.5 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] = 1.289999999999969 y[1] (closed_form) = 0 y[1] (numeric) = 1.152116282740283 absolute error = 1.152116282740283 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.79 Order of pole (given) = 0.5 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] = 1.299999999999968 y[1] (closed_form) = 0 y[1] (numeric) = 1.16194098700109 absolute error = 1.16194098700109 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.8 Order of pole (given) = 0.5 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] = 1.309999999999967 y[1] (closed_form) = 0 y[1] (numeric) = 1.171767153848665 absolute error = 1.171767153848665 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.81 Order of pole (given) = 0.5 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] = 1.319999999999965 y[1] (closed_form) = 0 y[1] (numeric) = 1.181594768612946 absolute error = 1.181594768612946 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.82 Order of pole (given) = 0.5 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] = 1.329999999999964 y[1] (closed_form) = 0 y[1] (numeric) = 1.191423816799495 absolute error = 1.191423816799495 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.83 Order of pole (given) = 0.5 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] = 1.339999999999963 y[1] (closed_form) = 0 y[1] (numeric) = 1.201254284087017 absolute error = 1.201254284087017 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.84 Order of pole (given) = 0.5 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] = 1.349999999999962 y[1] (closed_form) = 0 y[1] (numeric) = 1.211086156324914 absolute error = 1.211086156324914 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.85 Order of pole (given) = 0.5 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] = 1.359999999999961 y[1] (closed_form) = 0 y[1] (numeric) = 1.220919419530889 absolute error = 1.220919419530889 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.86 Order of pole (given) = 0.5 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] = 1.36999999999996 y[1] (closed_form) = 0 y[1] (numeric) = 1.230754059888579 absolute error = 1.230754059888579 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.87 Order of pole (given) = 0.5 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] = 1.379999999999959 y[1] (closed_form) = 0 y[1] (numeric) = 1.240590063745233 absolute error = 1.240590063745233 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.88 Order of pole (given) = 0.5 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] = 1.389999999999958 y[1] (closed_form) = 0 y[1] (numeric) = 1.250427417609428 absolute error = 1.250427417609428 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.89 Order of pole (given) = 0.5 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] = 1.399999999999957 y[1] (closed_form) = 0 y[1] (numeric) = 1.260266108148818 absolute error = 1.260266108148818 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.9 Order of pole (given) = 0.5 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] = 1.409999999999956 y[1] (closed_form) = 0 y[1] (numeric) = 1.270106122187924 absolute error = 1.270106122187924 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.91 Order of pole (given) = 0.5 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] = 1.419999999999954 y[1] (closed_form) = 0 y[1] (numeric) = 1.279947446705956 absolute error = 1.279947446705956 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.92 Order of pole (given) = 0.5 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] = 1.429999999999953 y[1] (closed_form) = 0 y[1] (numeric) = 1.289790068834674 absolute error = 1.289790068834674 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.93 Order of pole (given) = 0.5 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] = 1.439999999999952 y[1] (closed_form) = 0 y[1] (numeric) = 1.299633975856281 absolute error = 1.299633975856281 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.94 Order of pole (given) = 0.5 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] = 1.449999999999951 y[1] (closed_form) = 0 y[1] (numeric) = 1.30947915520135 absolute error = 1.30947915520135 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.95 Order of pole (given) = 0.5 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] = 1.45999999999995 y[1] (closed_form) = 0 y[1] (numeric) = 1.319325594446785 absolute error = 1.319325594446785 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.96 Order of pole (given) = 0.5 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] = 1.469999999999949 y[1] (closed_form) = 0 y[1] (numeric) = 1.329173281313812 absolute error = 1.329173281313812 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.97 Order of pole (given) = 0.5 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] = 1.479999999999948 y[1] (closed_form) = 0 y[1] (numeric) = 1.339022203666011 absolute error = 1.339022203666011 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.98 Order of pole (given) = 0.5 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] = 1.489999999999947 y[1] (closed_form) = 0 y[1] (numeric) = 1.348872349507364 absolute error = 1.348872349507364 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.99 Order of pole (given) = 0.5 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] = 1.499999999999946 y[1] (closed_form) = 0 y[1] (numeric) = 1.35872370698035 absolute error = 1.35872370698035 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3 Order of pole (given) = 0.5 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] = 1.509999999999944 y[1] (closed_form) = 0 y[1] (numeric) = 1.368576264364058 absolute error = 1.368576264364058 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.01 Order of pole (given) = 0.5 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] = 1.519999999999943 y[1] (closed_form) = 0 y[1] (numeric) = 1.378430010072337 absolute error = 1.378430010072337 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.02 Order of pole (given) = 0.5 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] = 1.529999999999942 y[1] (closed_form) = 0 y[1] (numeric) = 1.388284932651972 absolute error = 1.388284932651972 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.03 Order of pole (given) = 0.5 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] = 1.539999999999941 y[1] (closed_form) = 0 y[1] (numeric) = 1.398141020780893 absolute error = 1.398141020780893 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.04 Order of pole (given) = 0.5 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] = 1.54999999999994 y[1] (closed_form) = 0 y[1] (numeric) = 1.407998263266402 absolute error = 1.407998263266402 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.05 Order of pole (given) = 0.5 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] = 1.559999999999939 y[1] (closed_form) = 0 y[1] (numeric) = 1.417856649043441 absolute error = 1.417856649043441 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.06 Order of pole (given) = 0.5 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] = 1.569999999999938 y[1] (closed_form) = 0 y[1] (numeric) = 1.427716167172876 absolute error = 1.427716167172876 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.07 Order of pole (given) = 0.5 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] = 1.579999999999937 y[1] (closed_form) = 0 y[1] (numeric) = 1.437576806839814 absolute error = 1.437576806839814 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.08 Order of pole (given) = 0.5 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] = 1.589999999999936 y[1] (closed_form) = 0 y[1] (numeric) = 1.447438557351947 absolute error = 1.447438557351947 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.09 Order of pole (given) = 0.5 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] = 1.599999999999935 y[1] (closed_form) = 0 y[1] (numeric) = 1.457301408137915 absolute error = 1.457301408137915 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.1 Order of pole (given) = 0.5 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] = 1.609999999999933 y[1] (closed_form) = 0 y[1] (numeric) = 1.467165348745698 absolute error = 1.467165348745698 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.11 Order of pole (given) = 0.5 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] = 1.619999999999932 y[1] (closed_form) = 0 y[1] (numeric) = 1.477030368841039 absolute error = 1.477030368841039 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.12 Order of pole (given) = 0.5 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] = 1.629999999999931 y[1] (closed_form) = 0 y[1] (numeric) = 1.48689645820588 absolute error = 1.48689645820588 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.13 Order of pole (given) = 0.5 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] = 1.63999999999993 y[1] (closed_form) = 0 y[1] (numeric) = 1.496763606736829 absolute error = 1.496763606736829 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.14 Order of pole (given) = 0.5 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] = 1.649999999999929 y[1] (closed_form) = 0 y[1] (numeric) = 1.506631804443651 absolute error = 1.506631804443651 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.15 Order of pole (given) = 0.5 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] = 1.659999999999928 y[1] (closed_form) = 0 y[1] (numeric) = 1.516501041447777 absolute error = 1.516501041447777 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.16 Order of pole (given) = 0.5 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] = 1.669999999999927 y[1] (closed_form) = 0 y[1] (numeric) = 1.526371307980843 absolute error = 1.526371307980843 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.17 Order of pole (given) = 0.5 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] = 1.679999999999926 y[1] (closed_form) = 0 y[1] (numeric) = 1.536242594383243 absolute error = 1.536242594383243 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.18 Order of pole (given) = 0.5 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] = 1.689999999999925 y[1] (closed_form) = 0 y[1] (numeric) = 1.546114891102709 absolute error = 1.546114891102709 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.19 Order of pole (given) = 0.5 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] = 1.699999999999924 y[1] (closed_form) = 0 y[1] (numeric) = 1.555988188692917 absolute error = 1.555988188692917 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.2 Order of pole (given) = 0.5 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] = 1.709999999999922 y[1] (closed_form) = 0 y[1] (numeric) = 1.5658624778121 absolute error = 1.5658624778121 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.21 Order of pole (given) = 0.5 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] = 1.719999999999921 y[1] (closed_form) = 0 y[1] (numeric) = 1.575737749221697 absolute error = 1.575737749221697 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.22 Order of pole (given) = 0.5 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] = 1.72999999999992 y[1] (closed_form) = 0 y[1] (numeric) = 1.585613993785014 absolute error = 1.585613993785014 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.23 Order of pole (given) = 0.5 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] = 1.739999999999919 y[1] (closed_form) = 0 y[1] (numeric) = 1.595491202465908 absolute error = 1.595491202465908 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.24 Order of pole (given) = 0.5 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] = 1.749999999999918 y[1] (closed_form) = 0 y[1] (numeric) = 1.605369366327488 absolute error = 1.605369366327488 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.25 Order of pole (given) = 0.5 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] = 1.759999999999917 y[1] (closed_form) = 0 y[1] (numeric) = 1.61524847653084 absolute error = 1.61524847653084 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.26 Order of pole (given) = 0.5 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] = 1.769999999999916 y[1] (closed_form) = 0 y[1] (numeric) = 1.625128524333766 absolute error = 1.625128524333766 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.27 Order of pole (given) = 0.5 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] = 1.779999999999915 y[1] (closed_form) = 0 y[1] (numeric) = 1.635009501089544 absolute error = 1.635009501089544 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.28 Order of pole (given) = 0.5 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] = 1.789999999999914 y[1] (closed_form) = 0 y[1] (numeric) = 1.644891398245709 absolute error = 1.644891398245709 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.29 Order of pole (given) = 0.5 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] = 1.799999999999913 y[1] (closed_form) = 0 y[1] (numeric) = 1.654774207342847 absolute error = 1.654774207342847 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.3 Order of pole (given) = 0.5 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] = 1.809999999999911 y[1] (closed_form) = 0 y[1] (numeric) = 1.664657920013413 absolute error = 1.664657920013413 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.31 Order of pole (given) = 0.5 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] = 1.81999999999991 y[1] (closed_form) = 0 y[1] (numeric) = 1.674542527980556 absolute error = 1.674542527980556 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.32 Order of pole (given) = 0.5 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] = 1.829999999999909 y[1] (closed_form) = 0 y[1] (numeric) = 1.684428023056977 absolute error = 1.684428023056977 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.33 Order of pole (given) = 0.5 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] = 1.839999999999908 y[1] (closed_form) = 0 y[1] (numeric) = 1.694314397143788 absolute error = 1.694314397143788 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.34 Order of pole (given) = 0.5 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] = 1.849999999999907 y[1] (closed_form) = 0 y[1] (numeric) = 1.704201642229396 absolute error = 1.704201642229396 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.35 Order of pole (given) = 0.5 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] = 1.859999999999906 y[1] (closed_form) = 0 y[1] (numeric) = 1.714089750388407 absolute error = 1.714089750388407 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.36 Order of pole (given) = 0.5 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] = 1.869999999999905 y[1] (closed_form) = 0 y[1] (numeric) = 1.723978713780535 absolute error = 1.723978713780535 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.37 Order of pole (given) = 0.5 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] = 1.879999999999904 y[1] (closed_form) = 0 y[1] (numeric) = 1.733868524649534 absolute error = 1.733868524649534 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.38 Order of pole (given) = 0.5 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] = 1.889999999999903 y[1] (closed_form) = 0 y[1] (numeric) = 1.743759175322147 absolute error = 1.743759175322147 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.39 Order of pole (given) = 0.5 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] = 1.899999999999902 y[1] (closed_form) = 0 y[1] (numeric) = 1.753650658207067 absolute error = 1.753650658207067 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.4 Order of pole (given) = 0.5 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] = 1.9099999999999 y[1] (closed_form) = 0 y[1] (numeric) = 1.763542965793913 absolute error = 1.763542965793913 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.41 Order of pole (given) = 0.5 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] = 1.919999999999899 y[1] (closed_form) = 0 y[1] (numeric) = 1.773436090652218 absolute error = 1.773436090652218 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.42 Order of pole (given) = 0.5 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] = 1.929999999999898 y[1] (closed_form) = 0 y[1] (numeric) = 1.783330025430444 absolute error = 1.783330025430444 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.43 Order of pole (given) = 0.5 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] = 1.939999999999897 y[1] (closed_form) = 0 y[1] (numeric) = 1.793224762854992 absolute error = 1.793224762854992 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.44 Order of pole (given) = 0.5 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] = 1.949999999999896 y[1] (closed_form) = 0 y[1] (numeric) = 1.803120295729245 absolute error = 1.803120295729245 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.45 Order of pole (given) = 0.5 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] = 1.959999999999895 y[1] (closed_form) = 0 y[1] (numeric) = 1.813016616932611 absolute error = 1.813016616932611 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.46 Order of pole (given) = 0.5 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] = 1.969999999999894 y[1] (closed_form) = 0 y[1] (numeric) = 1.822913719419587 absolute error = 1.822913719419587 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.47 Order of pole (given) = 0.5 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] = 1.979999999999893 y[1] (closed_form) = 0 y[1] (numeric) = 1.832811596218832 absolute error = 1.832811596218832 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.48 Order of pole (given) = 0.5 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] = 1.989999999999892 y[1] (closed_form) = 0 y[1] (numeric) = 1.842710240432259 absolute error = 1.842710240432259 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.49 Order of pole (given) = 0.5 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] = 1.999999999999891 y[1] (closed_form) = 0 y[1] (numeric) = 1.852609645234134 absolute error = 1.852609645234134 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 0.5 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] = 2.00999999999989 y[1] (closed_form) = 0 y[1] (numeric) = 1.86250980387019 absolute error = 1.86250980387019 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.51 Order of pole (given) = 0.5 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] = 2.019999999999889 y[1] (closed_form) = 0 y[1] (numeric) = 1.872410709656754 absolute error = 1.872410709656754 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.52 Order of pole (given) = 0.5 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] = 2.029999999999887 y[1] (closed_form) = 0 y[1] (numeric) = 1.882312355979887 absolute error = 1.882312355979887 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.53 Order of pole (given) = 0.5 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] = 2.039999999999886 y[1] (closed_form) = 0 y[1] (numeric) = 1.892214736294534 absolute error = 1.892214736294534 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.54 Order of pole (given) = 0.5 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] = 2.049999999999885 y[1] (closed_form) = 0 y[1] (numeric) = 1.902117844123685 absolute error = 1.902117844123685 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.55 Order of pole (given) = 0.5 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] = 2.059999999999884 y[1] (closed_form) = 0 y[1] (numeric) = 1.912021673057555 absolute error = 1.912021673057555 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.56 Order of pole (given) = 0.5 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] = 2.069999999999883 y[1] (closed_form) = 0 y[1] (numeric) = 1.921926216752764 absolute error = 1.921926216752764 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.57 Order of pole (given) = 0.5 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] = 2.079999999999882 y[1] (closed_form) = 0 y[1] (numeric) = 1.931831468931542 absolute error = 1.931831468931542 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.58 Order of pole (given) = 0.5 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] = 2.089999999999881 y[1] (closed_form) = 0 y[1] (numeric) = 1.941737423380929 absolute error = 1.941737423380929 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.59 Order of pole (given) = 0.5 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] = 2.09999999999988 y[1] (closed_form) = 0 y[1] (numeric) = 1.951644073952004 absolute error = 1.951644073952004 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.6 Order of pole (given) = 0.5 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] = 2.109999999999879 y[1] (closed_form) = 0 y[1] (numeric) = 1.961551414559109 absolute error = 1.961551414559109 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.61 Order of pole (given) = 0.5 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] = 2.119999999999878 y[1] (closed_form) = 0 y[1] (numeric) = 1.971459439179092 absolute error = 1.971459439179092 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.62 Order of pole (given) = 0.5 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] = 2.129999999999876 y[1] (closed_form) = 0 y[1] (numeric) = 1.981368141850563 absolute error = 1.981368141850563 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.63 Order of pole (given) = 0.5 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] = 2.139999999999875 y[1] (closed_form) = 0 y[1] (numeric) = 1.991277516673149 absolute error = 1.991277516673149 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.64 Order of pole (given) = 0.5 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] = 2.149999999999874 y[1] (closed_form) = 0 y[1] (numeric) = 2.001187557806772 absolute error = 2.001187557806772 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.65 Order of pole (given) = 0.5 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] = 2.159999999999873 y[1] (closed_form) = 0 y[1] (numeric) = 2.01109825947093 absolute error = 2.01109825947093 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.66 Order of pole (given) = 0.5 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] = 2.169999999999872 y[1] (closed_form) = 0 y[1] (numeric) = 2.021009615943989 absolute error = 2.021009615943989 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.67 Order of pole (given) = 0.5 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] = 2.179999999999871 y[1] (closed_form) = 0 y[1] (numeric) = 2.030921621562483 absolute error = 2.030921621562483 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.68 Order of pole (given) = 0.5 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] = 2.18999999999987 y[1] (closed_form) = 0 y[1] (numeric) = 2.04083427072043 absolute error = 2.04083427072043 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.69 Order of pole (given) = 0.5 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] = 2.199999999999869 y[1] (closed_form) = 0 y[1] (numeric) = 2.050747557868647 absolute error = 2.050747557868647 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.7 Order of pole (given) = 0.5 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] = 2.209999999999868 y[1] (closed_form) = 0 y[1] (numeric) = 2.060661477514086 absolute error = 2.060661477514086 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.71 Order of pole (given) = 0.5 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] = 2.219999999999867 y[1] (closed_form) = 0 y[1] (numeric) = 2.070576024219169 absolute error = 2.070576024219169 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.72 Order of pole (given) = 0.5 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] = 2.229999999999865 y[1] (closed_form) = 0 y[1] (numeric) = 2.080491192601139 absolute error = 2.080491192601139 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.73 Order of pole (given) = 0.5 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] = 2.239999999999864 y[1] (closed_form) = 0 y[1] (numeric) = 2.090406977331413 absolute error = 2.090406977331413 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.74 Order of pole (given) = 0.5 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] = 2.249999999999863 y[1] (closed_form) = 0 y[1] (numeric) = 2.100323373134954 absolute error = 2.100323373134954 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.75 Order of pole (given) = 0.5 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] = 2.259999999999862 y[1] (closed_form) = 0 y[1] (numeric) = 2.110240374789639 absolute error = 2.110240374789639 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.76 Order of pole (given) = 0.5 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] = 2.269999999999861 y[1] (closed_form) = 0 y[1] (numeric) = 2.120157977125643 absolute error = 2.120157977125643 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.77 Order of pole (given) = 0.5 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] = 2.27999999999986 y[1] (closed_form) = 0 y[1] (numeric) = 2.130076175024837 absolute error = 2.130076175024837 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.78 Order of pole (given) = 0.5 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] = 2.289999999999859 y[1] (closed_form) = 0 y[1] (numeric) = 2.139994963420176 absolute error = 2.139994963420176 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.79 Order of pole (given) = 0.5 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] = 2.299999999999858 y[1] (closed_form) = 0 y[1] (numeric) = 2.149914337295115 absolute error = 2.149914337295115 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.8 Order of pole (given) = 0.5 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] = 2.309999999999857 y[1] (closed_form) = 0 y[1] (numeric) = 2.159834291683017 absolute error = 2.159834291683017 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.81 Order of pole (given) = 0.5 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] = 2.319999999999856 y[1] (closed_form) = 0 y[1] (numeric) = 2.169754821666585 absolute error = 2.169754821666585 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.82 Order of pole (given) = 0.5 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] = 2.329999999999854 y[1] (closed_form) = 0 y[1] (numeric) = 2.179675922377282 absolute error = 2.179675922377282 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.83 Order of pole (given) = 0.5 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] = 2.339999999999853 y[1] (closed_form) = 0 y[1] (numeric) = 2.189597588994778 absolute error = 2.189597588994778 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.84 Order of pole (given) = 0.5 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] = 2.349999999999852 y[1] (closed_form) = 0 y[1] (numeric) = 2.199519816746391 absolute error = 2.199519816746391 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.85 Order of pole (given) = 0.5 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] = 2.359999999999851 y[1] (closed_form) = 0 y[1] (numeric) = 2.209442600906541 absolute error = 2.209442600906541 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.86 Order of pole (given) = 0.5 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] = 2.36999999999985 y[1] (closed_form) = 0 y[1] (numeric) = 2.219365936796208 absolute error = 2.219365936796208 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.87 Order of pole (given) = 0.5 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] = 2.379999999999849 y[1] (closed_form) = 0 y[1] (numeric) = 2.229289819782404 absolute error = 2.229289819782404 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.88 Order of pole (given) = 0.5 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] = 2.389999999999848 y[1] (closed_form) = 0 y[1] (numeric) = 2.239214245277646 absolute error = 2.239214245277646 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.89 Order of pole (given) = 0.5 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] = 2.399999999999847 y[1] (closed_form) = 0 y[1] (numeric) = 2.249139208739431 absolute error = 2.249139208739431 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.9 Order of pole (given) = 0.5 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] = 2.409999999999846 y[1] (closed_form) = 0 y[1] (numeric) = 2.259064705669734 absolute error = 2.259064705669734 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.91 Order of pole (given) = 0.5 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] = 2.419999999999844 y[1] (closed_form) = 0 y[1] (numeric) = 2.268990731614495 absolute error = 2.268990731614495 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.92 Order of pole (given) = 0.5 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] = 2.429999999999843 y[1] (closed_form) = 0 y[1] (numeric) = 2.278917282163123 absolute error = 2.278917282163123 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.93 Order of pole (given) = 0.5 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] = 2.439999999999842 y[1] (closed_form) = 0 y[1] (numeric) = 2.288844352948006 absolute error = 2.288844352948006 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.94 Order of pole (given) = 0.5 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] = 2.449999999999841 y[1] (closed_form) = 0 y[1] (numeric) = 2.298771939644019 absolute error = 2.298771939644019 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.95 Order of pole (given) = 0.5 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] = 2.45999999999984 y[1] (closed_form) = 0 y[1] (numeric) = 2.308700037968051 absolute error = 2.308700037968051 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.96 Order of pole (given) = 0.5 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] = 2.469999999999839 y[1] (closed_form) = 0 y[1] (numeric) = 2.318628643678531 absolute error = 2.318628643678531 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.97 Order of pole (given) = 0.5 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] = 2.479999999999838 y[1] (closed_form) = 0 y[1] (numeric) = 2.328557752574954 absolute error = 2.328557752574954 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.98 Order of pole (given) = 0.5 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] = 2.489999999999837 y[1] (closed_form) = 0 y[1] (numeric) = 2.33848736049743 absolute error = 2.33848736049743 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.99 Order of pole (given) = 0.5 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] = 2.499999999999836 y[1] (closed_form) = 0 y[1] (numeric) = 2.348417463326221 absolute error = 2.348417463326221 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 0.5 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] = 2.509999999999835 y[1] (closed_form) = 0 y[1] (numeric) = 2.358348056981296 absolute error = 2.358348056981296 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.01 Order of pole (given) = 0.5 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] = 2.519999999999833 y[1] (closed_form) = 0 y[1] (numeric) = 2.368279137421885 absolute error = 2.368279137421885 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.02 Order of pole (given) = 0.5 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] = 2.529999999999832 y[1] (closed_form) = 0 y[1] (numeric) = 2.378210700646044 absolute error = 2.378210700646044 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.03 Order of pole (given) = 0.5 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] = 2.539999999999831 y[1] (closed_form) = 0 y[1] (numeric) = 2.38814274269022 absolute error = 2.38814274269022 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.04 Order of pole (given) = 0.5 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] = 2.54999999999983 y[1] (closed_form) = 0 y[1] (numeric) = 2.398075259628822 absolute error = 2.398075259628822 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.05 Order of pole (given) = 0.5 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] = 2.559999999999829 y[1] (closed_form) = 0 y[1] (numeric) = 2.408008247573811 absolute error = 2.408008247573811 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.06 Order of pole (given) = 0.5 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] = 2.569999999999828 y[1] (closed_form) = 0 y[1] (numeric) = 2.417941702674269 absolute error = 2.417941702674269 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.07 Order of pole (given) = 0.5 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] = 2.579999999999827 y[1] (closed_form) = 0 y[1] (numeric) = 2.427875621115998 absolute error = 2.427875621115998 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.08 Order of pole (given) = 0.5 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] = 2.589999999999826 y[1] (closed_form) = 0 y[1] (numeric) = 2.437809999121114 absolute error = 2.437809999121114 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.09 Order of pole (given) = 0.5 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] = 2.599999999999825 y[1] (closed_form) = 0 y[1] (numeric) = 2.447744832947644 absolute error = 2.447744832947644 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.1 Order of pole (given) = 0.5 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] = 2.609999999999824 y[1] (closed_form) = 0 y[1] (numeric) = 2.45768011888913 absolute error = 2.45768011888913 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.11 Order of pole (given) = 0.5 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] = 2.619999999999822 y[1] (closed_form) = 0 y[1] (numeric) = 2.467615853274243 absolute error = 2.467615853274243 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.12 Order of pole (given) = 0.5 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] = 2.629999999999821 y[1] (closed_form) = 0 y[1] (numeric) = 2.477552032466394 absolute error = 2.477552032466394 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.13 Order of pole (given) = 0.5 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] = 2.63999999999982 y[1] (closed_form) = 0 y[1] (numeric) = 2.487488652863356 absolute error = 2.487488652863356 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.14 Order of pole (given) = 0.5 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] = 2.649999999999819 y[1] (closed_form) = 0 y[1] (numeric) = 2.497425710896888 absolute error = 2.497425710896888 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.15 Order of pole (given) = 0.5 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] = 2.659999999999818 y[1] (closed_form) = 0 y[1] (numeric) = 2.507363203032361 absolute error = 2.507363203032361 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.16 Order of pole (given) = 0.5 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] = 2.669999999999817 y[1] (closed_form) = 0 y[1] (numeric) = 2.517301125768395 absolute error = 2.517301125768395 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.17 Order of pole (given) = 0.5 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] = 2.679999999999816 y[1] (closed_form) = 0 y[1] (numeric) = 2.527239475636499 absolute error = 2.527239475636499 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.18 Order of pole (given) = 0.5 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] = 2.689999999999815 y[1] (closed_form) = 0 y[1] (numeric) = 2.537178249200708 absolute error = 2.537178249200708 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.19 Order of pole (given) = 0.5 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] = 2.699999999999814 y[1] (closed_form) = 0 y[1] (numeric) = 2.547117443057235 absolute error = 2.547117443057235 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.2 Order of pole (given) = 0.5 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] = 2.709999999999813 y[1] (closed_form) = 0 y[1] (numeric) = 2.55705705383412 absolute error = 2.55705705383412 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.21 Order of pole (given) = 0.5 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] = 2.719999999999811 y[1] (closed_form) = 0 y[1] (numeric) = 2.566997078190887 absolute error = 2.566997078190887 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.22 Order of pole (given) = 0.5 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] = 2.72999999999981 y[1] (closed_form) = 0 y[1] (numeric) = 2.576937512818207 absolute error = 2.576937512818207 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.23 Order of pole (given) = 0.5 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] = 2.739999999999809 y[1] (closed_form) = 0 y[1] (numeric) = 2.586878354437555 absolute error = 2.586878354437555 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.24 Order of pole (given) = 0.5 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] = 2.749999999999808 y[1] (closed_form) = 0 y[1] (numeric) = 2.596819599800889 absolute error = 2.596819599800889 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.25 Order of pole (given) = 0.5 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] = 2.759999999999807 y[1] (closed_form) = 0 y[1] (numeric) = 2.606761245690312 absolute error = 2.606761245690312 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.26 Order of pole (given) = 0.5 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] = 2.769999999999806 y[1] (closed_form) = 0 y[1] (numeric) = 2.616703288917756 absolute error = 2.616703288917756 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.27 Order of pole (given) = 0.5 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] = 2.779999999999805 y[1] (closed_form) = 0 y[1] (numeric) = 2.626645726324659 absolute error = 2.626645726324659 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.28 Order of pole (given) = 0.5 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] = 2.789999999999804 y[1] (closed_form) = 0 y[1] (numeric) = 2.636588554781651 absolute error = 2.636588554781651 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.29 Order of pole (given) = 0.5 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] = 2.799999999999803 y[1] (closed_form) = 0 y[1] (numeric) = 2.646531771188245 absolute error = 2.646531771188245 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.3 Order of pole (given) = 0.5 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] = 2.809999999999802 y[1] (closed_form) = 0 y[1] (numeric) = 2.656475372472523 absolute error = 2.656475372472523 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.31 Order of pole (given) = 0.5 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] = 2.8199999999998 y[1] (closed_form) = 0 y[1] (numeric) = 2.666419355590834 absolute error = 2.666419355590834 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.32 Order of pole (given) = 0.5 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] = 2.829999999999799 y[1] (closed_form) = 0 y[1] (numeric) = 2.676363717527502 absolute error = 2.676363717527502 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.33 Order of pole (given) = 0.5 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] = 2.839999999999798 y[1] (closed_form) = 0 y[1] (numeric) = 2.686308455294516 absolute error = 2.686308455294516 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.34 Order of pole (given) = 0.5 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] = 2.849999999999797 y[1] (closed_form) = 0 y[1] (numeric) = 2.696253565931246 absolute error = 2.696253565931246 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.35 Order of pole (given) = 0.5 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] = 2.859999999999796 y[1] (closed_form) = 0 y[1] (numeric) = 2.706199046504149 absolute error = 2.706199046504149 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.36 Order of pole (given) = 0.5 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] = 2.869999999999795 y[1] (closed_form) = 0 y[1] (numeric) = 2.716144894106489 absolute error = 2.716144894106489 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.37 Order of pole (given) = 0.5 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] = 2.879999999999794 y[1] (closed_form) = 0 y[1] (numeric) = 2.726091105858046 absolute error = 2.726091105858046 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.38 Order of pole (given) = 0.5 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] = 2.889999999999793 y[1] (closed_form) = 0 y[1] (numeric) = 2.736037678904845 absolute error = 2.736037678904845 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.39 Order of pole (given) = 0.5 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] = 2.899999999999792 y[1] (closed_form) = 0 y[1] (numeric) = 2.745984610418873 absolute error = 2.745984610418873 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.4 Order of pole (given) = 0.5 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] = 2.909999999999791 y[1] (closed_form) = 0 y[1] (numeric) = 2.755931897597813 absolute error = 2.755931897597813 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.41 Order of pole (given) = 0.5 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] = 2.919999999999789 y[1] (closed_form) = 0 y[1] (numeric) = 2.76587953766477 absolute error = 2.76587953766477 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.42 Order of pole (given) = 0.5 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] = 2.929999999999788 y[1] (closed_form) = 0 y[1] (numeric) = 2.775827527868008 absolute error = 2.775827527868008 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.43 Order of pole (given) = 0.5 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] = 2.939999999999787 y[1] (closed_form) = 0 y[1] (numeric) = 2.785775865480685 absolute error = 2.785775865480685 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.44 Order of pole (given) = 0.5 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] = 2.949999999999786 y[1] (closed_form) = 0 y[1] (numeric) = 2.795724547800596 absolute error = 2.795724547800596 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.45 Order of pole (given) = 0.5 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] = 2.959999999999785 y[1] (closed_form) = 0 y[1] (numeric) = 2.805673572149915 absolute error = 2.805673572149915 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.46 Order of pole (given) = 0.5 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] = 2.969999999999784 y[1] (closed_form) = 0 y[1] (numeric) = 2.815622935874939 absolute error = 2.815622935874939 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.47 Order of pole (given) = 0.5 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] = 2.979999999999783 y[1] (closed_form) = 0 y[1] (numeric) = 2.825572636345843 absolute error = 2.825572636345843 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.48 Order of pole (given) = 0.5 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] = 2.989999999999782 y[1] (closed_form) = 0 y[1] (numeric) = 2.835522670956428 absolute error = 2.835522670956428 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.49 Order of pole (given) = 0.5 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] = 2.999999999999781 y[1] (closed_form) = 0 y[1] (numeric) = 2.845473037123877 absolute error = 2.845473037123877 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.5 Order of pole (given) = 0.5 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] = 3.00999999999978 y[1] (closed_form) = 0 y[1] (numeric) = 2.855423732288516 absolute error = 2.855423732288516 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.51 Order of pole (given) = 0.5 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] = 3.019999999999778 y[1] (closed_form) = 0 y[1] (numeric) = 2.865374753913572 absolute error = 2.865374753913572 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.52 Order of pole (given) = 0.5 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] = 3.029999999999777 y[1] (closed_form) = 0 y[1] (numeric) = 2.875326099484942 absolute error = 2.875326099484942 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.53 Order of pole (given) = 0.5 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] = 3.039999999999776 y[1] (closed_form) = 0 y[1] (numeric) = 2.885277766510951 absolute error = 2.885277766510951 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.54 Order of pole (given) = 0.5 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] = 3.049999999999775 y[1] (closed_form) = 0 y[1] (numeric) = 2.895229752522131 absolute error = 2.895229752522131 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.55 Order of pole (given) = 0.5 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] = 3.059999999999774 y[1] (closed_form) = 0 y[1] (numeric) = 2.905182055070985 absolute error = 2.905182055070985 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.56 Order of pole (given) = 0.5 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] = 3.069999999999773 y[1] (closed_form) = 0 y[1] (numeric) = 2.915134671731769 absolute error = 2.915134671731769 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.57 Order of pole (given) = 0.5 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] = 3.079999999999772 y[1] (closed_form) = 0 y[1] (numeric) = 2.925087600100265 absolute error = 2.925087600100265 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.58 Order of pole (given) = 0.5 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] = 3.089999999999771 y[1] (closed_form) = 0 y[1] (numeric) = 2.935040837793566 absolute error = 2.935040837793566 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.59 Order of pole (given) = 0.5 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] = 3.09999999999977 y[1] (closed_form) = 0 y[1] (numeric) = 2.944994382449848 absolute error = 2.944994382449848 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.6 Order of pole (given) = 0.5 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] = 3.109999999999769 y[1] (closed_form) = 0 y[1] (numeric) = 2.954948231728167 absolute error = 2.954948231728167 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.61 Order of pole (given) = 0.5 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] = 3.119999999999767 y[1] (closed_form) = 0 y[1] (numeric) = 2.964902383308244 absolute error = 2.964902383308244 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.62 Order of pole (given) = 0.5 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] = 3.129999999999766 y[1] (closed_form) = 0 y[1] (numeric) = 2.974856834890249 absolute error = 2.974856834890249 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.63 Order of pole (given) = 0.5 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] = 3.139999999999765 y[1] (closed_form) = 0 y[1] (numeric) = 2.984811584194599 absolute error = 2.984811584194599 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.64 Order of pole (given) = 0.5 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] = 3.149999999999764 y[1] (closed_form) = 0 y[1] (numeric) = 2.994766628961755 absolute error = 2.994766628961755 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.65 Order of pole (given) = 0.5 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] = 3.159999999999763 y[1] (closed_form) = 0 y[1] (numeric) = 3.004721966952013 absolute error = 3.004721966952013 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.66 Order of pole (given) = 0.5 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] = 3.169999999999762 y[1] (closed_form) = 0 y[1] (numeric) = 3.014677595945308 absolute error = 3.014677595945308 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.67 Order of pole (given) = 0.5 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] = 3.179999999999761 y[1] (closed_form) = 0 y[1] (numeric) = 3.024633513741016 absolute error = 3.024633513741016 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.68 Order of pole (given) = 0.5 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] = 3.18999999999976 y[1] (closed_form) = 0 y[1] (numeric) = 3.034589718157756 absolute error = 3.034589718157756 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.69 Order of pole (given) = 0.5 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] = 3.199999999999759 y[1] (closed_form) = 0 y[1] (numeric) = 3.044546207033198 absolute error = 3.044546207033198 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.7 Order of pole (given) = 0.5 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] = 3.209999999999757 y[1] (closed_form) = 0 y[1] (numeric) = 3.054502978223872 absolute error = 3.054502978223872 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.71 Order of pole (given) = 0.5 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] = 3.219999999999756 y[1] (closed_form) = 0 y[1] (numeric) = 3.06446002960498 absolute error = 3.06446002960498 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.72 Order of pole (given) = 0.5 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] = 3.229999999999755 y[1] (closed_form) = 0 y[1] (numeric) = 3.074417359070206 absolute error = 3.074417359070206 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.73 Order of pole (given) = 0.5 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] = 3.239999999999754 y[1] (closed_form) = 0 y[1] (numeric) = 3.084374964531533 absolute error = 3.084374964531533 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.74 Order of pole (given) = 0.5 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] = 3.249999999999753 y[1] (closed_form) = 0 y[1] (numeric) = 3.09433284391906 absolute error = 3.09433284391906 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.75 Order of pole (given) = 0.5 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] = 3.259999999999752 y[1] (closed_form) = 0 y[1] (numeric) = 3.104290995180825 absolute error = 3.104290995180825 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.76 Order of pole (given) = 0.5 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] = 3.269999999999751 y[1] (closed_form) = 0 y[1] (numeric) = 3.11424941628262 absolute error = 3.11424941628262 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.77 Order of pole (given) = 0.5 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] = 3.27999999999975 y[1] (closed_form) = 0 y[1] (numeric) = 3.12420810520782 absolute error = 3.12420810520782 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.78 Order of pole (given) = 0.5 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] = 3.289999999999749 y[1] (closed_form) = 0 y[1] (numeric) = 3.134167059957203 absolute error = 3.134167059957203 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.79 Order of pole (given) = 0.5 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] = 3.299999999999748 y[1] (closed_form) = 0 y[1] (numeric) = 3.144126278548786 absolute error = 3.144126278548786 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.8 Order of pole (given) = 0.5 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] = 3.309999999999746 y[1] (closed_form) = 0 y[1] (numeric) = 3.154085759017643 absolute error = 3.154085759017643 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.81 Order of pole (given) = 0.5 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] = 3.319999999999745 y[1] (closed_form) = 0 y[1] (numeric) = 3.164045499415748 absolute error = 3.164045499415748 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.82 Order of pole (given) = 0.5 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] = 3.329999999999744 y[1] (closed_form) = 0 y[1] (numeric) = 3.174005497811801 absolute error = 3.174005497811801 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.83 Order of pole (given) = 0.5 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] = 3.339999999999743 y[1] (closed_form) = 0 y[1] (numeric) = 3.183965752291064 absolute error = 3.183965752291064 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.84 Order of pole (given) = 0.5 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] = 3.349999999999742 y[1] (closed_form) = 0 y[1] (numeric) = 3.193926260955201 absolute error = 3.193926260955201 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.85 Order of pole (given) = 0.5 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] = 3.359999999999741 y[1] (closed_form) = 0 y[1] (numeric) = 3.203887021922113 absolute error = 3.203887021922113 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.86 Order of pole (given) = 0.5 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] = 3.36999999999974 y[1] (closed_form) = 0 y[1] (numeric) = 3.213848033325781 absolute error = 3.213848033325781 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.87 Order of pole (given) = 0.5 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] = 3.379999999999739 y[1] (closed_form) = 0 y[1] (numeric) = 3.223809293316108 absolute error = 3.223809293316108 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.88 Order of pole (given) = 0.5 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] = 3.389999999999738 y[1] (closed_form) = 0 y[1] (numeric) = 3.233770800058764 absolute error = 3.233770800058764 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.89 Order of pole (given) = 0.5 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] = 3.399999999999737 y[1] (closed_form) = 0 y[1] (numeric) = 3.243732551735029 absolute error = 3.243732551735029 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.9 Order of pole (given) = 0.5 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] = 3.409999999999735 y[1] (closed_form) = 0 y[1] (numeric) = 3.253694546541644 absolute error = 3.253694546541644 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.91 Order of pole (given) = 0.5 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] = 3.419999999999734 y[1] (closed_form) = 0 y[1] (numeric) = 3.263656782690657 absolute error = 3.263656782690657 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.92 Order of pole (given) = 0.5 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] = 3.429999999999733 y[1] (closed_form) = 0 y[1] (numeric) = 3.273619258409278 absolute error = 3.273619258409278 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.93 Order of pole (given) = 0.5 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] = 3.439999999999732 y[1] (closed_form) = 0 y[1] (numeric) = 3.283581971939729 absolute error = 3.283581971939729 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.94 Order of pole (given) = 0.5 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] = 3.449999999999731 y[1] (closed_form) = 0 y[1] (numeric) = 3.293544921539097 absolute error = 3.293544921539097 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.95 Order of pole (given) = 0.5 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] = 3.45999999999973 y[1] (closed_form) = 0 y[1] (numeric) = 3.303508105479194 absolute error = 3.303508105479194 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.96 Order of pole (given) = 0.5 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] = 3.469999999999729 y[1] (closed_form) = 0 y[1] (numeric) = 3.31347152204641 absolute error = 3.31347152204641 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.97 Order of pole (given) = 0.5 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] = 3.479999999999728 y[1] (closed_form) = 0 y[1] (numeric) = 3.323435169541575 absolute error = 3.323435169541575 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.98 Order of pole (given) = 0.5 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] = 3.489999999999727 y[1] (closed_form) = 0 y[1] (numeric) = 3.333399046279819 absolute error = 3.333399046279819 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.99 Order of pole (given) = 0.5 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] = 3.499999999999726 y[1] (closed_form) = 0 y[1] (numeric) = 3.343363150590432 absolute error = 3.343363150590432 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5 Order of pole (given) = 0.5 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] = 3.509999999999724 y[1] (closed_form) = 0 y[1] (numeric) = 3.353327480816732 absolute error = 3.353327480816732 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.01 Order of pole (given) = 0.5 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] = 3.519999999999723 y[1] (closed_form) = 0 y[1] (numeric) = 3.363292035315926 absolute error = 3.363292035315926 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.02 Order of pole (given) = 0.5 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] = 3.529999999999722 y[1] (closed_form) = 0 y[1] (numeric) = 3.373256812458977 absolute error = 3.373256812458977 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.03 Order of pole (given) = 0.5 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] = 3.539999999999721 y[1] (closed_form) = 0 y[1] (numeric) = 3.383221810630475 absolute error = 3.383221810630475 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.04 Order of pole (given) = 0.5 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] = 3.54999999999972 y[1] (closed_form) = 0 y[1] (numeric) = 3.393187028228505 absolute error = 3.393187028228505 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.05 Order of pole (given) = 0.5 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] = 3.559999999999719 y[1] (closed_form) = 0 y[1] (numeric) = 3.403152463664514 absolute error = 3.403152463664514 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.06 Order of pole (given) = 0.5 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] = 3.569999999999718 y[1] (closed_form) = 0 y[1] (numeric) = 3.413118115363192 absolute error = 3.413118115363192 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.07 Order of pole (given) = 0.5 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] = 3.579999999999717 y[1] (closed_form) = 0 y[1] (numeric) = 3.423083981762336 absolute error = 3.423083981762336 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.08 Order of pole (given) = 0.5 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] = 3.589999999999716 y[1] (closed_form) = 0 y[1] (numeric) = 3.433050061312734 absolute error = 3.433050061312734 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.09 Order of pole (given) = 0.5 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] = 3.599999999999715 y[1] (closed_form) = 0 y[1] (numeric) = 3.443016352478033 absolute error = 3.443016352478033 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.1 Order of pole (given) = 0.5 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] = 3.609999999999713 y[1] (closed_form) = 0 y[1] (numeric) = 3.452982853734622 absolute error = 3.452982853734622 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.11 Order of pole (given) = 0.5 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] = 3.619999999999712 y[1] (closed_form) = 0 y[1] (numeric) = 3.462949563571512 absolute error = 3.462949563571512 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.12 Order of pole (given) = 0.5 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] = 3.629999999999711 y[1] (closed_form) = 0 y[1] (numeric) = 3.472916480490212 absolute error = 3.472916480490212 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.13 Order of pole (given) = 0.5 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] = 3.63999999999971 y[1] (closed_form) = 0 y[1] (numeric) = 3.482883603004614 absolute error = 3.482883603004614 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.14 Order of pole (given) = 0.5 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] = 3.649999999999709 y[1] (closed_form) = 0 y[1] (numeric) = 3.492850929640875 absolute error = 3.492850929640875 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.15 Order of pole (given) = 0.5 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] = 3.659999999999708 y[1] (closed_form) = 0 y[1] (numeric) = 3.5028184589373 absolute error = 3.5028184589373 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.16 Order of pole (given) = 0.5 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] = 3.669999999999707 y[1] (closed_form) = 0 y[1] (numeric) = 3.51278618944423 absolute error = 3.51278618944423 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.17 Order of pole (given) = 0.5 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] = 3.679999999999706 y[1] (closed_form) = 0 y[1] (numeric) = 3.522754119723927 absolute error = 3.522754119723927 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.18 Order of pole (given) = 0.5 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] = 3.689999999999705 y[1] (closed_form) = 0 y[1] (numeric) = 3.532722248350462 absolute error = 3.532722248350462 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.19 Order of pole (given) = 0.5 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] = 3.699999999999704 y[1] (closed_form) = 0 y[1] (numeric) = 3.542690573909605 absolute error = 3.542690573909605 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.2 Order of pole (given) = 0.5 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] = 3.709999999999702 y[1] (closed_form) = 0 y[1] (numeric) = 3.552659094998712 absolute error = 3.552659094998712 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.21 Order of pole (given) = 0.5 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] = 3.719999999999701 y[1] (closed_form) = 0 y[1] (numeric) = 3.562627810226622 absolute error = 3.562627810226622 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.22 Order of pole (given) = 0.5 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] = 3.7299999999997 y[1] (closed_form) = 0 y[1] (numeric) = 3.572596718213545 absolute error = 3.572596718213545 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.23 Order of pole (given) = 0.5 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] = 3.739999999999699 y[1] (closed_form) = 0 y[1] (numeric) = 3.582565817590957 absolute error = 3.582565817590957 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.24 Order of pole (given) = 0.5 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] = 3.749999999999698 y[1] (closed_form) = 0 y[1] (numeric) = 3.592535107001496 absolute error = 3.592535107001496 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.25 Order of pole (given) = 0.5 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] = 3.759999999999697 y[1] (closed_form) = 0 y[1] (numeric) = 3.602504585098858 absolute error = 3.602504585098858 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.26 Order of pole (given) = 0.5 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] = 3.769999999999696 y[1] (closed_form) = 0 y[1] (numeric) = 3.61247425054769 absolute error = 3.61247425054769 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.27 Order of pole (given) = 0.5 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] = 3.779999999999695 y[1] (closed_form) = 0 y[1] (numeric) = 3.622444102023495 absolute error = 3.622444102023495 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.28 Order of pole (given) = 0.5 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] = 3.789999999999694 y[1] (closed_form) = 0 y[1] (numeric) = 3.632414138212526 absolute error = 3.632414138212526 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.29 Order of pole (given) = 0.5 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] = 3.799999999999693 y[1] (closed_form) = 0 y[1] (numeric) = 3.642384357811688 absolute error = 3.642384357811688 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.3 Order of pole (given) = 0.5 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] = 3.809999999999691 y[1] (closed_form) = 0 y[1] (numeric) = 3.652354759528436 absolute error = 3.652354759528436 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.31 Order of pole (given) = 0.5 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] = 3.81999999999969 y[1] (closed_form) = 0 y[1] (numeric) = 3.662325342080689 absolute error = 3.662325342080689 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.32 Order of pole (given) = 0.5 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] = 3.829999999999689 y[1] (closed_form) = 0 y[1] (numeric) = 3.672296104196716 absolute error = 3.672296104196716 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.33 Order of pole (given) = 0.5 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] = 3.839999999999688 y[1] (closed_form) = 0 y[1] (numeric) = 3.682267044615055 absolute error = 3.682267044615055 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.34 Order of pole (given) = 0.5 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] = 3.849999999999687 y[1] (closed_form) = 0 y[1] (numeric) = 3.69223816208441 absolute error = 3.69223816208441 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.35 Order of pole (given) = 0.5 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] = 3.859999999999686 y[1] (closed_form) = 0 y[1] (numeric) = 3.702209455363564 absolute error = 3.702209455363564 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.36 Order of pole (given) = 0.5 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] = 3.869999999999685 y[1] (closed_form) = 0 y[1] (numeric) = 3.712180923221277 absolute error = 3.712180923221277 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.37 Order of pole (given) = 0.5 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] = 3.879999999999684 y[1] (closed_form) = 0 y[1] (numeric) = 3.722152564436206 absolute error = 3.722152564436206 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.38 Order of pole (given) = 0.5 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] = 3.889999999999683 y[1] (closed_form) = 0 y[1] (numeric) = 3.732124377796805 absolute error = 3.732124377796805 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.39 Order of pole (given) = 0.5 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] = 3.899999999999681 y[1] (closed_form) = 0 y[1] (numeric) = 3.742096362101238 absolute error = 3.742096362101238 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.4 Order of pole (given) = 0.5 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] = 3.90999999999968 y[1] (closed_form) = 0 y[1] (numeric) = 3.752068516157292 absolute error = 3.752068516157292 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.41 Order of pole (given) = 0.5 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] = 3.919999999999679 y[1] (closed_form) = 0 y[1] (numeric) = 3.762040838782291 absolute error = 3.762040838782291 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.42 Order of pole (given) = 0.5 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] = 3.929999999999678 y[1] (closed_form) = 0 y[1] (numeric) = 3.772013328803 absolute error = 3.772013328803 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.43 Order of pole (given) = 0.5 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] = 3.939999999999677 y[1] (closed_form) = 0 y[1] (numeric) = 3.781985985055548 absolute error = 3.781985985055548 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.44 Order of pole (given) = 0.5 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] = 3.949999999999676 y[1] (closed_form) = 0 y[1] (numeric) = 3.79195880638534 absolute error = 3.79195880638534 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.45 Order of pole (given) = 0.5 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] = 3.959999999999675 y[1] (closed_form) = 0 y[1] (numeric) = 3.801931791646972 absolute error = 3.801931791646972 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.46 Order of pole (given) = 0.5 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] = 3.969999999999674 y[1] (closed_form) = 0 y[1] (numeric) = 3.811904939704146 absolute error = 3.811904939704146 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.47 Order of pole (given) = 0.5 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] = 3.979999999999673 y[1] (closed_form) = 0 y[1] (numeric) = 3.821878249429591 absolute error = 3.821878249429591 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.48 Order of pole (given) = 0.5 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] = 3.989999999999672 y[1] (closed_form) = 0 y[1] (numeric) = 3.831851719704979 absolute error = 3.831851719704979 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.49 Order of pole (given) = 0.5 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] = 3.99999999999967 y[1] (closed_form) = 0 y[1] (numeric) = 3.841825349420847 absolute error = 3.841825349420847 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.5 Order of pole (given) = 0.5 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] = 4.009999999999674 y[1] (closed_form) = 0 y[1] (numeric) = 3.85179913747651 absolute error = 3.85179913747651 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.51 Order of pole (given) = 0.5 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] = 4.019999999999677 y[1] (closed_form) = 0 y[1] (numeric) = 3.861773082779991 absolute error = 3.861773082779991 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.52 Order of pole (given) = 0.5 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] = 4.029999999999681 y[1] (closed_form) = 0 y[1] (numeric) = 3.871747184247934 absolute error = 3.871747184247934 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.53 Order of pole (given) = 0.5 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] = 4.039999999999684 y[1] (closed_form) = 0 y[1] (numeric) = 3.881721440805532 absolute error = 3.881721440805532 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.54 Order of pole (given) = 0.5 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] = 4.049999999999687 y[1] (closed_form) = 0 y[1] (numeric) = 3.891695851386448 absolute error = 3.891695851386448 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.55 Order of pole (given) = 0.5 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] = 4.059999999999691 y[1] (closed_form) = 0 y[1] (numeric) = 3.90167041493274 absolute error = 3.90167041493274 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.56 Order of pole (given) = 0.5 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] = 4.069999999999694 y[1] (closed_form) = 0 y[1] (numeric) = 3.911645130394785 absolute error = 3.911645130394785 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.57 Order of pole (given) = 0.5 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] = 4.079999999999697 y[1] (closed_form) = 0 y[1] (numeric) = 3.921619996731202 absolute error = 3.921619996731202 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.58 Order of pole (given) = 0.5 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] = 4.089999999999701 y[1] (closed_form) = 0 y[1] (numeric) = 3.931595012908785 absolute error = 3.931595012908785 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.59 Order of pole (given) = 0.5 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] = 4.099999999999704 y[1] (closed_form) = 0 y[1] (numeric) = 3.941570177902422 absolute error = 3.941570177902422 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.6 Order of pole (given) = 0.5 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] = 4.109999999999707 y[1] (closed_form) = 0 y[1] (numeric) = 3.951545490695027 absolute error = 3.951545490695027 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.61 Order of pole (given) = 0.5 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] = 4.119999999999711 y[1] (closed_form) = 0 y[1] (numeric) = 3.961520950277469 absolute error = 3.961520950277469 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.62 Order of pole (given) = 0.5 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] = 4.129999999999714 y[1] (closed_form) = 0 y[1] (numeric) = 3.9714965556485 absolute error = 3.9714965556485 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.63 Order of pole (given) = 0.5 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] = 4.139999999999717 y[1] (closed_form) = 0 y[1] (numeric) = 3.981472305814683 absolute error = 3.981472305814683 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.64 Order of pole (given) = 0.5 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] = 4.149999999999721 y[1] (closed_form) = 0 y[1] (numeric) = 3.991448199790328 absolute error = 3.991448199790328 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.65 Order of pole (given) = 0.5 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] = 4.159999999999724 y[1] (closed_form) = 0 y[1] (numeric) = 4.001424236597415 absolute error = 4.001424236597415 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.66 Order of pole (given) = 0.5 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] = 4.169999999999727 y[1] (closed_form) = 0 y[1] (numeric) = 4.011400415265534 absolute error = 4.011400415265534 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.67 Order of pole (given) = 0.5 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] = 4.179999999999731 y[1] (closed_form) = 0 y[1] (numeric) = 4.021376734831815 absolute error = 4.021376734831815 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.68 Order of pole (given) = 0.5 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] = 4.189999999999734 y[1] (closed_form) = 0 y[1] (numeric) = 4.031353194340856 absolute error = 4.031353194340856 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.69 Order of pole (given) = 0.5 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] = 4.199999999999737 y[1] (closed_form) = 0 y[1] (numeric) = 4.041329792844668 absolute error = 4.041329792844668 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.7 Order of pole (given) = 0.5 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] = 4.209999999999741 y[1] (closed_form) = 0 y[1] (numeric) = 4.051306529402598 absolute error = 4.051306529402598 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.71 Order of pole (given) = 0.5 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] = 4.219999999999744 y[1] (closed_form) = 0 y[1] (numeric) = 4.061283403081272 absolute error = 4.061283403081272 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.72 Order of pole (given) = 0.5 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] = 4.229999999999747 y[1] (closed_form) = 0 y[1] (numeric) = 4.071260412954531 absolute error = 4.071260412954531 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.73 Order of pole (given) = 0.5 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] = 4.239999999999751 y[1] (closed_form) = 0 y[1] (numeric) = 4.08123755810336 absolute error = 4.08123755810336 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.74 Order of pole (given) = 0.5 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] = 4.249999999999754 y[1] (closed_form) = 0 y[1] (numeric) = 4.091214837615833 absolute error = 4.091214837615833 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.75 Order of pole (given) = 0.5 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] = 4.259999999999757 y[1] (closed_form) = 0 y[1] (numeric) = 4.101192250587049 absolute error = 4.101192250587049 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.76 Order of pole (given) = 0.5 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] = 4.269999999999761 y[1] (closed_form) = 0 y[1] (numeric) = 4.111169796119071 absolute error = 4.111169796119071 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.77 Order of pole (given) = 0.5 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] = 4.279999999999764 y[1] (closed_form) = 0 y[1] (numeric) = 4.12114747332086 absolute error = 4.12114747332086 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.78 Order of pole (given) = 0.5 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] = 4.289999999999767 y[1] (closed_form) = 0 y[1] (numeric) = 4.131125281308218 absolute error = 4.131125281308218 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.79 Order of pole (given) = 0.5 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] = 4.299999999999771 y[1] (closed_form) = 0 y[1] (numeric) = 4.141103219203732 absolute error = 4.141103219203732 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.8 Order of pole (given) = 0.5 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] = 4.309999999999774 y[1] (closed_form) = 0 y[1] (numeric) = 4.151081286136713 absolute error = 4.151081286136713 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.81 Order of pole (given) = 0.5 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] = 4.319999999999777 y[1] (closed_form) = 0 y[1] (numeric) = 4.161059481243131 absolute error = 4.161059481243131 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.82 Order of pole (given) = 0.5 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] = 4.329999999999781 y[1] (closed_form) = 0 y[1] (numeric) = 4.171037803665567 absolute error = 4.171037803665567 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.83 Order of pole (given) = 0.5 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] = 4.339999999999784 y[1] (closed_form) = 0 y[1] (numeric) = 4.181016252553145 absolute error = 4.181016252553145 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.84 Order of pole (given) = 0.5 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] = 4.349999999999787 y[1] (closed_form) = 0 y[1] (numeric) = 4.190994827061487 absolute error = 4.190994827061487 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.85 Order of pole (given) = 0.5 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] = 4.359999999999791 y[1] (closed_form) = 0 y[1] (numeric) = 4.200973526352645 absolute error = 4.200973526352645 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.86 Order of pole (given) = 0.5 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] = 4.369999999999794 y[1] (closed_form) = 0 y[1] (numeric) = 4.210952349595056 absolute error = 4.210952349595056 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.87 Order of pole (given) = 0.5 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] = 4.379999999999797 y[1] (closed_form) = 0 y[1] (numeric) = 4.220931295963476 absolute error = 4.220931295963476 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.88 Order of pole (given) = 0.5 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] = 4.389999999999801 y[1] (closed_form) = 0 y[1] (numeric) = 4.230910364638935 absolute error = 4.230910364638935 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.89 Order of pole (given) = 0.5 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] = 4.399999999999804 y[1] (closed_form) = 0 y[1] (numeric) = 4.240889554808677 absolute error = 4.240889554808677 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.9 Order of pole (given) = 0.5 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] = 4.409999999999807 y[1] (closed_form) = 0 y[1] (numeric) = 4.250868865666111 absolute error = 4.250868865666111 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.91 Order of pole (given) = 0.5 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] = 4.419999999999811 y[1] (closed_form) = 0 y[1] (numeric) = 4.26084829641075 absolute error = 4.26084829641075 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.92 Order of pole (given) = 0.5 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] = 4.429999999999814 y[1] (closed_form) = 0 y[1] (numeric) = 4.270827846248167 absolute error = 4.270827846248167 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.93 Order of pole (given) = 0.5 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] = 4.439999999999817 y[1] (closed_form) = 0 y[1] (numeric) = 4.280807514389939 absolute error = 4.280807514389939 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.94 Order of pole (given) = 0.5 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] = 4.449999999999821 y[1] (closed_form) = 0 y[1] (numeric) = 4.290787300053595 absolute error = 4.290787300053595 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.95 Order of pole (given) = 0.5 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] = 4.459999999999824 y[1] (closed_form) = 0 y[1] (numeric) = 4.300767202462567 absolute error = 4.300767202462567 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.96 Order of pole (given) = 0.5 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] = 4.469999999999827 y[1] (closed_form) = 0 y[1] (numeric) = 4.31074722084614 absolute error = 4.31074722084614 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.97 Order of pole (given) = 0.5 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] = 4.479999999999831 y[1] (closed_form) = 0 y[1] (numeric) = 4.320727354439395 absolute error = 4.320727354439395 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.98 Order of pole (given) = 0.5 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] = 4.489999999999834 y[1] (closed_form) = 0 y[1] (numeric) = 4.330707602483171 absolute error = 4.330707602483171 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.99 Order of pole (given) = 0.5 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] = 4.499999999999837 y[1] (closed_form) = 0 y[1] (numeric) = 4.340687964224006 absolute error = 4.340687964224006 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6 Order of pole (given) = 0.5 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] = 4.509999999999841 y[1] (closed_form) = 0 y[1] (numeric) = 4.350668438914094 absolute error = 4.350668438914094 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.01 Order of pole (given) = 0.5 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] = 4.519999999999844 y[1] (closed_form) = 0 y[1] (numeric) = 4.360649025811232 absolute error = 4.360649025811232 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.02 Order of pole (given) = 0.5 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] = 4.529999999999847 y[1] (closed_form) = 0 y[1] (numeric) = 4.370629724178777 absolute error = 4.370629724178777 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.03 Order of pole (given) = 0.5 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] = 4.539999999999851 y[1] (closed_form) = 0 y[1] (numeric) = 4.3806105332856 absolute error = 4.3806105332856 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.04 Order of pole (given) = 0.5 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] = 4.549999999999854 y[1] (closed_form) = 0 y[1] (numeric) = 4.390591452406031 absolute error = 4.390591452406031 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.05 Order of pole (given) = 0.5 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] = 4.559999999999858 y[1] (closed_form) = 0 y[1] (numeric) = 4.400572480819821 absolute error = 4.400572480819821 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.06 Order of pole (given) = 0.5 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] = 4.569999999999861 y[1] (closed_form) = 0 y[1] (numeric) = 4.410553617812091 absolute error = 4.410553617812091 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.07 Order of pole (given) = 0.5 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] = 4.579999999999864 y[1] (closed_form) = 0 y[1] (numeric) = 4.420534862673288 absolute error = 4.420534862673288 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.08 Order of pole (given) = 0.5 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] = 4.589999999999868 y[1] (closed_form) = 0 y[1] (numeric) = 4.430516214699145 absolute error = 4.430516214699145 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.09 Order of pole (given) = 0.5 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] = 4.599999999999871 y[1] (closed_form) = 0 y[1] (numeric) = 4.440497673190626 absolute error = 4.440497673190626 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.1 Order of pole (given) = 0.5 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] = 4.609999999999874 y[1] (closed_form) = 0 y[1] (numeric) = 4.450479237453894 absolute error = 4.450479237453894 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.11 Order of pole (given) = 0.5 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] = 4.619999999999878 y[1] (closed_form) = 0 y[1] (numeric) = 4.460460906800256 absolute error = 4.460460906800256 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.12 Order of pole (given) = 0.5 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] = 4.629999999999881 y[1] (closed_form) = 0 y[1] (numeric) = 4.470442680546125 absolute error = 4.470442680546125 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.13 Order of pole (given) = 0.5 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] = 4.639999999999884 y[1] (closed_form) = 0 y[1] (numeric) = 4.480424558012981 absolute error = 4.480424558012981 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.14 Order of pole (given) = 0.5 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] = 4.649999999999888 y[1] (closed_form) = 0 y[1] (numeric) = 4.490406538527319 absolute error = 4.490406538527319 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.15 Order of pole (given) = 0.5 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] = 4.659999999999891 y[1] (closed_form) = 0 y[1] (numeric) = 4.500388621420614 absolute error = 4.500388621420614 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.16 Order of pole (given) = 0.5 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] = 4.669999999999894 y[1] (closed_form) = 0 y[1] (numeric) = 4.51037080602928 absolute error = 4.51037080602928 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.17 Order of pole (given) = 0.5 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] = 4.679999999999898 y[1] (closed_form) = 0 y[1] (numeric) = 4.520353091694622 absolute error = 4.520353091694622 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.18 Order of pole (given) = 0.5 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] = 4.689999999999901 y[1] (closed_form) = 0 y[1] (numeric) = 4.530335477762801 absolute error = 4.530335477762801 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.19 Order of pole (given) = 0.5 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] = 4.699999999999904 y[1] (closed_form) = 0 y[1] (numeric) = 4.540317963584791 absolute error = 4.540317963584791 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.2 Order of pole (given) = 0.5 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] = 4.709999999999908 y[1] (closed_form) = 0 y[1] (numeric) = 4.550300548516343 absolute error = 4.550300548516343 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.21 Order of pole (given) = 0.5 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] = 4.719999999999911 y[1] (closed_form) = 0 y[1] (numeric) = 4.560283231917937 absolute error = 4.560283231917937 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.22 Order of pole (given) = 0.5 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] = 4.729999999999914 y[1] (closed_form) = 0 y[1] (numeric) = 4.570266013154751 absolute error = 4.570266013154751 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.23 Order of pole (given) = 0.5 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] = 4.739999999999918 y[1] (closed_form) = 0 y[1] (numeric) = 4.580248891596614 absolute error = 4.580248891596614 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.24 Order of pole (given) = 0.5 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] = 4.749999999999921 y[1] (closed_form) = 0 y[1] (numeric) = 4.590231866617978 absolute error = 4.590231866617978 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.25 Order of pole (given) = 0.5 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] = 4.759999999999924 y[1] (closed_form) = 0 y[1] (numeric) = 4.600214937597866 absolute error = 4.600214937597866 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.26 Order of pole (given) = 0.5 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] = 4.769999999999928 y[1] (closed_form) = 0 y[1] (numeric) = 4.610198103919846 absolute error = 4.610198103919846 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.27 Order of pole (given) = 0.5 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] = 4.779999999999931 y[1] (closed_form) = 0 y[1] (numeric) = 4.620181364971986 absolute error = 4.620181364971986 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.28 Order of pole (given) = 0.5 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] = 4.789999999999934 y[1] (closed_form) = 0 y[1] (numeric) = 4.630164720146821 absolute error = 4.630164720146821 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.29 Order of pole (given) = 0.5 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] = 4.799999999999938 y[1] (closed_form) = 0 y[1] (numeric) = 4.640148168841317 absolute error = 4.640148168841317 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.3 Order of pole (given) = 0.5 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] = 4.809999999999941 y[1] (closed_form) = 0 y[1] (numeric) = 4.650131710456828 absolute error = 4.650131710456828 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.31 Order of pole (given) = 0.5 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] = 4.819999999999944 y[1] (closed_form) = 0 y[1] (numeric) = 4.660115344399063 absolute error = 4.660115344399063 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.32 Order of pole (given) = 0.5 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] = 4.829999999999948 y[1] (closed_form) = 0 y[1] (numeric) = 4.670099070078056 absolute error = 4.670099070078056 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.33 Order of pole (given) = 0.5 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] = 4.839999999999951 y[1] (closed_form) = 0 y[1] (numeric) = 4.680082886908121 absolute error = 4.680082886908121 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.34 Order of pole (given) = 0.5 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] = 4.849999999999954 y[1] (closed_form) = 0 y[1] (numeric) = 4.690066794307824 absolute error = 4.690066794307824 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.35 Order of pole (given) = 0.5 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] = 4.859999999999958 y[1] (closed_form) = 0 y[1] (numeric) = 4.700050791699946 absolute error = 4.700050791699946 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.36 Order of pole (given) = 0.5 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] = 4.869999999999961 y[1] (closed_form) = 0 y[1] (numeric) = 4.710034878511442 absolute error = 4.710034878511442 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.37 Order of pole (given) = 0.5 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] = 4.879999999999964 y[1] (closed_form) = 0 y[1] (numeric) = 4.720019054173417 absolute error = 4.720019054173417 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.38 Order of pole (given) = 0.5 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] = 4.889999999999968 y[1] (closed_form) = 0 y[1] (numeric) = 4.730003318121086 absolute error = 4.730003318121086 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.39 Order of pole (given) = 0.5 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] = 4.899999999999971 y[1] (closed_form) = 0 y[1] (numeric) = 4.739987669793745 absolute error = 4.739987669793745 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.4 Order of pole (given) = 0.5 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] = 4.909999999999974 y[1] (closed_form) = 0 y[1] (numeric) = 4.749972108634732 absolute error = 4.749972108634732 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.41 Order of pole (given) = 0.5 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] = 4.919999999999978 y[1] (closed_form) = 0 y[1] (numeric) = 4.759956634091397 absolute error = 4.759956634091397 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.42 Order of pole (given) = 0.5 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] = 4.929999999999981 y[1] (closed_form) = 0 y[1] (numeric) = 4.769941245615067 absolute error = 4.769941245615067 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.43 Order of pole (given) = 0.5 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] = 4.939999999999984 y[1] (closed_form) = 0 y[1] (numeric) = 4.779925942661016 absolute error = 4.779925942661016 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.44 Order of pole (given) = 0.5 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] = 4.949999999999988 y[1] (closed_form) = 0 y[1] (numeric) = 4.789910724688435 absolute error = 4.789910724688435 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.45 Order of pole (given) = 0.5 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] = 4.959999999999991 y[1] (closed_form) = 0 y[1] (numeric) = 4.799895591160396 absolute error = 4.799895591160396 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.46 Order of pole (given) = 0.5 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] = 4.969999999999994 y[1] (closed_form) = 0 y[1] (numeric) = 4.809880541543823 absolute error = 4.809880541543823 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.47 Order of pole (given) = 0.5 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] = 4.979999999999998 y[1] (closed_form) = 0 y[1] (numeric) = 4.819865575309458 absolute error = 4.819865575309458 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.48 Order of pole (given) = 0.5 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] = 4.990000000000001 y[1] (closed_form) = 0 y[1] (numeric) = 4.829850691931831 absolute error = 4.829850691931831 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.49 Order of pole (given) = 0.5 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 ) = tanh ( sqrt ( 2.0 * x + 3.0 ) ) ; Iterations = 4900 Total Elapsed Time = 1.0 Seconds Elapsed Time(since restart) = 1.0 Seconds Time to Timeout = 2 Minutes 59.0 Seconds Percent Done = 100 %