##############ECHO OF PROBLEM################# ##############temp/diff2postode.ode################# diff ( y , x , 3 ) = neg ( diff ( y , x , 1 ) ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=40; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=c(-1.0); x_end=c(1.0); array_y_init[0 + 1] = exact_soln_y(x_start); array_y_init[1 + 1] = exact_soln_yp(x_start); array_y_init[2 + 1] = exact_soln_ypp(x_start); glob_look_poles=true; glob_type_given_pole=3; // 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(neg(cos(c(x)))); } double exact_soln_yp (double x) { return(sin(c(x))); } double exact_soln_ypp (double x) { return(cos(c(x))); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = -1 y[1] (closed_form) = -0.5403023058681398 y[1] (numeric) = -0.5403023058681398 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4546 Order of pole (three term test) = 32.71 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.99 y[1] (closed_form) = -0.5486898605815875 y[1] (numeric) = -0.5486898605815874 absolute error = 1.110223024625157e-16 relative error = 2.023407218512054e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4587 Order of pole (three term test) = 32.7 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.98 y[1] (closed_form) = -0.5570225467662173 y[1] (numeric) = -0.5570225467662171 absolute error = 2.220446049250313e-16 relative error = 3.986276789227054e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4626 Order of pole (three term test) = 32.69 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.97 y[1] (closed_form) = -0.5652995311603544 y[1] (numeric) = -0.5652995311603539 absolute error = 4.440892098500626e-16 relative error = 7.855821301293297e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4663 Order of pole (three term test) = 32.68 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.96 y[1] (closed_form) = -0.5735199860724567 y[1] (numeric) = -0.5735199860724564 absolute error = 3.33066907387547e-16 relative error = 5.807415878711301e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4698 Order of pole (three term test) = 32.67 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.95 y[1] (closed_form) = -0.5816830894638836 y[1] (numeric) = -0.5816830894638831 absolute error = 4.440892098500626e-16 relative error = 7.63455596172417e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4732 Order of pole (three term test) = 32.66 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9399999999999999 y[1] (closed_form) = -0.5897880250310983 y[1] (numeric) = -0.5897880250310978 absolute error = 4.440892098500626e-16 relative error = 7.529641006642119e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4763 Order of pole (three term test) = 32.65 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9299999999999999 y[1] (closed_form) = -0.5978339822872983 y[1] (numeric) = -0.597833982287298 absolute error = 3.33066907387547e-16 relative error = 5.57122741857599e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4792 Order of pole (three term test) = 32.64 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9199999999999999 y[1] (closed_form) = -0.6058201566434629 y[1] (numeric) = -0.6058201566434627 absolute error = 2.220446049250313e-16 relative error = 3.665190114427126e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.482 Order of pole (three term test) = 32.63 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9099999999999999 y[1] (closed_form) = -0.6137457494888117 y[1] (numeric) = -0.6137457494888114 absolute error = 2.220446049250313e-16 relative error = 3.617859758865492e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4846 Order of pole (three term test) = 32.62 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8999999999999999 y[1] (closed_form) = -0.6216099682706645 y[1] (numeric) = -0.6216099682706642 absolute error = 3.33066907387547e-16 relative error = 5.358133305264521e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4869 Order of pole (three term test) = 32.61 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8899999999999999 y[1] (closed_form) = -0.629412026573697 y[1] (numeric) = -0.6294120265736965 absolute error = 4.440892098500626e-16 relative error = 7.055620024732158e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4891 Order of pole (three term test) = 32.6 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8799999999999999 y[1] (closed_form) = -0.6371511441985803 y[1] (numeric) = -0.63715114419858 absolute error = 3.33066907387547e-16 relative error = 5.227439523890117e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4911 Order of pole (three term test) = 32.59 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8699999999999999 y[1] (closed_form) = -0.6448265472400013 y[1] (numeric) = -0.644826547240001 absolute error = 3.33066907387547e-16 relative error = 5.165217046555329e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4929 Order of pole (three term test) = 32.58 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8599999999999999 y[1] (closed_form) = -0.6524374681640519 y[1] (numeric) = -0.6524374681640517 absolute error = 2.220446049250313e-16 relative error = 3.403308604422445e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4944 Order of pole (three term test) = 32.57 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8499999999999999 y[1] (closed_form) = -0.6599831458849823 y[1] (numeric) = -0.6599831458849821 absolute error = 2.220446049250313e-16 relative error = 3.364398110913697e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4958 Order of pole (three term test) = 32.56 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8399999999999999 y[1] (closed_form) = -0.6674628258413082 y[1] (numeric) = -0.6674628258413081 absolute error = 1.110223024625157e-16 relative error = 1.663348102159499e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.497 Order of pole (three term test) = 32.55 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8299999999999998 y[1] (closed_form) = -0.6748757600712673 y[1] (numeric) = -0.6748757600712672 absolute error = 1.110223024625157e-16 relative error = 1.645077642895214e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.498 Order of pole (three term test) = 32.54 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8199999999999998 y[1] (closed_form) = -0.6822212072876137 y[1] (numeric) = -0.6822212072876136 absolute error = 1.110223024625157e-16 relative error = 1.627365160692086e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4988 Order of pole (three term test) = 32.53 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8099999999999998 y[1] (closed_form) = -0.6894984329517472 y[1] (numeric) = -0.6894984329517471 absolute error = 1.110223024625157e-16 relative error = 1.610189337011666e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4994 Order of pole (three term test) = 32.52 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7999999999999998 y[1] (closed_form) = -0.6967067093471655 y[1] (numeric) = -0.6967067093471655 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4998 Order of pole (three term test) = 32.51 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7899999999999998 y[1] (closed_form) = -0.7038453156522362 y[1] (numeric) = -0.7038453156522362 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5 Order of pole (three term test) = 32.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7799999999999998 y[1] (closed_form) = -0.7109135380122775 y[1] (numeric) = -0.7109135380122775 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5 Order of pole (three term test) = 32.49 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7699999999999998 y[1] (closed_form) = -0.7179106696109435 y[1] (numeric) = -0.7179106696109435 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4998 Order of pole (three term test) = 32.48 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7599999999999998 y[1] (closed_form) = -0.7248360107409053 y[1] (numeric) = -0.7248360107409053 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4994 Order of pole (three term test) = 32.47 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7499999999999998 y[1] (closed_form) = -0.731688868873821 y[1] (numeric) = -0.7316888688738209 absolute error = 1.110223024625157e-16 relative error = 1.517343056392202e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4987 Order of pole (three term test) = 32.46 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7399999999999998 y[1] (closed_form) = -0.7384685587295881 y[1] (numeric) = -0.7384685587295881 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4979 Order of pole (three term test) = 32.45 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7299999999999998 y[1] (closed_form) = -0.7451744023448705 y[1] (numeric) = -0.7451744023448703 absolute error = 2.220446049250313e-16 relative error = 2.979766940817002e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4969 Order of pole (three term test) = 32.44 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7199999999999998 y[1] (closed_form) = -0.7518057291408952 y[1] (numeric) = -0.7518057291408948 absolute error = 3.33066907387547e-16 relative error = 4.430225714935025e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4957 Order of pole (three term test) = 32.43 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7099999999999997 y[1] (closed_form) = -0.7583618759905083 y[1] (numeric) = -0.758361875990508 absolute error = 3.33066907387547e-16 relative error = 4.391925780189347e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4943 Order of pole (three term test) = 32.42 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.6999999999999997 y[1] (closed_form) = -0.7648421872844886 y[1] (numeric) = -0.7648421872844882 absolute error = 4.440892098500626e-16 relative error = 5.806285495662394e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4927 Order of pole (three term test) = 32.42 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.6899999999999997 y[1] (closed_form) = -0.7712460149971068 y[1] (numeric) = -0.7712460149971061 absolute error = 6.661338147750939e-16 relative error = 8.637111917882556e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4909 Order of pole (three term test) = 32.41 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.6799999999999997 y[1] (closed_form) = -0.7775727187509281 y[1] (numeric) = -0.7775727187509275 absolute error = 6.661338147750939e-16 relative error = 8.566836241955008e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4889 Order of pole (three term test) = 32.4 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.6699999999999997 y[1] (closed_form) = -0.7838216658808494 y[1] (numeric) = -0.7838216658808488 absolute error = 6.661338147750939e-16 relative error = 8.498537917123032e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4867 Order of pole (three term test) = 32.39 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.6599999999999997 y[1] (closed_form) = -0.7899922314973653 y[1] (numeric) = -0.7899922314973645 absolute error = 7.771561172376096e-16 relative error = 9.837515943221038e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4844 Order of pole (three term test) = 32.38 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.6499999999999997 y[1] (closed_form) = -0.796083798549056 y[1] (numeric) = -0.7960837985490552 absolute error = 7.771561172376096e-16 relative error = 9.762240088971236e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4818 Order of pole (three term test) = 32.37 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.6399999999999997 y[1] (closed_form) = -0.8020957578842928 y[1] (numeric) = -0.8020957578842921 absolute error = 6.661338147750939e-16 relative error = 8.30491631737551e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.479 Order of pole (three term test) = 32.36 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.6299999999999997 y[1] (closed_form) = -0.8080275083121521 y[1] (numeric) = -0.8080275083121515 absolute error = 5.551115123125783e-16 relative error = 6.869958096749982e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.476 Order of pole (three term test) = 32.35 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.6199999999999997 y[1] (closed_form) = -0.8138784566625341 y[1] (numeric) = -0.8138784566625337 absolute error = 4.440892098500626e-16 relative error = 5.456456135614355e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4729 Order of pole (three term test) = 32.34 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.6099999999999997 y[1] (closed_form) = -0.8196480178454797 y[1] (numeric) = -0.8196480178454792 absolute error = 4.440892098500626e-16 relative error = 5.418047749537564e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4695 Order of pole (three term test) = 32.33 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.5999999999999996 y[1] (closed_form) = -0.8253356149096785 y[1] (numeric) = -0.8253356149096781 absolute error = 4.440892098500626e-16 relative error = 5.380710608237377e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.466 Order of pole (three term test) = 32.32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.5899999999999996 y[1] (closed_form) = -0.8309406791001637 y[1] (numeric) = -0.8309406791001633 absolute error = 3.33066907387547e-16 relative error = 4.008311492803907e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4623 Order of pole (three term test) = 32.31 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.5799999999999996 y[1] (closed_form) = -0.8364626499151872 y[1] (numeric) = -0.8364626499151867 absolute error = 4.440892098500626e-16 relative error = 5.30913376580641e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4584 Order of pole (three term test) = 32.3 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.5699999999999996 y[1] (closed_form) = -0.8419009751622689 y[1] (numeric) = -0.8419009751622686 absolute error = 3.33066907387547e-16 relative error = 3.956129250513711e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4543 Order of pole (three term test) = 32.29 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.5599999999999996 y[1] (closed_form) = -0.8472551110134163 y[1] (numeric) = -0.8472551110134159 absolute error = 4.440892098500626e-16 relative error = 5.241505233516738e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4501 Order of pole (three term test) = 32.28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.5499999999999996 y[1] (closed_form) = -0.8525245220595059 y[1] (numeric) = -0.8525245220595056 absolute error = 3.33066907387547e-16 relative error = 3.90683081564543e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4456 Order of pole (three term test) = 32.27 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.5399999999999996 y[1] (closed_form) = -0.8577086813638244 y[1] (numeric) = -0.8577086813638239 absolute error = 4.440892098500626e-16 relative error = 5.177622886408539e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.441 Order of pole (three term test) = 32.26 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.5299999999999996 y[1] (closed_form) = -0.8628070705147612 y[1] (numeric) = -0.8628070705147609 absolute error = 3.33066907387547e-16 relative error = 3.860270954766692e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4362 Order of pole (three term test) = 32.26 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.5199999999999996 y[1] (closed_form) = -0.8678191796776501 y[1] (numeric) = -0.8678191796776497 absolute error = 4.440892098500626e-16 relative error = 5.117301164224312e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4312 Order of pole (three term test) = 32.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.5099999999999996 y[1] (closed_form) = -0.8727445076457515 y[1] (numeric) = -0.8727445076457512 absolute error = 3.33066907387547e-16 relative error = 3.816316281221897e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4261 Order of pole (three term test) = 32.24 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.4999999999999996 y[1] (closed_form) = -0.877582561890373 y[1] (numeric) = -0.8775825618903728 absolute error = 2.220446049250313e-16 relative error = 2.530184789072518e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4207 Order of pole (three term test) = 32.23 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.4899999999999995 y[1] (closed_form) = -0.8823328586101217 y[1] (numeric) = -0.8823328586101216 absolute error = 1.110223024625157e-16 relative error = 1.258281400030839e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4152 Order of pole (three term test) = 32.22 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.4799999999999995 y[1] (closed_form) = -0.8869949227792844 y[1] (numeric) = -0.8869949227792842 absolute error = 2.220446049250313e-16 relative error = 2.503335692489458e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4096 Order of pole (three term test) = 32.21 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.4699999999999995 y[1] (closed_form) = -0.8915682881953292 y[1] (numeric) = -0.891568288195329 absolute error = 2.220446049250313e-16 relative error = 2.490494647072784e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4038 Order of pole (three term test) = 32.21 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.4599999999999995 y[1] (closed_form) = -0.8960524975255254 y[1] (numeric) = -0.8960524975255253 absolute error = 1.110223024625157e-16 relative error = 1.23901560197764e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3978 Order of pole (three term test) = 32.2 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.4499999999999995 y[1] (closed_form) = -0.9004471023526771 y[1] (numeric) = -0.9004471023526769 absolute error = 2.220446049250313e-16 relative error = 2.465937247672583e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3917 Order of pole (three term test) = 32.19 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.4399999999999995 y[1] (closed_form) = -0.9047516632199636 y[1] (numeric) = -0.9047516632199635 absolute error = 1.110223024625157e-16 relative error = 1.227102496472823e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3854 Order of pole (three term test) = 32.18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.4299999999999995 y[1] (closed_form) = -0.9089657496748853 y[1] (numeric) = -0.9089657496748853 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3789 Order of pole (three term test) = 32.17 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.4199999999999995 y[1] (closed_form) = -0.9130889403123085 y[1] (numeric) = -0.9130889403123084 absolute error = 1.110223024625157e-16 relative error = 1.215898009065164e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3723 Order of pole (three term test) = 32.17 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.4099999999999995 y[1] (closed_form) = -0.9171208228166053 y[1] (numeric) = -0.9171208228166051 absolute error = 2.220446049250313e-16 relative error = 2.421105261170513e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3656 Order of pole (three term test) = 32.16 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.3999999999999995 y[1] (closed_form) = -0.9210609940028853 y[1] (numeric) = -0.921060994002885 absolute error = 3.33066907387547e-16 relative error = 3.616122162985697e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3587 Order of pole (three term test) = 32.15 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.3899999999999995 y[1] (closed_form) = -0.9249090598573132 y[1] (numeric) = -0.924909059857313 absolute error = 2.220446049250313e-16 relative error = 2.400718238821084e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3516 Order of pole (three term test) = 32.14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.3799999999999994 y[1] (closed_form) = -0.9286646355765105 y[1] (numeric) = -0.9286646355765104 absolute error = 1.110223024625157e-16 relative error = 1.19550479483472e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3445 Order of pole (three term test) = 32.14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.3699999999999994 y[1] (closed_form) = -0.9323273456060346 y[1] (numeric) = -0.9323273456060346 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3371 Order of pole (three term test) = 32.13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.3599999999999994 y[1] (closed_form) = -0.935896823677935 y[1] (numeric) = -0.9358968236779349 absolute error = 1.110223024625157e-16 relative error = 1.186266473543681e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3297 Order of pole (three term test) = 32.12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.3499999999999994 y[1] (closed_form) = -0.9393727128473791 y[1] (numeric) = -0.9393727128473791 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3221 Order of pole (three term test) = 32.12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.3399999999999994 y[1] (closed_form) = -0.9427546655283464 y[1] (numeric) = -0.9427546655283465 absolute error = 1.110223024625157e-16 relative error = 1.177637263670243e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3144 Order of pole (three term test) = 32.11 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.3299999999999994 y[1] (closed_form) = -0.9460423435283871 y[1] (numeric) = -0.9460423435283872 absolute error = 1.110223024625157e-16 relative error = 1.173544749048374e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3066 Order of pole (three term test) = 32.11 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.3199999999999994 y[1] (closed_form) = -0.9492354180824411 y[1] (numeric) = -0.9492354180824411 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2986 Order of pole (three term test) = 32.1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.3099999999999994 y[1] (closed_form) = -0.9523335698857136 y[1] (numeric) = -0.9523335698857136 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2905 Order of pole (three term test) = 32.09 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.2999999999999994 y[1] (closed_form) = -0.9553364891256062 y[1] (numeric) = -0.9553364891256063 absolute error = 1.110223024625157e-16 relative error = 1.16212772909084e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2823 Order of pole (three term test) = 32.09 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.2899999999999994 y[1] (closed_form) = -0.9582438755126973 y[1] (numeric) = -0.9582438755126973 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.274 Order of pole (three term test) = 32.08 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.2799999999999994 y[1] (closed_form) = -0.9610554383107711 y[1] (numeric) = -0.9610554383107709 absolute error = 2.220446049250313e-16 relative error = 2.310424519477408e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2656 Order of pole (three term test) = 32.08 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.2699999999999994 y[1] (closed_form) = -0.9637708963658906 y[1] (numeric) = -0.9637708963658905 absolute error = 1.110223024625157e-16 relative error = 1.151957408977067e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2571 Order of pole (three term test) = 32.07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.2599999999999993 y[1] (closed_form) = -0.9663899781345134 y[1] (numeric) = -0.9663899781345132 absolute error = 2.220446049250313e-16 relative error = 2.2976708156024e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2484 Order of pole (three term test) = 32.07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.2499999999999993 y[1] (closed_form) = -0.968912421710645 y[1] (numeric) = -0.9689124217106446 absolute error = 3.33066907387547e-16 relative error = 3.437533670994815e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2397 Order of pole (three term test) = 32.06 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.2399999999999993 y[1] (closed_form) = -0.9713379748520298 y[1] (numeric) = -0.9713379748520296 absolute error = 2.220446049250313e-16 relative error = 2.285966477928105e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2309 Order of pole (three term test) = 32.06 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.2299999999999993 y[1] (closed_form) = -0.973666395005375 y[1] (numeric) = -0.9736663950053749 absolute error = 1.110223024625157e-16 relative error = 1.140249915494955e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.222 Order of pole (three term test) = 32.05 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.2199999999999993 y[1] (closed_form) = -0.9758974493306056 y[1] (numeric) = -0.9758974493306055 absolute error = 1.110223024625157e-16 relative error = 1.137643125706178e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.213 Order of pole (three term test) = 32.05 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.2099999999999993 y[1] (closed_form) = -0.9780309147241484 y[1] (numeric) = -0.978030914724148 absolute error = 3.33066907387547e-16 relative error = 3.405484452211695e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2039 Order of pole (three term test) = 32.04 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.1999999999999993 y[1] (closed_form) = -0.9800665778412417 y[1] (numeric) = -0.9800665778412414 absolute error = 3.33066907387547e-16 relative error = 3.398411035719448e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1947 Order of pole (three term test) = 32.04 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.1899999999999993 y[1] (closed_form) = -0.9820042351172704 y[1] (numeric) = -0.9820042351172701 absolute error = 3.33066907387547e-16 relative error = 3.391705406930066e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1855 Order of pole (three term test) = 32.04 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.1799999999999993 y[1] (closed_form) = -0.9838436927881216 y[1] (numeric) = -0.9838436927881212 absolute error = 3.33066907387547e-16 relative error = 3.385364055581495e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1761 Order of pole (three term test) = 32.03 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.1699999999999993 y[1] (closed_form) = -0.9855847669095609 y[1] (numeric) = -0.9855847669095605 absolute error = 3.33066907387547e-16 relative error = 3.379383677285567e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1667 Order of pole (three term test) = 32.03 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.1599999999999993 y[1] (closed_form) = -0.987227283375627 y[1] (numeric) = -0.9872272833756269 absolute error = 1.110223024625157e-16 relative error = 1.124587056416198e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1573 Order of pole (three term test) = 32.03 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.1499999999999992 y[1] (closed_form) = -0.9887710779360424 y[1] (numeric) = -0.9887710779360424 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1478 Order of pole (three term test) = 32.02 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.1399999999999992 y[1] (closed_form) = -0.9902159962126372 y[1] (numeric) = -0.9902159962126375 absolute error = 2.220446049250313e-16 relative error = 2.242385558042933e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1382 Order of pole (three term test) = 32.02 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.1299999999999992 y[1] (closed_form) = -0.9915618937147881 y[1] (numeric) = -0.9915618937147883 absolute error = 2.220446049250313e-16 relative error = 2.239341853821785e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1285 Order of pole (three term test) = 32.02 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.1199999999999992 y[1] (closed_form) = -0.9928086358538664 y[1] (numeric) = -0.9928086358538665 absolute error = 1.110223024625157e-16 relative error = 1.118264874549875e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1189 Order of pole (three term test) = 32.01 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.1099999999999992 y[1] (closed_form) = -0.9939560979566969 y[1] (numeric) = -0.9939560979566971 absolute error = 2.220446049250313e-16 relative error = 2.233947810989787e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1091 Order of pole (three term test) = 32.01 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.0999999999999992 y[1] (closed_form) = -0.9950041652780258 y[1] (numeric) = -0.995004165278026 absolute error = 2.220446049250313e-16 relative error = 2.231594727676212e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09933 Order of pole (three term test) = 32.01 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.08999999999999919 y[1] (closed_form) = -0.9959527330119943 y[1] (numeric) = -0.9959527330119945 absolute error = 2.220446049250313e-16 relative error = 2.229469306776401e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08951 Order of pole (three term test) = 32.01 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.07999999999999918 y[1] (closed_form) = -0.9968017063026194 y[1] (numeric) = -0.9968017063026196 absolute error = 1.110223024625157e-16 relative error = 1.113785236928661e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07966 Order of pole (three term test) = 32.01 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.06999999999999917 y[1] (closed_form) = -0.9975510002532796 y[1] (numeric) = -0.9975510002532798 absolute error = 2.220446049250313e-16 relative error = 2.225897271103471e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06977 Order of pole (three term test) = 32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.05999999999999917 y[1] (closed_form) = -0.9982005399352042 y[1] (numeric) = -0.9982005399352044 absolute error = 2.220446049250313e-16 relative error = 2.224448856133105e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05986 Order of pole (three term test) = 32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.04999999999999916 y[1] (closed_form) = -0.9987502603949663 y[1] (numeric) = -0.9987502603949665 absolute error = 2.220446049250313e-16 relative error = 2.223224500960044e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04992 Order of pole (three term test) = 32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.03999999999999915 y[1] (closed_form) = -0.999200106660978 y[1] (numeric) = -0.9992001066609782 absolute error = 2.220446049250313e-16 relative error = 2.22222359109865e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03996 Order of pole (three term test) = 32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.02999999999999914 y[1] (closed_form) = -0.9995500337489875 y[1] (numeric) = -0.9995500337489879 absolute error = 3.33066907387547e-16 relative error = 3.332168437214905e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02998 Order of pole (three term test) = 32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.01999999999999913 y[1] (closed_form) = -0.9998000066665778 y[1] (numeric) = -0.9998000066665781 absolute error = 3.33066907387547e-16 relative error = 3.33133531873061e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01999 Order of pole (three term test) = 32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.009999999999999121 y[1] (closed_form) = -0.9999500004166653 y[1] (numeric) = -0.9999500004166656 absolute error = 3.33066907387547e-16 relative error = 3.33083561426834e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 SETTING H FOR POLE NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.009999 Order of pole (three term test) = 32 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = 7.79000777999079e-05 y[1] (closed_form) = -0.9999999969657889 y[1] (numeric) = -0.9999999975166649 absolute error = 5.508760114736333e-10 relative error = 5.508760131451074e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.01005576457605521 y[1] (closed_form) = -0.9999494412254328 y[1] (numeric) = -0.9999494604131096 absolute error = 1.918767678077415e-08 relative error = 1.91886469352488e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.0200336290743105 y[1] (closed_form) = -0.9997993335645853 y[1] (numeric) = -0.9997994559823848 absolute error = 1.224177995640119e-07 relative error = 1.224423696378708e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.03001149357256572 y[1] (closed_form) = -0.999549688927508 y[1] (numeric) = -0.9995501212955468 absolute error = 4.323680388162998e-07 relative error = 4.325628266466873e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.03998935807082115 y[1] (closed_form) = -0.9992005321680603 y[1] (numeric) = -0.9992016589619945 absolute error = 1.126793934269621e-06 relative error = 0.000112769549053853 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.05011840233420169 y[1] (closed_form) = -0.9987443357438808 y[1] (numeric) = -0.9987468008623663 absolute error = 2.465118485561746e-06 relative error = 0.0002468217738352114 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.06009626683245714 y[1] (closed_form) = -0.9981947627649345 y[1] (numeric) = -0.9981994631968197 absolute error = 4.700431885273915e-06 relative error = 0.0004708932625787401 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.07007413133071225 y[1] (closed_form) = -0.9975458125559394 y[1] (numeric) = -0.9975540052583364 absolute error = 8.192702396936369e-06 relative error = 0.0008212858290633089 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.08005199582896724 y[1] (closed_form) = -0.9967975497244019 y[1] (numeric) = -0.9968108925336168 absolute error = 1.334280921483355e-05 relative error = 0.001338567617719628 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.09002986032722224 y[1] (closed_form) = -0.9959500487650901 y[1] (numeric) = -0.9959706558809009 absolute error = 2.060711581086672e-05 relative error = 0.002069091299952054 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1000077248254772 y[1] (closed_form) = -0.995003394052618 y[1] (numeric) = -0.9950338914771168 absolute error = 3.04974244988987e-05 relative error = 0.003065057333591962 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1099855893237322 y[1] (closed_form) = -0.9939576798330452 y[1] (numeric) = -0.9940012607585295 absolute error = 4.358092548428782e-05 relative error = 0.004384585618535399 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1201146335871123 y[1] (closed_form) = -0.9927949062909743 y[1] (numeric) = -0.9928556752561177 absolute error = 6.076896514339847e-05 relative error = 0.006120998884898381 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1300924980853673 y[1] (closed_form) = -0.9915498985629645 y[1] (numeric) = -0.9916321338292552 absolute error = 8.223526629069777e-05 relative error = 0.008293608461851478 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1400703625836223 y[1] (closed_form) = -0.9902061751473454 y[1] (numeric) = -0.9903151147429337 absolute error = 0.00010893959558822 relative error = 0.01100170836361523 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1500482270818773 y[1] (closed_form) = -0.9887638698211274 y[1] (numeric) = -0.9889055407308915 absolute error = 0.0001416709097641355 relative error = 0.01432808318428591 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1600260915801323 y[1] (closed_form) = -0.9872231261758354 y[1] (numeric) = -0.9874043993906806 absolute error = 0.000181273214845179 relative error = 0.01836192954143704 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1700039560783873 y[1] (closed_form) = -0.9855840976032136 y[1] (numeric) = -0.9858127430853415 absolute error = 0.000228645482127865 relative error = 0.0231989824799218 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1801330003417674 y[1] (closed_form) = -0.9838198730920893 y[1] (numeric) = -0.9841055368229856 absolute error = 0.000285663730896335 relative error = 0.02903618220259267 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1901108648400223 y[1] (closed_form) = -0.9819832912712215 y[1] (numeric) = -0.9823349390164948 absolute error = 0.000351647745273298 relative error = 0.03580995200214396 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2000887293382773 y[1] (closed_form) = -0.9800489461850265 y[1] (numeric) = -0.9804773902208176 absolute error = 0.0004284440357911201 relative error = 0.04371659573319237 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2100665938365323 y[1] (closed_form) = -0.9780170304110086 y[1] (numeric) = -0.9785342017223152 absolute error = 0.0005171713113065746 relative error = 0.05287958135956333 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2200444583347873 y[1] (closed_form) = -0.9758877462405133 y[1] (numeric) = -0.9765067489827002 absolute error = 0.0006190027421868471 relative error = 0.06342970741988292 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2300223228330423 y[1] (closed_form) = -0.9736613056585867 y[1] (numeric) = -0.9743964715021034 absolute error = 0.0007351658435167385 relative error = 0.07550529524427087 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2400001873312973 y[1] (closed_form) = -0.9713379303228712 y[1] (numeric) = -0.9722048726757616 absolute error = 0.0008669423528904208 relative error = 0.08925239361364695 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2501292315946774 y[1] (closed_form) = -0.9688804412117411 y[1] (numeric) = -0.9698985001948083 absolute error = 0.001018058983067172 relative error = 0.105075811190277 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2601070960929324 y[1] (closed_form) = -0.9663624402698491 y[1] (numeric) = -0.967547852868443 absolute error = 0.001185412598593949 relative error = 0.1226674950511251 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2700849605911874 y[1] (closed_form) = -0.9637482312269737 y[1] (numeric) = -0.9651208023801947 absolute error = 0.001372571153220981 relative error = 0.1424200957000485 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2800628250894424 y[1] (closed_form) = -0.9610380743458045 y[1] (numeric) = -0.9626191071027335 absolute error = 0.001581032756929002 relative error = 0.164513019737042 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2900406895876974 y[1] (closed_form) = -0.9582322394413051 y[1] (numeric) = -0.9600445884894616 absolute error = 0.001812349048156525 relative error = 0.1891346349621059 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3000185540859524 y[1] (closed_form) = -0.955331005853852 y[1] (numeric) = -0.9573991308931784 absolute error = 0.002068125039326407 relative error = 0.2164825622379928 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3099964185842074 y[1] (closed_form) = -0.9523346624214241 y[1] (numeric) = -0.9546846813784784 absolute error = 0.002350018957054334 relative error = 0.2467639843202947 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3201254628475875 y[1] (closed_form) = -0.9491959441951714 y[1] (numeric) = -0.951860602114688 absolute error = 0.002664657919516644 relative error = 0.2807279082693535 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3301033273458425 y[1] (closed_form) = -0.9460088559721541 y[1] (numeric) = -0.9490132925923926 absolute error = 0.003004436620238526 relative error = 0.3175907499461044 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3400811918440975 y[1] (closed_form) = -0.9427275859890085 y[1] (numeric) = -0.9461032394567941 absolute error = 0.003375653467785567 relative error = 0.3580730550325621 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3500590563423525 y[1] (closed_form) = -0.9393524609189793 y[1] (numeric) = -0.9431326395552897 absolute error = 0.003780178636310416 relative error = 0.4024238817251007 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3600369208406075 y[1] (closed_form) = -0.9358838167792378 y[1] (numeric) = -0.9401037514124544 absolute error = 0.004219934633216571 relative error = 0.4509036867139242 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3700147853388625 y[1] (closed_form) = -0.9323219988974288 y[1] (numeric) = -0.9370188950051886 absolute error = 0.004696896107759807 relative error = 0.5037847560514921 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3799926498371174 y[1] (closed_form) = -0.9286673618772914 y[1] (numeric) = -0.9338804515317505 absolute error = 0.005213089654459102 relative error = 0.5613516602888784 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3901216941004975 y[1] (closed_form) = -0.9248627863215301 y[1] (numeric) = -0.930642155599213 absolute error = 0.005779369277682966 relative error = 0.6248893742032084 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4000995585987525 y[1] (closed_form) = -0.9210222194937214 y[1] (numeric) = -0.9274032078444917 absolute error = 0.006380988350770278 relative error = 0.6928158969148276 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4100774230970075 y[1] (closed_form) = -0.9170899584992022 y[1] (numeric) = -0.924118220849062 absolute error = 0.007028262349859871 relative error = 0.7663656421842705 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4200552875952625 y[1] (closed_form) = -0.9130663948218991 y[1] (numeric) = -0.9207898191760497 absolute error = 0.007723424354150632 relative error = 0.8458776270763034 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4300331520935175 y[1] (closed_form) = -0.9089519290355562 y[1] (numeric) = -0.9174206873601405 absolute error = 0.008468758324584269 relative error = 0.9317058530884079 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4400110165917725 y[1] (closed_form) = -0.9047469707638544 y[1] (numeric) = -0.9140135696403139 absolute error = 0.009266598876459531 relative error = 1.024219939486062 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4499888810900275 y[1] (closed_form) = -0.9004519386396306 y[1] (numeric) = -0.9105712696866378 absolute error = 0.01011933104700724 relative error = 1.123805792710619 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4601179253534076 y[1] (closed_form) = -0.8960001385578108 y[1] (numeric) = -0.9070437710378043 absolute error = 0.01104363247999351 relative error = 1.232548077254674 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4700957898516626 y[1] (closed_form) = -0.8915249021949192 y[1] (numeric) = -0.9035393313017669 absolute error = 0.01201442910684769 relative error = 1.347626866873642 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4800736543499176 y[1] (closed_form) = -0.8869609083283776 y[1] (numeric) = -0.9000085197124288 absolute error = 0.01304761138405119 relative error = 1.471046949367988 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4900515188481726 y[1] (closed_form) = -0.8823086113355132 y[1] (numeric) = -0.8964543756949189 absolute error = 0.01414576435940573 relative error = 1.603267176322113 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5000293833464275 y[1] (closed_form) = -0.8775684743848436 y[1] (numeric) = -0.8928799966465989 absolute error = 0.01531152226175525 relative error = 1.74476667162506 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5100072478446862 y[1] (closed_form) = -0.8727409693899634 y[1] (numeric) = -0.8892885376286938 absolute error = 0.01654756823873038 relative error = 1.896045770636499 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5199851123429449 y[1] (closed_form) = -0.8678265769625666 y[1] (numeric) = -0.8856832110521851 absolute error = 0.01785663408961846 relative error = 2.057627014848694 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5301141566063287 y[1] (closed_form) = -0.8627493549223337 y[1] (numeric) = -0.8820124352254968 absolute error = 0.01926308030316304 relative error = 2.232755109379031 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5400920211045873 y[1] (closed_form) = -0.8576613663705422 y[1] (numeric) = -0.8783891542490867 absolute error = 0.02072778787854446 relative error = 2.416779942678363 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.550069885602846 y[1] (closed_form) = -0.852487991665578 y[1] (numeric) = -0.8747620355011109 absolute error = 0.02227404383553289 relative error = 2.612827870104563 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5600477501011046 y[1] (closed_form) = -0.8472297458528683 y[1] (numeric) = -0.8711345183832016 absolute error = 0.0239047725303333 relative error = 2.821521865508798 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5700256145993633 y[1] (closed_form) = -0.8418871524273495 y[1] (numeric) = -0.8675100979859787 absolute error = 0.02562294555862921 relative error = 3.043513074733652 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.580003479097622 y[1] (closed_form) = -0.8364607432813493 y[1] (numeric) = -0.8638923247410869 absolute error = 0.02743158145973756 relative error = 3.279482232737701 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5901325233610057 y[1] (closed_form) = -0.8308669409710169 y[1] (numeric) = -0.8602302423495398 absolute error = 0.02936330137852294 relative error = 3.534055807324175 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6001103878592644 y[1] (closed_form) = -0.8252732802073619 y[1] (numeric) = -0.8566368735213301 absolute error = 0.03136359331396821 relative error = 3.800388800433191 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6100882523575231 y[1] (closed_form) = -0.8195974577497375 y[1] (numeric) = -0.8530611883173806 absolute error = 0.03346373056764318 relative error = 4.082947092042014 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6200661168557817 y[1] (closed_form) = -0.8138400386657387 y[1] (numeric) = -0.8495069557578873 absolute error = 0.03566691709214853 relative error = 4.382546372457067 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6300439813540404 y[1] (closed_form) = -0.8080015961464723 y[1] (numeric) = -0.8459779983766103 absolute error = 0.03797640223013798 relative error = 4.700040496362303 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.640021845852299 y[1] (closed_form) = -0.8020827114494914 y[1] (numeric) = -0.8424781918403188 absolute error = 0.04039548039082741 relative error = 5.036323537983549 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6499997103505577 y[1] (closed_form) = -0.7960839738409273 y[1] (numeric) = -0.8390114645629361 absolute error = 0.04292749072200874 relative error = 5.392331981624149 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6601287546139415 y[1] (closed_form) = -0.7899132833258593 y[1] (numeric) = -0.8355301384376372 absolute error = 0.04561685511177793 relative error = 5.774919358199958 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6701066191122002 y[1] (closed_form) = -0.7837554524512488 y[1] (numeric) = -0.8321422178460481 absolute error = 0.04838676539479936 relative error = 6.173707020916593 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6800844836104588 y[1] (closed_form) = -0.7775195932711357 y[1] (numeric) = -0.8287995365786215 absolute error = 0.05127994330748575 relative error = 6.595324896153899 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6900623481087175 y[1] (closed_form) = -0.7712063266086653 y[1] (numeric) = -0.8255062308468456 absolute error = 0.05429990423818032 relative error = 7.040904925788274 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7000402126069761 y[1] (closed_form) = -0.764816280993436 y[1] (numeric) = -0.8222664875958571 absolute error = 0.05745020660242106 relative error = 7.511634889335486 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7100180771052348 y[1] (closed_form) = -0.7583500925989251 y[1] (numeric) = -0.819084544087602 absolute error = 0.06073445148867695 relative error = 8.008761663170006 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7199959416034935 y[1] (closed_form) = -0.7518084051791528 y[1] (numeric) = -0.8159646874789865 absolute error = 0.06415628229983372 relative error = 8.533594710815391 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7301249858668772 y[1] (closed_form) = -0.7450910472453037 y[1] (numeric) = -0.8128655236840325 absolute error = 0.0677744764387288 relative error = 9.096133511374168 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7401028503651359 y[1] (closed_form) = -0.7383992040659594 y[1] (numeric) = -0.8098840066324351 absolute error = 0.07148480256647571 relative error = 9.681050869617426 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7500807148633946 y[1] (closed_form) = -0.7316338481110449 y[1] (numeric) = -0.8069778005854693 absolute error = 0.07534395247442438 relative error = 10.29804083954696 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7600585793616532 y[1] (closed_form) = -0.724795652918792 y[1] (numeric) = -0.8041513886889369 absolute error = 0.07935573577014488 relative error = 10.94870470739925 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7700364438599119 y[1] (closed_form) = -0.7178852992790844 y[1] (numeric) = -0.8014093017939024 absolute error = 0.08352400251481795 relative error = 11.6347280824241 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7800143083581705 y[1] (closed_form) = -0.7109034751656814 y[1] (numeric) = -0.7987561180056163 absolute error = 0.08785264283993488 relative error = 12.35788625445391 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7899921728564292 y[1] (closed_form) = -0.703850875667725 y[1] (numeric) = -0.796196462227733 absolute error = 0.09234558656000802 relative error = 13.12004996404987 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.800121217119813 y[1] (closed_form) = -0.6966197483895978 y[1] (numeric) = -0.7936984904214829 absolute error = 0.09707874203188505 relative error = 13.93568618407756 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8100990816180716 y[1] (closed_form) = -0.6894266660222187 y[1] (numeric) = -0.7913415461133658 absolute error = 0.1019148800911471 relative error = 14.78255558044554 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8200769461163303 y[1] (closed_form) = -0.6821649464359852 y[1] (numeric) = -0.7890923531956973 absolute error = 0.106927406759712 relative error = 15.67471435147191 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.830054810614589 y[1] (closed_form) = -0.6748353125855803 y[1] (numeric) = -0.7869557197925091 absolute error = 0.1121204072069288 relative error = 16.61448432171517 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8400326751128476 y[1] (closed_form) = -0.6674384941870235 y[1] (numeric) = -0.7849364984710747 absolute error = 0.1174980042840512 relative error = 17.60431939532798 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8500105396111063 y[1] (closed_form) = -0.6599752276450238 y[1] (numeric) = -0.7830395857588059 absolute error = 0.1230643581137821 relative error = 18.64681475286734 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 2 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8599884041093649 y[1] (closed_form) = -0.6524462559796647 y[1] (numeric) = -0.7812699216557685 absolute error = 0.1288236656761038 relative error = 19.74471682463283 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 2 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8701174483727487 y[1] (closed_form) = -0.6447367736029017 y[1] (numeric) = -0.7796087223991544 absolute error = 0.1348719487962526 relative error = 20.91891672977867 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 2 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8800953128710074 y[1] (closed_form) = -0.6370776799692329 y[1] (numeric) = -0.7781106654604951 absolute error = 0.1410329854912622 relative error = 22.13748651468581 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 2 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8900731773692661 y[1] (closed_form) = -0.6293551608223048 y[1] (numeric) = -0.776755010127556 absolute error = 0.1473998493052512 relative error = 23.42077390970482 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 2 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9000510418675247 y[1] (closed_form) = -0.6215699849926005 y[1] (numeric) = -0.7755468659549428 absolute error = 0.1539768809623423 relative error = 24.7722516659448 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 2 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9100289063657834 y[1] (closed_form) = -0.6137229275485117 y[1] (numeric) = -0.7744913834608267 absolute error = 0.160768455912315 relative error = 26.1956085874936 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 2 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.920006770864042 y[1] (closed_form) = -0.6058147697191753 y[1] (numeric) = -0.7735937536141727 absolute error = 0.1677789838949975 relative error = 27.69476616966127 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 2 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9301358151274258 y[1] (closed_form) = -0.597725104659467 y[1] (numeric) = -0.7728493592055004 absolute error = 0.1751242545460333 relative error = 29.29846064367737 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 2 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9401136796256845 y[1] (closed_form) = -0.5896962183177912 y[1] (numeric) = -0.7722857583251959 absolute error = 0.1825895400074047 relative error = 30.9633221878669 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 2 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9500915441239431 y[1] (closed_form) = -0.5816086236168526 y[1] (numeric) = -0.7718959012550644 absolute error = 0.1902872776382117 relative error = 32.71740994053204 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 2 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9600694086222018 y[1] (closed_form) = -0.5734631257329447 y[1] (numeric) = -0.7716851361369088 absolute error = 0.1982220104039641 relative error = 34.56578139189265 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 2 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9700472731204605 y[1] (closed_form) = -0.565260535607025 y[1] (numeric) = -0.7716588489320086 absolute error = 0.2063983133249836 relative error = 36.51383748262833 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 2 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9800251376187191 y[1] (closed_form) = -0.5570016698639816 y[1] (numeric) = -0.7718224628849104 absolute error = 0.2148207930209288 relative error = 38.5673517053167 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 2 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9900030021169778 y[1] (closed_form) = -0.5486873507313308 y[1] (numeric) = -0.7721814379835068 absolute error = 0.223494087252176 relative error = 40.73250220809477 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 2 h = 0.0001511797651250803 NO POLE (given) for Equation 1 NO 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 , 3 ) = neg ( diff ( y , x , 1 ) ) ; Iterations = 7654 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100 %