##############ECHO OF PROBLEM################# ##############temp/sub_c_sinpostode.ode################# diff ( y , x , 1 ) = 1.0 - sin ( x ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=40; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(0.1); x_end=c(5.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_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(c(2.0) + cos(c(x)) + c(x)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 3.095004165278026 y[1] (numeric) = 3.095004165278026 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 = 0.09933 Order of pole (three term test) = 32.01 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (closed_form) = 3.103956097956697 y[1] (numeric) = 3.103956097956697 absolute error = 0 relative error = 0 % 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 = 0.1091 Order of pole (three term test) = 32.01 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (closed_form) = 3.112808635853866 y[1] (numeric) = 3.112808635853866 absolute error = 0 relative error = 0 % 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 = 0.1189 Order of pole (three term test) = 32.01 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (closed_form) = 3.121561893714788 y[1] (numeric) = 3.121561893714788 absolute error = 0 relative error = 0 % 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 = 0.1285 Order of pole (three term test) = 32.02 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (closed_form) = 3.130215996212637 y[1] (numeric) = 3.130215996212637 absolute error = 0 relative error = 0 % 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 = 0.1382 Order of pole (three term test) = 32.02 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (closed_form) = 3.138771077936042 y[1] (numeric) = 3.138771077936043 absolute error = 4.440892098500626e-16 relative error = 1.414850585860762e-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 = 0.1478 Order of pole (three term test) = 32.02 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1600000000000001 y[1] (closed_form) = 3.147227283375627 y[1] (numeric) = 3.147227283375627 absolute error = 4.440892098500626e-16 relative error = 1.411049059582837e-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 = 0.1573 Order of pole (three term test) = 32.03 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1700000000000001 y[1] (closed_form) = 3.15558476690956 y[1] (numeric) = 3.155584766909561 absolute error = 4.440892098500626e-16 relative error = 1.407311933138097e-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 = 0.1667 Order of pole (three term test) = 32.03 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1800000000000001 y[1] (closed_form) = 3.163843692788121 y[1] (numeric) = 3.163843692788122 absolute error = 8.881784197001252e-16 relative error = 2.807276546956789e-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 = 0.1761 Order of pole (three term test) = 32.03 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1900000000000001 y[1] (closed_form) = 3.17200423511727 y[1] (numeric) = 3.172004235117272 absolute error = 1.332267629550188e-15 relative error = 4.20008149674155e-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 = 0.1855 Order of pole (three term test) = 32.04 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2000000000000001 y[1] (closed_form) = 3.180066577841242 y[1] (numeric) = 3.180066577841243 absolute error = 1.332267629550188e-15 relative error = 4.189433135876624e-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 = 0.1947 Order of pole (three term test) = 32.04 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2100000000000001 y[1] (closed_form) = 3.188030914724148 y[1] (numeric) = 3.188030914724149 absolute error = 8.881784197001252e-16 relative error = 2.785978064384538e-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 = 0.2039 Order of pole (three term test) = 32.04 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2200000000000001 y[1] (closed_form) = 3.195897449330606 y[1] (numeric) = 3.195897449330606 absolute error = 4.440892098500626e-16 relative error = 1.389560262464238e-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 = 0.213 Order of pole (three term test) = 32.05 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2300000000000001 y[1] (closed_form) = 3.203666395005375 y[1] (numeric) = 3.203666395005376 absolute error = 8.881784197001252e-16 relative error = 2.772381110233031e-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 = 0.222 Order of pole (three term test) = 32.05 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2400000000000001 y[1] (closed_form) = 3.21133797485203 y[1] (numeric) = 3.21133797485203 absolute error = 0 relative error = 0 % 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 = 0.2309 Order of pole (three term test) = 32.06 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2500000000000001 y[1] (closed_form) = 3.218912421710645 y[1] (numeric) = 3.218912421710645 absolute error = 4.440892098500626e-16 relative error = 1.379625015128737e-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 = 0.2397 Order of pole (three term test) = 32.06 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2600000000000001 y[1] (closed_form) = 3.226389978134514 y[1] (numeric) = 3.226389978134514 absolute error = 0 relative error = 0 % 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 = 0.2484 Order of pole (three term test) = 32.07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2700000000000001 y[1] (closed_form) = 3.233770896365891 y[1] (numeric) = 3.233770896365891 absolute error = 4.440892098500626e-16 relative error = 1.373285937940532e-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 = 0.2571 Order of pole (three term test) = 32.07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2800000000000001 y[1] (closed_form) = 3.241055438310771 y[1] (numeric) = 3.241055438310771 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 = 0.2656 Order of pole (three term test) = 32.08 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2900000000000001 y[1] (closed_form) = 3.248243875512697 y[1] (numeric) = 3.248243875512697 absolute error = 4.440892098500626e-16 relative error = 1.367167081258541e-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 = 0.274 Order of pole (three term test) = 32.08 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3000000000000002 y[1] (closed_form) = 3.255336489125606 y[1] (numeric) = 3.255336489125606 absolute error = 4.440892098500626e-16 relative error = 1.364188345301737e-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] = 0.3100000000000002 y[1] (closed_form) = 3.262333569885713 y[1] (numeric) = 3.262333569885713 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] = 0.3200000000000002 y[1] (closed_form) = 3.269235418082441 y[1] (numeric) = 3.269235418082441 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] = 0.3300000000000002 y[1] (closed_form) = 3.276042343528387 y[1] (numeric) = 3.276042343528387 absolute error = 4.440892098500626e-16 relative error = 1.355566147450239e-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] = 0.3400000000000002 y[1] (closed_form) = 3.282754665528346 y[1] (numeric) = 3.282754665528346 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 = 0.3144 Order of pole (three term test) = 32.11 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3500000000000002 y[1] (closed_form) = 3.289372712847379 y[1] (numeric) = 3.289372712847379 absolute error = 4.440892098500626e-16 relative error = 1.350072638821296e-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 = 0.3221 Order of pole (three term test) = 32.12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3600000000000002 y[1] (closed_form) = 3.295896823677935 y[1] (numeric) = 3.295896823677935 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 = 0.3297 Order of pole (three term test) = 32.12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3700000000000002 y[1] (closed_form) = 3.302327345606034 y[1] (numeric) = 3.302327345606034 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] = 0.3800000000000002 y[1] (closed_form) = 3.30866463557651 y[1] (numeric) = 3.30866463557651 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 = 0.3445 Order of pole (three term test) = 32.14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3900000000000002 y[1] (closed_form) = 3.314909059857313 y[1] (numeric) = 3.314909059857313 absolute error = 4.440892098500626e-16 relative error = 1.339672376620727e-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] = 0.4000000000000002 y[1] (closed_form) = 3.321060994002885 y[1] (numeric) = 3.321060994002885 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 = 0.3587 Order of pole (three term test) = 32.15 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4100000000000003 y[1] (closed_form) = 3.327120822816605 y[1] (numeric) = 3.327120822816606 absolute error = 8.881784197001252e-16 relative error = 2.669510567843549e-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] = 0.4200000000000003 y[1] (closed_form) = 3.333088940312309 y[1] (numeric) = 3.333088940312309 absolute error = 4.440892098500626e-16 relative error = 1.332365315785578e-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] = 0.4300000000000003 y[1] (closed_form) = 3.338965749674885 y[1] (numeric) = 3.338965749674887 absolute error = 1.332267629550188e-15 relative error = 3.990060783582194e-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 = 0.3789 Order of pole (three term test) = 32.17 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4400000000000003 y[1] (closed_form) = 3.344751663219964 y[1] (numeric) = 3.344751663219965 absolute error = 8.881784197001252e-16 relative error = 2.655439055361986e-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] = 0.4500000000000003 y[1] (closed_form) = 3.350447102352677 y[1] (numeric) = 3.350447102352679 absolute error = 1.77635683940025e-15 relative error = 5.30185012666786e-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] = 0.4600000000000003 y[1] (closed_form) = 3.356052497525525 y[1] (numeric) = 3.356052497525526 absolute error = 8.881784197001252e-16 relative error = 2.64649739643523e-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] = 0.4700000000000003 y[1] (closed_form) = 3.361568288195329 y[1] (numeric) = 3.361568288195329 absolute error = 4.440892098500626e-16 relative error = 1.321077460807657e-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] = 0.4800000000000003 y[1] (closed_form) = 3.366994922779285 y[1] (numeric) = 3.366994922779285 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 = 0.4096 Order of pole (three term test) = 32.21 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4900000000000003 y[1] (closed_form) = 3.372332858610122 y[1] (numeric) = 3.372332858610121 absolute error = 4.440892098500626e-16 relative error = 1.316860548673983e-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] = 0.5000000000000003 y[1] (closed_form) = 3.377582561890373 y[1] (numeric) = 3.377582561890372 absolute error = 8.881784197001252e-16 relative error = 2.629627561799785e-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] = 0.5100000000000003 y[1] (closed_form) = 3.382744507645751 y[1] (numeric) = 3.382744507645751 absolute error = 8.881784197001252e-16 relative error = 2.62561484526143e-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] = 0.5200000000000004 y[1] (closed_form) = 3.38781917967765 y[1] (numeric) = 3.387819179677649 absolute error = 8.881784197001252e-16 relative error = 2.621681892079716e-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] = 0.5300000000000004 y[1] (closed_form) = 3.392807070514761 y[1] (numeric) = 3.392807070514759 absolute error = 2.220446049250313e-15 relative error = 6.544569152036765e-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] = 0.5400000000000004 y[1] (closed_form) = 3.397708681363824 y[1] (numeric) = 3.397708681363822 absolute error = 2.220446049250313e-15 relative error = 6.5351278096009e-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] = 0.5500000000000004 y[1] (closed_form) = 3.402524522059506 y[1] (numeric) = 3.402524522059504 absolute error = 2.220446049250313e-15 relative error = 6.525878167385858e-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] = 0.5600000000000004 y[1] (closed_form) = 3.407255111013416 y[1] (numeric) = 3.407255111013415 absolute error = 1.77635683940025e-15 relative error = 5.213454177993471e-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] = 0.5700000000000004 y[1] (closed_form) = 3.411900975162269 y[1] (numeric) = 3.411900975162267 absolute error = 1.77635683940025e-15 relative error = 5.206355202954762e-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] = 0.5800000000000004 y[1] (closed_form) = 3.416462649915187 y[1] (numeric) = 3.416462649915186 absolute error = 1.332267629550188e-15 relative error = 3.899552742317441e-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] = 0.5900000000000004 y[1] (closed_form) = 3.420940679100164 y[1] (numeric) = 3.420940679100162 absolute error = 1.332267629550188e-15 relative error = 3.894448207446335e-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] = 0.6000000000000004 y[1] (closed_form) = 3.425335614909679 y[1] (numeric) = 3.425335614909677 absolute error = 1.332267629550188e-15 relative error = 3.889451368651705e-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] = 0.6100000000000004 y[1] (closed_form) = 3.42964801784548 y[1] (numeric) = 3.429648017845479 absolute error = 4.440892098500626e-16 relative error = 1.29485360462454e-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] = 0.6200000000000004 y[1] (closed_form) = 3.433878456662534 y[1] (numeric) = 3.433878456662534 absolute error = 4.440892098500626e-16 relative error = 1.293258382481258e-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] = 0.6300000000000004 y[1] (closed_form) = 3.438027508312152 y[1] (numeric) = 3.438027508312152 absolute error = 4.440892098500626e-16 relative error = 1.291697663198982e-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] = 0.6400000000000005 y[1] (closed_form) = 3.442095757884293 y[1] (numeric) = 3.442095757884294 absolute error = 8.881784197001252e-16 relative error = 2.580341983995384e-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] = 0.6500000000000005 y[1] (closed_form) = 3.446083798549056 y[1] (numeric) = 3.446083798549056 absolute error = 4.440892098500626e-16 relative error = 1.288677919083229e-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] = 0.6600000000000005 y[1] (closed_form) = 3.449992231497365 y[1] (numeric) = 3.449992231497366 absolute error = 4.440892098500626e-16 relative error = 1.287217999494796e-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] = 0.6700000000000005 y[1] (closed_form) = 3.453821665880849 y[1] (numeric) = 3.45382166588085 absolute error = 4.440892098500626e-16 relative error = 1.285790792955733e-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] = 0.6800000000000005 y[1] (closed_form) = 3.457572718750928 y[1] (numeric) = 3.457572718750928 absolute error = 4.440892098500626e-16 relative error = 1.284395863727467e-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] = 0.6900000000000005 y[1] (closed_form) = 3.461246014997107 y[1] (numeric) = 3.461246014997108 absolute error = 8.881784197001252e-16 relative error = 2.566065560933171e-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] = 0.7000000000000005 y[1] (closed_form) = 3.464842187284489 y[1] (numeric) = 3.464842187284489 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 = 0.4927 Order of pole (three term test) = 32.42 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7100000000000005 y[1] (closed_form) = 3.468361875990508 y[1] (numeric) = 3.468361875990509 absolute error = 4.440892098500626e-16 relative error = 1.280400447612572e-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] = 0.7200000000000005 y[1] (closed_form) = 3.471805729140895 y[1] (numeric) = 3.471805729140896 absolute error = 8.881784197001252e-16 relative error = 2.558260712127768e-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] = 0.7300000000000005 y[1] (closed_form) = 3.47517440234487 y[1] (numeric) = 3.475174402344871 absolute error = 4.440892098500626e-16 relative error = 1.277890426306127e-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] = 0.7400000000000005 y[1] (closed_form) = 3.478468558729588 y[1] (numeric) = 3.478468558729587 absolute error = 8.881784197001252e-16 relative error = 2.553360493862009e-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 = 0.4979 Order of pole (three term test) = 32.45 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7500000000000006 y[1] (closed_form) = 3.481688868873821 y[1] (numeric) = 3.481688868873821 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 = 0.4987 Order of pole (three term test) = 32.46 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7600000000000006 y[1] (closed_form) = 3.484836010740906 y[1] (numeric) = 3.484836010740905 absolute error = 4.440892098500626e-16 relative error = 1.274347511565244e-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) = 32.47 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7700000000000006 y[1] (closed_form) = 3.487910669610943 y[1] (numeric) = 3.487910669610943 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] = 0.7800000000000006 y[1] (closed_form) = 3.490913538012278 y[1] (numeric) = 3.490913538012277 absolute error = 8.881784197001252e-16 relative error = 2.544257856944383e-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 = 0.5 Order of pole (three term test) = 32.49 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7900000000000006 y[1] (closed_form) = 3.493845315652236 y[1] (numeric) = 3.493845315652236 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] = 0.8000000000000006 y[1] (closed_form) = 3.496706709347166 y[1] (numeric) = 3.496706709347165 absolute error = 4.440892098500626e-16 relative error = 1.270021327962544e-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 = 0.4998 Order of pole (three term test) = 32.51 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8100000000000006 y[1] (closed_form) = 3.499498432951747 y[1] (numeric) = 3.499498432951747 absolute error = 4.440892098500626e-16 relative error = 1.269008168909176e-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] = 0.8200000000000006 y[1] (closed_form) = 3.502221207287614 y[1] (numeric) = 3.502221207287613 absolute error = 4.440892098500626e-16 relative error = 1.268021588487836e-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] = 0.8300000000000006 y[1] (closed_form) = 3.504875760071267 y[1] (numeric) = 3.504875760071267 absolute error = 4.440892098500626e-16 relative error = 1.267061203450569e-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] = 0.8400000000000006 y[1] (closed_form) = 3.507462825841309 y[1] (numeric) = 3.507462825841309 absolute error = 4.440892098500626e-16 relative error = 1.266126633127016e-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] = 0.8500000000000006 y[1] (closed_form) = 3.509983145884982 y[1] (numeric) = 3.509983145884983 absolute error = 8.881784197001252e-16 relative error = 2.530434998644947e-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] = 0.8600000000000007 y[1] (closed_form) = 3.512437468164052 y[1] (numeric) = 3.512437468164053 absolute error = 8.881784197001252e-16 relative error = 2.528666852436167e-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] = 0.8700000000000007 y[1] (closed_form) = 3.514826547240001 y[1] (numeric) = 3.514826547240003 absolute error = 1.77635683940025e-15 relative error = 5.053896161092573e-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] = 0.8800000000000007 y[1] (closed_form) = 3.51715114419858 y[1] (numeric) = 3.517151144198582 absolute error = 1.77635683940025e-15 relative error = 5.05055588051793e-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] = 0.8900000000000007 y[1] (closed_form) = 3.519412026573697 y[1] (numeric) = 3.519412026573698 absolute error = 1.332267629550188e-15 relative error = 3.785483539553648e-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] = 0.9000000000000007 y[1] (closed_form) = 3.521609968270665 y[1] (numeric) = 3.521609968270665 absolute error = 4.440892098500626e-16 relative error = 1.261040302166508e-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 = 0.4869 Order of pole (three term test) = 32.61 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9100000000000007 y[1] (closed_form) = 3.523745749488812 y[1] (numeric) = 3.523745749488813 absolute error = 8.881784197001252e-16 relative error = 2.520551943422629e-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 = 0.4846 Order of pole (three term test) = 32.62 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9200000000000007 y[1] (closed_form) = 3.525820156643463 y[1] (numeric) = 3.525820156643464 absolute error = 8.881784197001252e-16 relative error = 2.51906898321683e-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 = 0.482 Order of pole (three term test) = 32.63 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9300000000000007 y[1] (closed_form) = 3.527833982287298 y[1] (numeric) = 3.527833982287299 absolute error = 4.440892098500626e-16 relative error = 1.258815500048372e-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 = 0.4792 Order of pole (three term test) = 32.64 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9400000000000007 y[1] (closed_form) = 3.529788025031098 y[1] (numeric) = 3.529788025031099 absolute error = 8.881784197001252e-16 relative error = 2.516237273744789e-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 = 0.4763 Order of pole (three term test) = 32.65 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9500000000000007 y[1] (closed_form) = 3.531683089463884 y[1] (numeric) = 3.531683089463885 absolute error = 1.332267629550188e-15 relative error = 3.772330630471232e-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 = 0.4732 Order of pole (three term test) = 32.66 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9600000000000007 y[1] (closed_form) = 3.533519986072457 y[1] (numeric) = 3.533519986072458 absolute error = 1.332267629550188e-15 relative error = 3.770369588403027e-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 = 0.4698 Order of pole (three term test) = 32.67 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9700000000000008 y[1] (closed_form) = 3.535299531160354 y[1] (numeric) = 3.535299531160356 absolute error = 1.77635683940025e-15 relative error = 5.024628956452852e-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 = 0.4663 Order of pole (three term test) = 32.68 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9800000000000008 y[1] (closed_form) = 3.537022546766218 y[1] (numeric) = 3.537022546766218 absolute error = 8.881784197001252e-16 relative error = 2.511090636140155e-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 = 0.4626 Order of pole (three term test) = 32.69 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9900000000000008 y[1] (closed_form) = 3.538689860581588 y[1] (numeric) = 3.538689860581589 absolute error = 1.77635683940025e-15 relative error = 5.019814986296381e-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 = 0.4587 Order of pole (three term test) = 32.7 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.000000000000001 y[1] (closed_form) = 3.54030230586814 y[1] (numeric) = 3.540302305868142 absolute error = 1.332267629550188e-15 relative error = 3.763146518143156e-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 = 0.4546 Order of pole (three term test) = 32.71 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.01 y[1] (closed_form) = 3.541860721374356 y[1] (numeric) = 3.541860721374357 absolute error = 1.332267629550188e-15 relative error = 3.761490737086989e-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 = 0.4504 Order of pole (three term test) = 32.72 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.019999999999998 y[1] (closed_form) = 3.54336595125165 y[1] (numeric) = 3.543365951251652 absolute error = 2.220446049250313e-15 relative error = 6.26648807884483e-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 = 0.446 Order of pole (three term test) = 32.73 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.029999999999997 y[1] (closed_form) = 3.544818844969955 y[1] (numeric) = 3.544818844969958 absolute error = 3.108624468950438e-15 relative error = 8.769487539148948e-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 = 0.4414 Order of pole (three term test) = 32.73 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.039999999999996 y[1] (closed_form) = 3.546220257232778 y[1] (numeric) = 3.546220257232781 absolute error = 3.108624468950438e-15 relative error = 8.76602197116823e-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 = 0.4366 Order of pole (three term test) = 32.74 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.049999999999995 y[1] (closed_form) = 3.547571047891727 y[1] (numeric) = 3.54757104789173 absolute error = 3.108624468950438e-15 relative error = 8.762684177383429e-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 = 0.4316 Order of pole (three term test) = 32.75 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.059999999999994 y[1] (closed_form) = 3.548872081860527 y[1] (numeric) = 3.54887208186053 absolute error = 3.108624468950438e-15 relative error = 8.759471734243842e-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 = 0.4265 Order of pole (three term test) = 32.76 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.069999999999993 y[1] (closed_form) = 3.550124229028533 y[1] (numeric) = 3.550124229028536 absolute error = 3.108624468950438e-15 relative error = 8.756382223280935e-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 = 0.4212 Order of pole (three term test) = 32.77 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.079999999999992 y[1] (closed_form) = 3.551328364173739 y[1] (numeric) = 3.551328364173742 absolute error = 3.108624468950438e-15 relative error = 8.753413230695999e-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 = 0.4157 Order of pole (three term test) = 32.78 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.089999999999991 y[1] (closed_form) = 3.5524853668753 y[1] (numeric) = 3.552485366875303 absolute error = 3.552713678800501e-15 relative error = 1.000064268223968e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.4101 Order of pole (three term test) = 32.79 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.09999999999999 y[1] (closed_form) = 3.553596121425576 y[1] (numeric) = 3.55359612142558 absolute error = 3.552713678800501e-15 relative error = 9.997516761627033e-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 = 0.4042 Order of pole (three term test) = 32.79 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.109999999999989 y[1] (closed_form) = 3.554661516741706 y[1] (numeric) = 3.554661516741709 absolute error = 3.108624468950438e-15 relative error = 8.745205286943562e-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 = 0.3983 Order of pole (three term test) = 32.8 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.119999999999987 y[1] (closed_form) = 3.555682446276711 y[1] (numeric) = 3.555682446276715 absolute error = 3.996802888650564e-15 relative error = 1.124060696937593e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.3922 Order of pole (three term test) = 32.81 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.129999999999986 y[1] (closed_form) = 3.556659807930156 y[1] (numeric) = 3.556659807930159 absolute error = 3.108624468950438e-15 relative error = 8.740291837918403e-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 = 0.3859 Order of pole (three term test) = 32.82 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.139999999999985 y[1] (closed_form) = 3.557594503958357 y[1] (numeric) = 3.55759450395836 absolute error = 3.108624468950438e-15 relative error = 8.73799547838189e-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 = 0.3794 Order of pole (three term test) = 32.83 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.149999999999984 y[1] (closed_form) = 3.558487440884156 y[1] (numeric) = 3.558487440884159 absolute error = 2.664535259100376e-15 relative error = 7.487831005069767e-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 = 0.3729 Order of pole (three term test) = 32.83 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.159999999999983 y[1] (closed_form) = 3.559339529406272 y[1] (numeric) = 3.559339529406276 absolute error = 3.552713678800501e-15 relative error = 9.98138460646693e-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 = 0.3661 Order of pole (three term test) = 32.84 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.169999999999982 y[1] (closed_form) = 3.560151684308229 y[1] (numeric) = 3.560151684308233 absolute error = 4.440892098500626e-15 relative error = 1.247388452035445e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.3592 Order of pole (three term test) = 32.85 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.179999999999981 y[1] (closed_form) = 3.560924824366881 y[1] (numeric) = 3.560924824366886 absolute error = 5.773159728050814e-15 relative error = 1.62125290838659e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.3522 Order of pole (three term test) = 32.85 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.18999999999998 y[1] (closed_form) = 3.561659872260532 y[1] (numeric) = 3.561659872260538 absolute error = 5.773159728050814e-15 relative error = 1.620918317612029e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.345 Order of pole (three term test) = 32.86 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.199999999999979 y[1] (closed_form) = 3.562357754476672 y[1] (numeric) = 3.562357754476679 absolute error = 7.105427357601002e-15 relative error = 1.994585565885935e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.3377 Order of pole (three term test) = 32.87 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.209999999999978 y[1] (closed_form) = 3.563019401219329 y[1] (numeric) = 3.563019401219336 absolute error = 7.105427357601002e-15 relative error = 1.994215174682854e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.3303 Order of pole (three term test) = 32.88 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.219999999999976 y[1] (closed_form) = 3.563645746316046 y[1] (numeric) = 3.563645746316053 absolute error = 7.105427357601002e-15 relative error = 1.993864672139847e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.3227 Order of pole (three term test) = 32.88 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.229999999999975 y[1] (closed_form) = 3.564237727124501 y[1] (numeric) = 3.564237727124509 absolute error = 7.549516567451064e-15 relative error = 2.118129357645777e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.315 Order of pole (three term test) = 32.89 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.239999999999974 y[1] (closed_form) = 3.564796284438775 y[1] (numeric) = 3.564796284438783 absolute error = 7.993605777301127e-15 relative error = 2.242373796279807e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.3072 Order of pole (three term test) = 32.89 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.249999999999973 y[1] (closed_form) = 3.565322362395268 y[1] (numeric) = 3.565322362395276 absolute error = 7.993605777301127e-15 relative error = 2.242042924817276e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.2992 Order of pole (three term test) = 32.9 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.259999999999972 y[1] (closed_form) = 3.565816908378288 y[1] (numeric) = 3.565816908378296 absolute error = 8.43769498715119e-15 relative error = 2.366272639328698e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.2912 Order of pole (three term test) = 32.91 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.269999999999971 y[1] (closed_form) = 3.566280872925318 y[1] (numeric) = 3.566280872925326 absolute error = 8.43769498715119e-15 relative error = 2.365964792960907e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.283 Order of pole (three term test) = 32.91 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.27999999999997 y[1] (closed_form) = 3.566715209631954 y[1] (numeric) = 3.566715209631963 absolute error = 8.881784197001252e-15 relative error = 2.490185976445749e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.2747 Order of pole (three term test) = 32.92 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.289999999999969 y[1] (closed_form) = 3.567120875056556 y[1] (numeric) = 3.567120875056565 absolute error = 8.881784197001252e-15 relative error = 2.489902783813131e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.2663 Order of pole (three term test) = 32.92 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.299999999999968 y[1] (closed_form) = 3.567498828624586 y[1] (numeric) = 3.567498828624595 absolute error = 8.881784197001252e-15 relative error = 2.489638994618966e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.2578 Order of pole (three term test) = 32.93 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.309999999999967 y[1] (closed_form) = 3.567850032532669 y[1] (numeric) = 3.567850032532678 absolute error = 8.881784197001252e-15 relative error = 2.489393925197142e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.2491 Order of pole (three term test) = 32.93 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.319999999999965 y[1] (closed_form) = 3.568175451652372 y[1] (numeric) = 3.568175451652381 absolute error = 9.325873406851315e-15 relative error = 2.613625235982338e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.2404 Order of pole (three term test) = 32.94 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.329999999999964 y[1] (closed_form) = 3.568476053433722 y[1] (numeric) = 3.568476053433731 absolute error = 9.325873406851315e-15 relative error = 2.61340506905675e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.2316 Order of pole (three term test) = 32.94 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.339999999999963 y[1] (closed_form) = 3.568752807808458 y[1] (numeric) = 3.568752807808468 absolute error = 9.769962616701378e-15 relative error = 2.737640610838785e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.2227 Order of pole (three term test) = 32.95 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.349999999999962 y[1] (closed_form) = 3.569006687093041 y[1] (numeric) = 3.56900668709305 absolute error = 8.881784197001252e-15 relative error = 2.488587154829758e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.2137 Order of pole (three term test) = 32.95 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.359999999999961 y[1] (closed_form) = 3.569238665891419 y[1] (numeric) = 3.569238665891428 absolute error = 8.881784197001252e-15 relative error = 2.488425411805019e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.2046 Order of pole (three term test) = 32.96 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.36999999999996 y[1] (closed_form) = 3.569449720997572 y[1] (numeric) = 3.569449720997582 absolute error = 9.325873406851315e-15 relative error = 2.612692189496639e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.1954 Order of pole (three term test) = 32.96 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.379999999999959 y[1] (closed_form) = 3.569640831297834 y[1] (numeric) = 3.569640831297844 absolute error = 9.769962616701378e-15 relative error = 2.736959564962523e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.1862 Order of pole (three term test) = 32.96 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.389999999999958 y[1] (closed_form) = 3.569812977672999 y[1] (numeric) = 3.569812977673009 absolute error = 9.325873406851315e-15 relative error = 2.612426327423582e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.1769 Order of pole (three term test) = 32.97 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.399999999999957 y[1] (closed_form) = 3.56996714290024 y[1] (numeric) = 3.56996714290025 absolute error = 9.325873406851315e-15 relative error = 2.612313512576191e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.1675 Order of pole (three term test) = 32.97 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.409999999999956 y[1] (closed_form) = 3.570104311554831 y[1] (numeric) = 3.57010431155484 absolute error = 9.769962616701378e-15 relative error = 2.736604245730406e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.158 Order of pole (three term test) = 32.97 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.419999999999954 y[1] (closed_form) = 3.570225469911685 y[1] (numeric) = 3.570225469911695 absolute error = 9.769962616701378e-15 relative error = 2.73651137695319e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.1485 Order of pole (three term test) = 32.98 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.429999999999953 y[1] (closed_form) = 3.570331605846736 y[1] (numeric) = 3.570331605846746 absolute error = 1.021405182655144e-14 relative error = 2.860813211250468e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.1389 Order of pole (three term test) = 32.98 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.439999999999952 y[1] (closed_form) = 3.570423708738145 y[1] (numeric) = 3.570423708738155 absolute error = 9.769962616701378e-15 relative error = 2.736359439018588e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.1293 Order of pole (three term test) = 32.98 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.449999999999951 y[1] (closed_form) = 3.570502769367367 y[1] (numeric) = 3.570502769367376 absolute error = 9.769962616701378e-15 relative error = 2.736298848588333e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.1196 Order of pole (three term test) = 32.99 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.45999999999995 y[1] (closed_form) = 3.570569779820069 y[1] (numeric) = 3.57056977982008 absolute error = 1.110223024625157e-14 relative error = 3.109372153710167e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.1099 Order of pole (three term test) = 32.99 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.469999999999949 y[1] (closed_form) = 3.570625733386931 y[1] (numeric) = 3.570625733386942 absolute error = 1.110223024625157e-14 relative error = 3.109323428227383e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.1001 Order of pole (three term test) = 32.99 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.479999999999948 y[1] (closed_form) = 3.57067162446431 y[1] (numeric) = 3.57067162446432 absolute error = 1.06581410364015e-14 relative error = 2.984912127841073e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.0903 Order of pole (three term test) = 32.99 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.489999999999947 y[1] (closed_form) = 3.5707084484548 y[1] (numeric) = 3.570708448454812 absolute error = 1.154631945610163e-14 relative error = 3.233621457136389e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.08045 Order of pole (three term test) = 32.99 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.499999999999946 y[1] (closed_form) = 3.570737201667702 y[1] (numeric) = 3.570737201667714 absolute error = 1.199040866595169e-14 relative error = 3.357964473093009e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.07056 Order of pole (three term test) = 32.99 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.509999999999944 y[1] (closed_form) = 3.570758881219386 y[1] (numeric) = 3.570758881219397 absolute error = 1.110223024625157e-14 relative error = 3.109207486577823e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.06065 Order of pole (three term test) = 33 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.519999999999943 y[1] (closed_form) = 3.570774484933579 y[1] (numeric) = 3.57077448493359 absolute error = 1.154631945610163e-14 relative error = 3.233561655831201e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.05071 Order of pole (three term test) = 33 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.529999999999942 y[1] (closed_form) = 3.570785011241591 y[1] (numeric) = 3.570785011241602 absolute error = 1.154631945610163e-14 relative error = 3.233552123623057e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.04075 Order of pole (three term test) = 33 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.539999999999941 y[1] (closed_form) = 3.570791459082466 y[1] (numeric) = 3.570791459082477 absolute error = 1.110223024625157e-14 relative error = 3.109179119943438e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.03078 Order of pole (three term test) = 33 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.54999999999994 y[1] (closed_form) = 3.570794827803092 y[1] (numeric) = 3.570794827803103 absolute error = 1.110223024625157e-14 relative error = 3.109176186715309e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.02079 Order of pole (three term test) = 33 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.559999999999939 y[1] (closed_form) = 3.570796117058268 y[1] (numeric) = 3.570796117058278 absolute error = 1.021405182655144e-14 relative error = 2.860441059000056e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.0108 Order of pole (three term test) = 33 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 SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE 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] = 1.569989505414941 y[1] (closed_form) = 3.570796326707362 y[1] (numeric) = 3.570796326707372 absolute error = 1.021405182655144e-14 relative error = 2.86044089105744e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 1.57999406075702 y[1] (closed_form) = 3.570796456479806 y[1] (numeric) = 3.570796456479818 absolute error = 1.154631945610163e-14 relative error = 3.233541759331844e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 1.589998616099098 y[1] (closed_form) = 3.570797506843156 y[1] (numeric) = 3.570797506843167 absolute error = 1.154631945610163e-14 relative error = 3.233540808173525e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 1.600003171441177 y[1] (closed_form) = 3.570800479051151 y[1] (numeric) = 3.570800479051162 absolute error = 1.06581410364015e-14 relative error = 2.984804415404814e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 1.610007726783255 y[1] (closed_form) = 3.570806374165177 y[1] (numeric) = 3.570806374165188 absolute error = 1.154631945610163e-14 relative error = 3.233532778377281e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 1.620012282125334 y[1] (closed_form) = 3.570816192954062 y[1] (numeric) = 3.570816192954073 absolute error = 1.110223024625157e-14 relative error = 3.109157583680307e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 1.630016837467412 y[1] (closed_form) = 3.570830935793914 y[1] (numeric) = 3.570830935793926 absolute error = 1.154631945610163e-14 relative error = 3.233510536822572e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 1.64002139280949 y[1] (closed_form) = 3.570851602567991 y[1] (numeric) = 3.570851602568003 absolute error = 1.199040866595169e-14 relative error = 3.357856892548753e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 1.650025948151569 y[1] (closed_form) = 3.570879192566622 y[1] (numeric) = 3.570879192566633 absolute error = 1.06581410364015e-14 relative error = 2.984738620838306e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 1.660030503493647 y[1] (closed_form) = 3.57091470438719 y[1] (numeric) = 3.570914704387199 absolute error = 9.325873406851315e-15 relative error = 2.611620321088499e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 1.670035058835726 y[1] (closed_form) = 3.570959135834177 y[1] (numeric) = 3.570959135834186 absolute error = 9.325873406851315e-15 relative error = 2.611587826157744e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 1.680039614177804 y[1] (closed_form) = 3.571013483819302 y[1] (numeric) = 3.571013483819311 absolute error = 9.769962616701378e-15 relative error = 2.735907512242749e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 1.690044169519883 y[1] (closed_form) = 3.571078744261731 y[1] (numeric) = 3.571078744261742 absolute error = 1.06581410364015e-14 relative error = 2.984571833798899e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 1.700048724861961 y[1] (closed_form) = 3.5711559119884 y[1] (numeric) = 3.571155911988412 absolute error = 1.154631945610163e-14 relative error = 3.233216286452388e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 1.71005328020404 y[1] (closed_form) = 3.571245980634442 y[1] (numeric) = 3.571245980634454 absolute error = 1.199040866595169e-14 relative error = 3.357486079360336e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 1.720057835546118 y[1] (closed_form) = 3.571349942543733 y[1] (numeric) = 3.571349942543747 absolute error = 1.376676550535194e-14 relative error = 3.854779208655876e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 1.730062390888196 y[1] (closed_form) = 3.571468788669568 y[1] (numeric) = 3.571468788669582 absolute error = 1.376676550535194e-14 relative error = 3.854650934939373e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 1.740066946230275 y[1] (closed_form) = 3.571603508475476 y[1] (numeric) = 3.571603508475491 absolute error = 1.465494392505207e-14 relative error = 4.103183315358391e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 1.750071501572353 y[1] (closed_form) = 3.571755089836185 y[1] (numeric) = 3.5717550898362 absolute error = 1.465494392505207e-14 relative error = 4.103009180767823e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 1.760076056914432 y[1] (closed_form) = 3.571924518938746 y[1] (numeric) = 3.57192451893876 absolute error = 1.376676550535194e-14 relative error = 3.854159132523377e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 1.77008061225651 y[1] (closed_form) = 3.572112780183823 y[1] (numeric) = 3.572112780183837 absolute error = 1.376676550535194e-14 relative error = 3.853956006574769e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 1.780085167598589 y[1] (closed_form) = 3.572320856087165 y[1] (numeric) = 3.572320856087178 absolute error = 1.287858708565182e-14 relative error = 3.605103685943259e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 1.790089722940667 y[1] (closed_form) = 3.572549727181269 y[1] (numeric) = 3.572549727181281 absolute error = 1.243449787580175e-14 relative error = 3.480566773135594e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 1.800094278282746 y[1] (closed_form) = 3.57280037191723 y[1] (numeric) = 3.572800371917243 absolute error = 1.243449787580175e-14 relative error = 3.480322598916763e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 1.810098833624824 y[1] (closed_form) = 3.573073766566819 y[1] (numeric) = 3.573073766566831 absolute error = 1.243449787580175e-14 relative error = 3.480056301146398e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 1.820103388966902 y[1] (closed_form) = 3.573370885124757 y[1] (numeric) = 3.573370885124769 absolute error = 1.199040866595169e-14 relative error = 3.355489550739167e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 1.830107944308981 y[1] (closed_form) = 3.573692699211234 y[1] (numeric) = 3.573692699211247 absolute error = 1.287858708565182e-14 relative error = 3.603719784998388e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 1.840112499651059 y[1] (closed_form) = 3.574040177974656 y[1] (numeric) = 3.574040177974668 absolute error = 1.287858708565182e-14 relative error = 3.603369420695735e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 1.850117054993138 y[1] (closed_form) = 3.574414287994645 y[1] (numeric) = 3.574414287994658 absolute error = 1.287858708565182e-14 relative error = 3.602992280135802e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 1.860121610335216 y[1] (closed_form) = 3.574815993185293 y[1] (numeric) = 3.574815993185307 absolute error = 1.376676550535194e-14 relative error = 3.851041712803026e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 1.870126165677295 y[1] (closed_form) = 3.575246254698683 y[1] (numeric) = 3.575246254698697 absolute error = 1.332267629550188e-14 relative error = 3.726366058839405e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 1.880130721019373 y[1] (closed_form) = 3.575706030828687 y[1] (numeric) = 3.575706030828702 absolute error = 1.4210854715202e-14 relative error = 3.974279371033353e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 1.890135276361452 y[1] (closed_form) = 3.57619627691505 y[1] (numeric) = 3.576196276915064 absolute error = 1.376676550535194e-14 relative error = 3.84955534857489e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 1.90013983170353 y[1] (closed_form) = 3.576717945247771 y[1] (numeric) = 3.576717945247785 absolute error = 1.4210854715202e-14 relative error = 3.973154979716347e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 1.910144387045609 y[1] (closed_form) = 3.577271984971786 y[1] (numeric) = 3.5772719849718 absolute error = 1.376676550535194e-14 relative error = 3.848397763207965e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 1.919987578591847 y[1] (closed_form) = 3.577849599187291 y[1] (numeric) = 3.577849599187305 absolute error = 1.376676550535194e-14 relative error = 3.847776471229831e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 1.929992133933925 y[1] (closed_form) = 3.578470656034392 y[1] (numeric) = 3.578470656034404 absolute error = 1.199040866595169e-14 relative error = 3.350707555958914e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 1.939996689276004 y[1] (closed_form) = 3.579126896769121 y[1] (numeric) = 3.579126896769133 absolute error = 1.243449787580175e-14 relative error = 3.474170722202216e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 1.950001244618082 y[1] (closed_form) = 3.579819257067023 y[1] (numeric) = 3.579819257067035 absolute error = 1.199040866595169e-14 relative error = 3.34944526662375e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 1.960005799960161 y[1] (closed_form) = 3.580548668988428 y[1] (numeric) = 3.58054866898844 absolute error = 1.199040866595169e-14 relative error = 3.348762933960958e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 1.970010355302239 y[1] (closed_form) = 3.581316060885155 y[1] (numeric) = 3.581316060885166 absolute error = 1.06581410364015e-14 relative error = 2.976040331320896e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 1.980014910644318 y[1] (closed_form) = 3.582122357307597 y[1] (numeric) = 3.582122357307607 absolute error = 9.769962616701378e-15 relative error = 2.727422919200532e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 1.990019465986396 y[1] (closed_form) = 3.582968478912183 y[1] (numeric) = 3.582968478912193 absolute error = 1.021405182655144e-14 relative error = 2.85072332806358e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.000024021328474 y[1] (closed_form) = 3.583855342369227 y[1] (numeric) = 3.583855342369237 absolute error = 1.021405182655144e-14 relative error = 2.850017885989533e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.010028576670553 y[1] (closed_form) = 3.584783860271178 y[1] (numeric) = 3.584783860271188 absolute error = 1.06581410364015e-14 relative error = 2.973161409958827e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.020033132012631 y[1] (closed_form) = 3.58575494104128 y[1] (numeric) = 3.58575494104129 absolute error = 9.769962616701378e-15 relative error = 2.724659877025574e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.03003768735471 y[1] (closed_form) = 3.586769488842649 y[1] (numeric) = 3.586769488842656 absolute error = 7.105427357601002e-15 relative error = 1.981010315746197e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.040042242696788 y[1] (closed_form) = 3.58782840348777 y[1] (numeric) = 3.587828403487777 absolute error = 7.105427357601002e-15 relative error = 1.980425638721666e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.050046798038867 y[1] (closed_form) = 3.58893258034844 y[1] (numeric) = 3.588932580348448 absolute error = 7.549516567451064e-15 relative error = 2.103554858842765e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.060051353380945 y[1] (closed_form) = 3.590082910266147 y[1] (numeric) = 3.590082910266155 absolute error = 7.993605777301127e-15 relative error = 2.226579713366155e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.070055908723023 y[1] (closed_form) = 3.591280279462905 y[1] (numeric) = 3.591280279462912 absolute error = 7.105427357601002e-15 relative error = 1.978522088135003e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.080060464065102 y[1] (closed_form) = 3.592525569452553 y[1] (numeric) = 3.592525569452559 absolute error = 6.217248937900877e-15 relative error = 1.730606732702613e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.09006501940718 y[1] (closed_form) = 3.593819656952525 y[1] (numeric) = 3.59381965695253 absolute error = 5.329070518200751e-15 relative error = 1.482843054712344e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.100069574749259 y[1] (closed_form) = 3.595163413796098 y[1] (numeric) = 3.595163413796103 absolute error = 5.329070518200751e-15 relative error = 1.482288815510013e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.110074130091337 y[1] (closed_form) = 3.596557706845128 y[1] (numeric) = 3.596557706845134 absolute error = 5.773159728050814e-15 relative error = 1.605190351057924e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.120078685433416 y[1] (closed_form) = 3.598003397903289 y[1] (numeric) = 3.598003397903296 absolute error = 7.105427357601002e-15 relative error = 1.974825082639344e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.130083240775494 y[1] (closed_form) = 3.599501343629813 y[1] (numeric) = 3.599501343629817 absolute error = 4.440892098500626e-15 relative error = 1.233752032447455e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.140087796117573 y[1] (closed_form) = 3.601052395453745 y[1] (numeric) = 3.60105239545375 absolute error = 4.884981308350689e-15 relative error = 1.356542691385962e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.150092351459651 y[1] (closed_form) = 3.602657399488729 y[1] (numeric) = 3.602657399488734 absolute error = 5.329070518200751e-15 relative error = 1.479205466208645e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.160096906801729 y[1] (closed_form) = 3.604317196448314 y[1] (numeric) = 3.604317196448317 absolute error = 3.552713678800501e-15 relative error = 9.85682858961841e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.0001613637958399319 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] = 2.170101462143808 y[1] (closed_form) = 3.606032621561807 y[1] (numeric) = 3.606032621561811 absolute error = 3.552713678800501e-15 relative error = 9.852139599507523e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.0001613637958399319 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] = 2.180106017485886 y[1] (closed_form) = 3.607804504490682 y[1] (numeric) = 3.607804504490685 absolute error = 2.220446049250313e-15 relative error = 6.154563104753859e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.0001613637958399319 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] = 2.190110572827965 y[1] (closed_form) = 3.60963366924553 y[1] (numeric) = 3.609633669245531 absolute error = 1.332267629550188e-15 relative error = 3.690866585441211e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.0001613637958399319 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] = 2.200115128170043 y[1] (closed_form) = 3.611520934103587 y[1] (numeric) = 3.611520934103586 absolute error = 1.332267629550188e-15 relative error = 3.688937857093908e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.0001613637958399319 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] = 2.210119683512122 y[1] (closed_form) = 3.613467111526836 y[1] (numeric) = 3.613467111526835 absolute error = 8.881784197001252e-16 relative error = 2.45796735458548e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.0001613637958399319 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] = 2.2201242388542 y[1] (closed_form) = 3.61547300808068 y[1] (numeric) = 3.615473008080679 absolute error = 1.332267629550188e-15 relative error = 3.684905478681583e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.0001613637958399319 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] = 2.230128794196279 y[1] (closed_form) = 3.617539424353219 y[1] (numeric) = 3.617539424353216 absolute error = 2.664535259100376e-15 relative error = 7.365601162941766e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.0001613637958399319 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] = 2.240133349538357 y[1] (closed_form) = 3.619667154875117 y[1] (numeric) = 3.619667154875114 absolute error = 3.552713678800501e-15 relative error = 9.815028638795032e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.0001613637958399319 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] = 2.250137904880436 y[1] (closed_form) = 3.621856988040076 y[1] (numeric) = 3.62185698804007 absolute error = 5.329070518200751e-15 relative error = 1.471364147120705e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.260142460222514 y[1] (closed_form) = 3.624109706025926 y[1] (numeric) = 3.624109706025918 absolute error = 7.993605777301127e-15 relative error = 2.205674338171909e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.269985651768752 y[1] (closed_form) = 3.626388214611307 y[1] (numeric) = 3.626388214611297 absolute error = 1.021405182655144e-14 relative error = 2.81659083972239e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.279990207110831 y[1] (closed_form) = 3.628767978249179 y[1] (numeric) = 3.628767978249169 absolute error = 1.06581410364015e-14 relative error = 2.937123866911954e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.289994762452909 y[1] (closed_form) = 3.631212922910579 y[1] (numeric) = 3.631212922910569 absolute error = 1.06581410364015e-14 relative error = 2.935146261778152e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.299999317794988 y[1] (closed_form) = 3.633723805239152 y[1] (numeric) = 3.63372380523914 absolute error = 1.199040866595169e-14 relative error = 3.299757854095503e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.310003873137066 y[1] (closed_form) = 3.636301375278824 y[1] (numeric) = 3.636301375278812 absolute error = 1.154631945610163e-14 relative error = 3.175292217140907e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.320008428479145 y[1] (closed_form) = 3.638946376398728 y[1] (numeric) = 3.638946376398715 absolute error = 1.287858708565182e-14 relative error = 3.539097791926538e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.330012983821223 y[1] (closed_form) = 3.641659545218801 y[1] (numeric) = 3.641659545218786 absolute error = 1.4210854715202e-14 relative error = 3.902301832102808e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.340017539163302 y[1] (closed_form) = 3.644441611536053 y[1] (numeric) = 3.644441611536037 absolute error = 1.598721155460225e-14 relative error = 4.386738287697245e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.35002209450538 y[1] (closed_form) = 3.647293298251527 y[1] (numeric) = 3.64729329825151 absolute error = 1.687538997430238e-14 relative error = 4.626825592115736e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.360026649847458 y[1] (closed_form) = 3.650215321297937 y[1] (numeric) = 3.650215321297918 absolute error = 1.865174681370263e-14 relative error = 5.109766184168685e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.370031205189537 y[1] (closed_form) = 3.653208389568013 y[1] (numeric) = 3.653208389567993 absolute error = 1.998401444325282e-14 relative error = 5.470264028824236e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.380035760531615 y[1] (closed_form) = 3.656273204843549 y[1] (numeric) = 3.656273204843529 absolute error = 1.998401444325282e-14 relative error = 5.465678663394064e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.390040315873694 y[1] (closed_form) = 3.659410461725161 y[1] (numeric) = 3.659410461725139 absolute error = 2.176037128265307e-14 relative error = 5.946414459446713e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.400044871215772 y[1] (closed_form) = 3.66262084756276 y[1] (numeric) = 3.662620847562737 absolute error = 2.264854970235319e-14 relative error = 6.18370031870057e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.410049426557851 y[1] (closed_form) = 3.665905042386763 y[1] (numeric) = 3.665905042386739 absolute error = 2.309263891220326e-14 relative error = 6.299300894375682e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.420053981899929 y[1] (closed_form) = 3.669263718840019 y[1] (numeric) = 3.669263718839995 absolute error = 2.398081733190338e-14 relative error = 6.535593832836998e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.430058537242008 y[1] (closed_form) = 3.672697542110495 y[1] (numeric) = 3.67269754211047 absolute error = 2.486899575160351e-14 relative error = 6.771316033095576e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.440063092584086 y[1] (closed_form) = 3.676207169864684 y[1] (numeric) = 3.676207169864659 absolute error = 2.575717417130363e-14 relative error = 7.006453385555993e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.450067647926164 y[1] (closed_form) = 3.679793252181792 y[1] (numeric) = 3.679793252181766 absolute error = 2.620126338115369e-14 relative error = 7.120308556905653e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.460072203268243 y[1] (closed_form) = 3.683456431488662 y[1] (numeric) = 3.683456431488636 absolute error = 2.575717417130363e-14 relative error = 6.992664268026625e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.470076758610321 y[1] (closed_form) = 3.687197342495478 y[1] (numeric) = 3.687197342495453 absolute error = 2.531308496145357e-14 relative error = 6.865128879790793e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.4800813139524 y[1] (closed_form) = 3.691016612132235 y[1] (numeric) = 3.691016612132207 absolute error = 2.797762022055394e-14 relative error = 7.579922596011229e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.490085869294478 y[1] (closed_form) = 3.694914859485991 y[1] (numeric) = 3.694914859485961 absolute error = 2.930988785010413e-14 relative error = 7.93249343076379e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.500090424636557 y[1] (closed_form) = 3.698892695738898 y[1] (numeric) = 3.698892695738867 absolute error = 3.108624468950438e-14 relative error = 8.404202891669592e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.510094979978635 y[1] (closed_form) = 3.702950724107036 y[1] (numeric) = 3.702950724107005 absolute error = 3.064215547965432e-14 relative error = 8.275064337250573e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.520099535320714 y[1] (closed_form) = 3.707089539780029 y[1] (numeric) = 3.707089539779997 absolute error = 3.197442310920451e-14 relative error = 8.625209282401579e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.530104090662792 y[1] (closed_form) = 3.711309729861479 y[1] (numeric) = 3.711309729861448 absolute error = 3.153033389935445e-14 relative error = 8.495743064950627e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.540108646004871 y[1] (closed_form) = 3.715611873310197 y[1] (numeric) = 3.715611873310167 absolute error = 3.019806626980426e-14 relative error = 8.127346800326896e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.550113201346949 y[1] (closed_form) = 3.71999654088226 y[1] (numeric) = 3.719996540882231 absolute error = 2.97539770599542e-14 relative error = 7.998388367559485e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.560117756689027 y[1] (closed_form) = 3.72446429507388 y[1] (numeric) = 3.724464295073849 absolute error = 3.064215547965432e-14 relative error = 8.227265198966417e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.570122312031106 y[1] (closed_form) = 3.729015690065104 y[1] (numeric) = 3.729015690065073 absolute error = 3.108624468950438e-14 relative error = 8.336313728130669e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.580126867373184 y[1] (closed_form) = 3.733651271664348 y[1] (numeric) = 3.733651271664315 absolute error = 3.286260152890463e-14 relative error = 8.80173297873518e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.590131422715263 y[1] (closed_form) = 3.738371577253766 y[1] (numeric) = 3.738371577253733 absolute error = 3.375077994860476e-14 relative error = 9.028203657967653e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.600135978057341 y[1] (closed_form) = 3.743177135735463 y[1] (numeric) = 3.743177135735429 absolute error = 3.375077994860476e-14 relative error = 9.016613086885981e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613637958399319 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] = 2.61014053339942 y[1] (closed_form) = 3.748068467478557 y[1] (numeric) = 3.748068467478519 absolute error = 3.819167204710538e-14 relative error = 1.018969433949485e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 2.620145088741498 y[1] (closed_form) = 3.753046084267093 y[1] (numeric) = 3.753046084267053 absolute error = 4.04121180963557e-14 relative error = 1.076781824389655e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 2.629988280287737 y[1] (closed_form) = 3.758028114075469 y[1] (numeric) = 3.758028114075426 absolute error = 4.218847493575595e-14 relative error = 1.122622653559763e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 2.639992835629815 y[1] (closed_form) = 3.763178390049243 y[1] (numeric) = 3.7631783900492 absolute error = 4.307665335545607e-14 relative error = 1.144688050647856e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 2.649997390971893 y[1] (closed_form) = 3.768416426637557 y[1] (numeric) = 3.768416426637513 absolute error = 4.440892098500626e-14 relative error = 1.178450467180215e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 2.660001946313972 y[1] (closed_form) = 3.773742700922668 y[1] (numeric) = 3.773742700922624 absolute error = 4.39648317751562e-14 relative error = 1.165019325891162e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 2.67000650165605 y[1] (closed_form) = 3.779157681155096 y[1] (numeric) = 3.779157681155048 absolute error = 4.796163466380676e-14 relative error = 1.269109116641763e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 2.680011056998129 y[1] (closed_form) = 3.784661826706757 y[1] (numeric) = 3.784661826706706 absolute error = 5.018208071305708e-14 relative error = 1.32593301623261e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 2.690015612340207 y[1] (closed_form) = 3.790255588024984 y[1] (numeric) = 3.790255588024933 absolute error = 5.151434834260726e-14 relative error = 1.359125978347286e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 2.700020167682286 y[1] (closed_form) = 3.795939406587444 y[1] (numeric) = 3.795939406587391 absolute error = 5.373479439185758e-14 relative error = 1.415586199785134e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 2.710024723024364 y[1] (closed_form) = 3.801713714857945 y[1] (numeric) = 3.801713714857891 absolute error = 5.417888360170764e-14 relative error = 1.425117398765838e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 2.720029278366443 y[1] (closed_form) = 3.807578936243154 y[1] (numeric) = 3.807578936243099 absolute error = 5.595524044110789e-14 relative error = 1.469575322746101e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 2.730033833708521 y[1] (closed_form) = 3.81353548505022 y[1] (numeric) = 3.813535485050164 absolute error = 5.595524044110789e-14 relative error = 1.467279920705157e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 2.740038389050599 y[1] (closed_form) = 3.819583766445302 y[1] (numeric) = 3.819583766445243 absolute error = 5.906386491005833e-14 relative error = 1.546342966187286e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 2.750042944392678 y[1] (closed_form) = 3.825724176413016 y[1] (numeric) = 3.825724176412953 absolute error = 6.306066779870889e-14 relative error = 1.64833283558446e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 2.760047499734756 y[1] (closed_form) = 3.831957101716804 y[1] (numeric) = 3.831957101716739 absolute error = 6.572520305780927e-14 relative error = 1.715186295492788e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 2.770052055076835 y[1] (closed_form) = 3.838282919860223 y[1] (numeric) = 3.838282919860156 absolute error = 6.705747068735946e-14 relative error = 1.747069512265174e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 2.780056610418913 y[1] (closed_form) = 3.844701999049153 y[1] (numeric) = 3.844701999049083 absolute error = 6.972200594645983e-14 relative error = 1.813456698690901e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 2.790061165760992 y[1] (closed_form) = 3.851214698154954 y[1] (numeric) = 3.851214698154881 absolute error = 7.283063041541027e-14 relative error = 1.891108030157396e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 2.80006572110307 y[1] (closed_form) = 3.857821366678537 y[1] (numeric) = 3.857821366678463 absolute error = 7.416289804496046e-14 relative error = 1.922403631374264e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 2.810070276445149 y[1] (closed_form) = 3.86452234471539 y[1] (numeric) = 3.864522344715316 absolute error = 7.460698725481052e-14 relative error = 1.930561673600702e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 2.820074831787227 y[1] (closed_form) = 3.871317962921533 y[1] (numeric) = 3.871317962921455 absolute error = 7.771561172376096e-14 relative error = 2.00747167936348e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 2.830079387129306 y[1] (closed_form) = 3.878208542480422 y[1] (numeric) = 3.878208542480342 absolute error = 7.993605777301127e-14 relative error = 2.061159344512346e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 2.840083942471384 y[1] (closed_form) = 3.885194395070805 y[1] (numeric) = 3.885194395070721 absolute error = 8.348877145181177e-14 relative error = 2.148895601150229e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 2.850088497813462 y[1] (closed_form) = 3.892275822835524 y[1] (numeric) = 3.892275822835438 absolute error = 8.615330671091215e-14 relative error = 2.213442999220683e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 2.860093053155541 y[1] (closed_form) = 3.899453118351274 y[1] (numeric) = 3.899453118351187 absolute error = 8.704148513061227e-14 relative error = 2.23214595710832e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 2.870097608497619 y[1] (closed_form) = 3.906726564599319 y[1] (numeric) = 3.906726564599231 absolute error = 8.79296635503124e-14 relative error = 2.250724797253135e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 2.880102163839698 y[1] (closed_form) = 3.914096434937168 y[1] (numeric) = 3.914096434937079 absolute error = 8.881784197001252e-14 relative error = 2.269178683928831e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 2.890106719181776 y[1] (closed_form) = 3.921562993071213 y[1] (numeric) = 3.921562993071122 absolute error = 9.14823772291129e-14 relative error = 2.33280397103777e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 2.900111274523855 y[1] (closed_form) = 3.92912649303034 y[1] (numeric) = 3.929126493030245 absolute error = 9.459100169806334e-14 relative error = 2.407430808497845e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 2.910115829865933 y[1] (closed_form) = 3.936787179140494 y[1] (numeric) = 3.936787179140399 absolute error = 9.50350909079134e-14 relative error = 2.414026630940769e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 2.920120385208012 y[1] (closed_form) = 3.944545286000235 y[1] (numeric) = 3.944545286000138 absolute error = 9.725553695716371e-14 relative error = 2.465570297857595e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 2.93012494055009 y[1] (closed_form) = 3.952401038457248 y[1] (numeric) = 3.952401038457148 absolute error = 9.947598300641403e-14 relative error = 2.516849429966823e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 2.940129495892168 y[1] (closed_form) = 3.960354651585842 y[1] (numeric) = 3.960354651585741 absolute error = 1.016964290556643e-13 relative error = 2.567861669028608e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 2.950134051234247 y[1] (closed_form) = 3.968406330665426 y[1] (numeric) = 3.968406330665321 absolute error = 1.043609643147647e-13 relative error = 2.629795328878668e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 2.960138606576325 y[1] (closed_form) = 3.976556271159954 y[1] (numeric) = 3.976556271159848 absolute error = 1.06137321154165e-13 relative error = 2.669076304136013e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 2.970143161918404 y[1] (closed_form) = 3.984804658698371 y[1] (numeric) = 3.984804658698262 absolute error = 1.092459456231154e-13 relative error = 2.741563388424676e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 2.979986353464642 y[1] (closed_form) = 3.993016256455877 y[1] (numeric) = 3.993016256455766 absolute error = 1.110223024625157e-13 relative error = 2.780411982621299e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 2.989990908806721 y[1] (closed_form) = 4.001460460905928 y[1] (numeric) = 4.001460460905815 absolute error = 1.13686837721616e-13 relative error = 2.841133601901877e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 2.999995464148799 y[1] (closed_form) = 4.010003607657896 y[1] (numeric) = 4.010003607657778 absolute error = 1.181277298201167e-13 relative error = 2.945826023560886e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.010000019490878 y[1] (closed_form) = 4.018645842984592 y[1] (numeric) = 4.018645842984468 absolute error = 1.234568003383174e-13 relative error = 3.072099537057682e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.020004574832956 y[1] (closed_form) = 4.027387303241026 y[1] (numeric) = 4.027387303240903 absolute error = 1.234568003383174e-13 relative error = 3.065431532720133e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.030009130175034 y[1] (closed_form) = 4.036228114850755 y[1] (numeric) = 4.036228114850632 absolute error = 1.225686219186173e-13 relative error = 3.036711960546596e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.040013685517113 y[1] (closed_form) = 4.045168394293229 y[1] (numeric) = 4.045168394293105 absolute error = 1.243449787580175e-13 relative error = 3.073913534315128e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.050018240859191 y[1] (closed_form) = 4.054208248092138 y[1] (numeric) = 4.054208248092011 absolute error = 1.270095140171179e-13 relative error = 3.132782191859214e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.06002279620127 y[1] (closed_form) = 4.063347772804737 y[1] (numeric) = 4.063347772804605 absolute error = 1.314504061156185e-13 relative error = 3.235027210700317e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.070027351543348 y[1] (closed_form) = 4.072587055012198 y[1] (numeric) = 4.072587055012061 absolute error = 1.367794766338193e-13 relative error = 3.358540278850089e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.080031906885427 y[1] (closed_form) = 4.081926171310931 y[1] (numeric) = 4.08192617131079 absolute error = 1.412203687323199e-13 relative error = 3.459650243673229e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.090036462227505 y[1] (closed_form) = 4.091365188304927 y[1] (numeric) = 4.091365188304787 absolute error = 1.394440118929197e-13 relative error = 3.408251414259406e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.100041017569584 y[1] (closed_form) = 4.100904162599083 y[1] (numeric) = 4.100904162598939 absolute error = 1.438849039914203e-13 relative error = 3.508614156450526e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.110045572911662 y[1] (closed_form) = 4.110543140793543 y[1] (numeric) = 4.110543140793399 absolute error = 1.438849039914203e-13 relative error = 3.500386665778752e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.120050128253741 y[1] (closed_form) = 4.12028215947903 y[1] (numeric) = 4.120282159478883 absolute error = 1.474376176702208e-13 relative error = 3.578337889579456e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.130054683595819 y[1] (closed_form) = 4.130121245233188 y[1] (numeric) = 4.130121245233038 absolute error = 1.501021529293212e-13 relative error = 3.634328001933666e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.140059238937897 y[1] (closed_form) = 4.140060414617914 y[1] (numeric) = 4.140060414617765 absolute error = 1.49213974509621e-13 relative error = 3.604149687834736e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.150063794279976 y[1] (closed_form) = 4.150099674177709 y[1] (numeric) = 4.150099674177557 absolute error = 1.518785097687214e-13 relative error = 3.659635230298758e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.160068349622054 y[1] (closed_form) = 4.160239020439016 y[1] (numeric) = 4.160239020438858 absolute error = 1.580957587066223e-13 relative error = 3.800160469864997e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.170072904964133 y[1] (closed_form) = 4.170478439910576 y[1] (numeric) = 4.170478439910417 absolute error = 1.589839371263224e-13 relative error = 3.812127059688898e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.180077460306211 y[1] (closed_form) = 4.180817909084765 y[1] (numeric) = 4.180817909084604 absolute error = 1.607602939657227e-13 relative error = 3.845187651353971e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.19008201564829 y[1] (closed_form) = 4.191257394439963 y[1] (numeric) = 4.191257394439799 absolute error = 1.63424829224823e-13 relative error = 3.899183797244691e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.200086570990368 y[1] (closed_form) = 4.201796852443895 y[1] (numeric) = 4.20179685244373 absolute error = 1.652011860642233e-13 relative error = 3.931679513923601e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.210091126332447 y[1] (closed_form) = 4.212436229558 y[1] (numeric) = 4.212436229557832 absolute error = 1.678657213233237e-13 relative error = 3.985003265935195e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.220095681674525 y[1] (closed_form) = 4.223175462242778 y[1] (numeric) = 4.223175462242611 absolute error = 1.669775429036235e-13 relative error = 3.953838631534095e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.230100237016603 y[1] (closed_form) = 4.23401447696416 y[1] (numeric) = 4.234014476963995 absolute error = 1.652011860642233e-13 relative error = 3.901762428140646e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.240104792358682 y[1] (closed_form) = 4.244953190200863 y[1] (numeric) = 4.244953190200694 absolute error = 1.687538997430238e-13 relative error = 3.97540072132194e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.25010934770076 y[1] (closed_form) = 4.255991508452749 y[1] (numeric) = 4.255991508452579 absolute error = 1.70530256582424e-13 relative error = 4.00682793289735e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.260113903042839 y[1] (closed_form) = 4.267129328250187 y[1] (numeric) = 4.267129328250014 absolute error = 1.731947918415244e-13 relative error = 4.058812811107042e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.270118458384917 y[1] (closed_form) = 4.278366536164404 y[1] (numeric) = 4.27836653616423 absolute error = 1.731947918415244e-13 relative error = 4.04815226506505e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.280123013726996 y[1] (closed_form) = 4.289703008818844 y[1] (numeric) = 4.289703008818668 absolute error = 1.758593271006248e-13 relative error = 4.099568821876252e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.290127569069074 y[1] (closed_form) = 4.301138612901513 y[1] (numeric) = 4.301138612901334 absolute error = 1.794120407794253e-13 relative error = 4.171268515766233e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.300132124411153 y[1] (closed_form) = 4.312673205178326 y[1] (numeric) = 4.312673205178144 absolute error = 1.820765760385257e-13 relative error = 4.221895965126737e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.310136679753231 y[1] (closed_form) = 4.324306632507435 y[1] (numeric) = 4.324306632507249 absolute error = 1.856292897173262e-13 relative error = 4.292694887126671e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.320141235095309 y[1] (closed_form) = 4.336038731854567 y[1] (numeric) = 4.336038731854376 absolute error = 1.918465386552271e-13 relative error = 4.424465520702864e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.329984426641548 y[1] (closed_form) = 4.347677733615503 y[1] (numeric) = 4.347677733615305 absolute error = 1.980637875931279e-13 relative error = 4.555622558262137e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.339988981983626 y[1] (closed_form) = 4.359605064163159 y[1] (numeric) = 4.359605064162954 absolute error = 2.042810365310288e-13 relative error = 4.685769319112424e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.349993537325705 y[1] (closed_form) = 4.371630521624148 y[1] (numeric) = 4.371630521623942 absolute error = 2.060573933704291e-13 relative error = 4.713513467141651e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.359998092667783 y[1] (closed_form) = 4.383753903725788 y[1] (numeric) = 4.383753903725575 absolute error = 2.131628207280301e-13 relative error = 4.86256357928444e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.370002648009862 y[1] (closed_form) = 4.395974998394087 y[1] (numeric) = 4.395974998393871 absolute error = 2.158273559871304e-13 relative error = 4.909658404926672e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.38000720335194 y[1] (closed_form) = 4.408293583774975 y[1] (numeric) = 4.408293583774753 absolute error = 2.220446049250313e-13 relative error = 5.036974074101634e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.390011758694019 y[1] (closed_form) = 4.42070942825651 y[1] (numeric) = 4.420709428256283 absolute error = 2.264854970235319e-13 relative error = 5.123283959263884e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.400016314036097 y[1] (closed_form) = 4.433222290492054 y[1] (numeric) = 4.433222290491821 absolute error = 2.327027459614328e-13 relative error = 5.249065594128026e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.410020869378176 y[1] (closed_form) = 4.445831919424437 y[1] (numeric) = 4.445831919424201 absolute error = 2.362554596402333e-13 relative error = 5.31408887969879e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.420025424720254 y[1] (closed_form) = 4.458538054311079 y[1] (numeric) = 4.458538054310842 absolute error = 2.371436380599334e-13 relative error = 5.31886540321514e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.430029980062332 y[1] (closed_form) = 4.471340424750094 y[1] (numeric) = 4.471340424749854 absolute error = 2.406963517387339e-13 relative error = 5.383091620723255e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.440034535404411 y[1] (closed_form) = 4.48423875070735 y[1] (numeric) = 4.484238750707108 absolute error = 2.415845301584341e-13 relative error = 5.387414533187516e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.450039090746489 y[1] (closed_form) = 4.497232742544498 y[1] (numeric) = 4.497232742544254 absolute error = 2.442490654175344e-13 relative error = 5.431096841106344e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.460043646088568 y[1] (closed_form) = 4.510322101047965 y[1] (numeric) = 4.510322101047717 absolute error = 2.478017790963349e-13 relative error = 5.494103825506357e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.470048201430646 y[1] (closed_form) = 4.523506517458899 y[1] (numeric) = 4.523506517458646 absolute error = 2.531308496145357e-13 relative error = 5.595898859381618e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.480052756772725 y[1] (closed_form) = 4.536785673504075 y[1] (numeric) = 4.53678567350382 absolute error = 2.549072064539359e-13 relative error = 5.618674206777182e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.490057312114803 y[1] (closed_form) = 4.55015924142775 y[1] (numeric) = 4.55015924142749 absolute error = 2.593480985524366e-13 relative error = 5.69975872912655e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.500061867456882 y[1] (closed_form) = 4.563626884024467 y[1] (numeric) = 4.563626884024205 absolute error = 2.620126338115369e-13 relative error = 5.741324618994251e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.51006642279896 y[1] (closed_form) = 4.577188254672812 y[1] (numeric) = 4.577188254672548 absolute error = 2.637889906509372e-13 relative error = 5.763123034794064e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.520070978141038 y[1] (closed_form) = 4.590842997370098 y[1] (numeric) = 4.59084299736983 absolute error = 2.682298827494378e-13 relative error = 5.842715224700463e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.530075533483117 y[1] (closed_form) = 4.604590746768003 y[1] (numeric) = 4.604590746767729 absolute error = 2.735589532676386e-13 relative error = 5.941004712734821e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.540080088825195 y[1] (closed_form) = 4.618431128209139 y[1] (numeric) = 4.618431128208867 absolute error = 2.726707748479384e-13 relative error = 5.903969709161178e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.550084644167274 y[1] (closed_form) = 4.63236375776455 y[1] (numeric) = 4.632363757764268 absolute error = 2.815525590449397e-13 relative error = 6.077945812718498e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.560089199509352 y[1] (closed_form) = 4.646388242272137 y[1] (numeric) = 4.646388242271849 absolute error = 2.877698079828406e-13 relative error = 6.19340857840407e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.570093754851431 y[1] (closed_form) = 4.660504179376012 y[1] (numeric) = 4.660504179375722 absolute error = 2.90434343241941e-13 relative error = 6.231822396537937e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.580098310193509 y[1] (closed_form) = 4.674711157566774 y[1] (numeric) = 4.674711157566479 absolute error = 2.948752353404416e-13 relative error = 6.307881394193488e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.590102865535588 y[1] (closed_form) = 4.689008756222687 y[1] (numeric) = 4.689008756222389 absolute error = 2.97539770599542e-13 relative error = 6.345472701553032e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.600107420877666 y[1] (closed_form) = 4.703396545651789 y[1] (numeric) = 4.703396545651489 absolute error = 3.002043058586423e-13 relative error = 6.382713065862502e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.610111976219744 y[1] (closed_form) = 4.717874087134899 y[1] (numeric) = 4.717874087134594 absolute error = 3.04645197957143e-13 relative error = 6.457255796373953e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.620116531561823 y[1] (closed_form) = 4.732440932969523 y[1] (numeric) = 4.732440932969211 absolute error = 3.11750625314744e-13 relative error = 6.587522797017267e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.630121086903901 y[1] (closed_form) = 4.74709662651467 y[1] (numeric) = 4.747096626514358 absolute error = 3.126388037344441e-13 relative error = 6.585895091922412e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.64012564224598 y[1] (closed_form) = 4.761840702236557 y[1] (numeric) = 4.761840702236244 absolute error = 3.135269821541442e-13 relative error = 6.584155198784491e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.650130197588058 y[1] (closed_form) = 4.776672685755202 y[1] (numeric) = 4.776672685754883 absolute error = 3.18856052672345e-13 relative error = 6.675275315037274e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.660134752930137 y[1] (closed_form) = 4.791592093891904 y[1] (numeric) = 4.791592093891583 absolute error = 3.206324095117452e-13 relative error = 6.691563122004319e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.670139308272215 y[1] (closed_form) = 4.806598434717608 y[1] (numeric) = 4.806598434717281 absolute error = 3.268496584496461e-13 relative error = 6.80002007425546e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.680143863614294 y[1] (closed_form) = 4.821691207602141 y[1] (numeric) = 4.821691207601809 absolute error = 3.321787289678468e-13 relative error = 6.889257620730995e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.689987055160532 y[1] (closed_form) = 4.83662440654883 y[1] (numeric) = 4.836624406548495 absolute error = 3.348432642269472e-13 relative error = 6.92307766907777e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.69999161050261 y[1] (closed_form) = 4.851887133763127 y[1] (numeric) = 4.85188713376279 absolute error = 3.375077994860476e-13 relative error = 6.956217038467592e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.709996165844689 y[1] (closed_form) = 4.867234748002779 y[1] (numeric) = 4.86723474800244 absolute error = 3.383959779057477e-13 relative error = 6.952530449545404e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.720000721186767 y[1] (closed_form) = 4.882666714479454 y[1] (numeric) = 4.882666714479111 absolute error = 3.428368700042483e-13 relative error = 7.021508737992955e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.730005276528846 y[1] (closed_form) = 4.898182489961984 y[1] (numeric) = 4.89818248996164 absolute error = 3.437250484239485e-13 relative error = 7.017399803464982e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.740009831870924 y[1] (closed_form) = 4.913781522830732 y[1] (numeric) = 4.913781522830383 absolute error = 3.490541189421492e-13 relative error = 7.103574249696516e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.750014387213003 y[1] (closed_form) = 4.929463253132804 y[1] (numeric) = 4.929463253132449 absolute error = 3.5438318946035e-13 relative error = 7.189082690394945e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.760018942555081 y[1] (closed_form) = 4.945227112638095 y[1] (numeric) = 4.945227112637737 absolute error = 3.588240815588506e-13 relative error = 7.255967691389431e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.77002349789716 y[1] (closed_form) = 4.961072524896168 y[1] (numeric) = 4.961072524895801 absolute error = 3.668176873361517e-13 relative error = 7.393919066801569e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.780028053239238 y[1] (closed_form) = 4.976998905293943 y[1] (numeric) = 4.976998905293573 absolute error = 3.694822225952521e-13 relative error = 7.423795536748874e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.790032608581317 y[1] (closed_form) = 4.993005661114216 y[1] (numeric) = 4.99300566111384 absolute error = 3.75699471533153e-13 relative error = 7.524515232560613e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.800037163923395 y[1] (closed_form) = 5.009092191594986 y[1] (numeric) = 5.009092191594607 absolute error = 3.792521852119535e-13 relative error = 7.571275806189398e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.810041719265473 y[1] (closed_form) = 5.025257887989579 y[1] (numeric) = 5.025257887989197 absolute error = 3.819167204710538e-13 relative error = 7.599942709086413e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.820046274607552 y[1] (closed_form) = 5.041502133627585 y[1] (numeric) = 5.041502133627195 absolute error = 3.89910326248355e-13 relative error = 7.734010933915784e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.83005082994963 y[1] (closed_form) = 5.057824303976574 y[1] (numeric) = 5.057824303976177 absolute error = 3.97015753605956e-13 relative error = 7.849536277759063e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.840055385291709 y[1] (closed_form) = 5.074223766704611 y[1] (numeric) = 5.07422376670421 absolute error = 4.005684672847565e-13 relative error = 7.894182158720613e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.850059940633787 y[1] (closed_form) = 5.090699881743545 y[1] (numeric) = 5.090699881743141 absolute error = 4.04121180963557e-13 relative error = 7.938420852756046e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.860064495975866 y[1] (closed_form) = 5.107252001353069 y[1] (numeric) = 5.107252001352665 absolute error = 4.032330025438569e-13 relative error = 7.895302648802683e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.870069051317944 y[1] (closed_form) = 5.12387947018556 y[1] (numeric) = 5.123879470185155 absolute error = 4.050093593832571e-13 relative error = 7.904349853268304e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.880073606660023 y[1] (closed_form) = 5.14058162535167 y[1] (numeric) = 5.140581625351259 absolute error = 4.11226608321158e-13 relative error = 7.999612462004739e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.890078162002101 y[1] (closed_form) = 5.157357796486669 y[1] (numeric) = 5.157357796486251 absolute error = 4.174438572590589e-13 relative error = 8.094141879072902e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.900082717344179 y[1] (closed_form) = 5.174207305817551 y[1] (numeric) = 5.174207305817127 absolute error = 4.236611061969597e-13 relative error = 8.187942251958517e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.910087272686258 y[1] (closed_form) = 5.191129468230868 y[1] (numeric) = 5.191129468230439 absolute error = 4.281019982954604e-13 relative error = 8.246798715296869e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.920091828028336 y[1] (closed_form) = 5.208123591341301 y[1] (numeric) = 5.208123591340871 absolute error = 4.298783551348606e-13 relative error = 8.253996810858124e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.930096383370415 y[1] (closed_form) = 5.225188975560968 y[1] (numeric) = 5.225188975560535 absolute error = 4.334310688136611e-13 relative error = 8.295031449405686e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.940100938712493 y[1] (closed_form) = 5.242324914169441 y[1] (numeric) = 5.242324914169002 absolute error = 4.387601393318619e-13 relative error = 8.369571640741695e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.950105494054572 y[1] (closed_form) = 5.259530693384477 y[1] (numeric) = 5.259530693384035 absolute error = 4.414246745909622e-13 relative error = 8.392852905035679e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.96011004939665 y[1] (closed_form) = 5.276805592433473 y[1] (numeric) = 5.27680559243303 absolute error = 4.432010314303625e-13 relative error = 8.399040360059468e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.970114604738729 y[1] (closed_form) = 5.2941488836256 y[1] (numeric) = 5.294148883625152 absolute error = 4.476419235288631e-13 relative error = 8.455408666601453e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.980119160080807 y[1] (closed_form) = 5.311559832424637 y[1] (numeric) = 5.311559832424184 absolute error = 4.529709940470639e-13 relative error = 8.528022056381323e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 3.990123715422885 y[1] (closed_form) = 5.329037697522494 y[1] (numeric) = 5.329037697522032 absolute error = 4.627409566637652e-13 relative error = 8.683386812573996e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 4.000128270764963 y[1] (closed_form) = 5.346581730913411 y[1] (numeric) = 5.346581730912944 absolute error = 4.671818487622659e-13 relative error = 8.737953935335287e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 4.010132826107042 y[1] (closed_form) = 5.364191177968824 y[1] (numeric) = 5.364191177968354 absolute error = 4.698463840213662e-13 relative error = 8.758941813093168e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 4.02013738144912 y[1] (closed_form) = 5.381865277512892 y[1] (numeric) = 5.381865277512412 absolute error = 4.805045250577678e-13 relative error = 8.928215410100755e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 4.030141936791199 y[1] (closed_form) = 5.399603261898694 y[1] (numeric) = 5.399603261898208 absolute error = 4.858335955759685e-13 relative error = 8.997579488925859e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 4.039985128337437 y[1] (closed_form) = 5.417116745983651 y[1] (numeric) = 5.417116745983162 absolute error = 4.884981308350689e-13 relative error = 9.017677737834435e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 4.049989683679516 y[1] (closed_form) = 5.434979172507433 y[1] (numeric) = 5.434979172506943 absolute error = 4.902744876744691e-13 relative error = 9.020724313986294e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 4.059994239021594 y[1] (closed_form) = 5.452903155613319 y[1] (numeric) = 5.452903155612822 absolute error = 4.9649173661237e-13 relative error = 9.10508993913219e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 4.069998794363673 y[1] (closed_form) = 5.470887902643464 y[1] (numeric) = 5.470887902642959 absolute error = 5.053735208093713e-13 relative error = 9.237504584314021e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 4.080003349705751 y[1] (closed_form) = 5.488932614858147 y[1] (numeric) = 5.488932614857634 absolute error = 5.124789481669723e-13 relative error = 9.336586621226294e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 4.09000790504783 y[1] (closed_form) = 5.507036487515713 y[1] (numeric) = 5.507036487515195 absolute error = 5.17808018685173e-13 relative error = 9.4026618465127e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 4.100012460389908 y[1] (closed_form) = 5.52519870995312 y[1] (numeric) = 5.525198709952599 absolute error = 5.213607323639735e-13 relative error = 9.436053972589107e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 4.110017015731986 y[1] (closed_form) = 5.54341846566708 y[1] (numeric) = 5.543418465666555 absolute error = 5.24913446042774e-13 relative error = 9.469129009361326e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 4.120021571074065 y[1] (closed_form) = 5.561694932395785 y[1] (numeric) = 5.561694932395256 absolute error = 5.284661597215745e-13 relative error = 9.501890451476628e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613637958399319 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] = 4.130026126416143 y[1] (closed_form) = 5.5800272822012 y[1] (numeric) = 5.580027282200668 absolute error = 5.32018873400375e-13 relative error = 9.534341796094322e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613637958399319 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] = 4.140030681758222 y[1] (closed_form) = 5.59841468155194 y[1] (numeric) = 5.598414681551408 absolute error = 5.32018873400375e-13 relative error = 9.50302726151207e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613637958399319 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] = 4.1500352371003 y[1] (closed_form) = 5.616856291406696 y[1] (numeric) = 5.61685629140616 absolute error = 5.364597654988756e-13 relative error = 9.55088999374281e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613637958399319 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] = 4.160039792442379 y[1] (closed_form) = 5.635351267298211 y[1] (numeric) = 5.635351267297672 absolute error = 5.39124300757976e-13 relative error = 9.566826896603581e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613637958399319 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] = 4.170044347784457 y[1] (closed_form) = 5.653898759417807 y[1] (numeric) = 5.653898759417263 absolute error = 5.435651928564766e-13 relative error = 9.613988788728305e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613637958399319 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] = 4.180048903126536 y[1] (closed_form) = 5.672497912700439 y[1] (numeric) = 5.672497912699891 absolute error = 5.480060849549773e-13 relative error = 9.660754281249167e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613637958399319 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] = 4.190053458468614 y[1] (closed_form) = 5.691147866910285 y[1] (numeric) = 5.691147866909731 absolute error = 5.542233338928781e-13 relative error = 9.738340082767259e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613637958399319 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] = 4.200058013810692 y[1] (closed_form) = 5.709847756726841 y[1] (numeric) = 5.709847756726278 absolute error = 5.631051180898794e-13 relative error = 9.86199881470532e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613637958399319 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] = 4.210062569152771 y[1] (closed_form) = 5.728596711831534 y[1] (numeric) = 5.728596711830962 absolute error = 5.719869022868806e-13 relative error = 9.984764699974949e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613637958399319 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] = 4.220067124494849 y[1] (closed_form) = 5.747393856994831 y[1] (numeric) = 5.747393856994254 absolute error = 5.773159728050814e-13 relative error = 1.004483052962279e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.230071679836928 y[1] (closed_form) = 5.766238312163845 y[1] (numeric) = 5.766238312163263 absolute error = 5.826450433232822e-13 relative error = 1.010442183935055e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.240076235179006 y[1] (closed_form) = 5.785129192550413 y[1] (numeric) = 5.785129192549825 absolute error = 5.879741138414829e-13 relative error = 1.016354335869672e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.250080790521085 y[1] (closed_form) = 5.804065608719661 y[1] (numeric) = 5.804065608719067 absolute error = 5.941913627793838e-13 relative error = 1.023750251697204e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.260085345863163 y[1] (closed_form) = 5.823046666679021 y[1] (numeric) = 5.823046666678422 absolute error = 5.986322548778844e-13 relative error = 1.028039597043611e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.270089901205242 y[1] (closed_form) = 5.842071467967722 y[1] (numeric) = 5.842071467967119 absolute error = 6.03073146976385e-13 relative error = 1.032293340269895e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.28009445654732 y[1] (closed_form) = 5.861139109746705 y[1] (numeric) = 5.861139109746097 absolute error = 6.075140390748857e-13 relative error = 1.036511892482859e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.290099011889398 y[1] (closed_form) = 5.880248684888995 y[1] (numeric) = 5.880248684888385 absolute error = 6.10178574333986e-13 relative error = 1.037674777092365e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.300103567231477 y[1] (closed_form) = 5.899399282070495 y[1] (numeric) = 5.899399282069878 absolute error = 6.17284001691587e-13 relative error = 1.04635060652301e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.310108122573555 y[1] (closed_form) = 5.9185899858612 y[1] (numeric) = 5.918589985860578 absolute error = 6.217248937900877e-13 relative error = 1.050461166046835e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.320112677915634 y[1] (closed_form) = 5.937819876816823 y[1] (numeric) = 5.937819876816195 absolute error = 6.279421427279885e-13 relative error = 1.057529793350045e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.330117233257712 y[1] (closed_form) = 5.957088031570821 y[1] (numeric) = 5.957088031570188 absolute error = 6.332712132461893e-13 relative error = 1.063054985741418e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.340121788599791 y[1] (closed_form) = 5.976393522926817 y[1] (numeric) = 5.976393522926179 absolute error = 6.3860028376439e-13 relative error = 1.06853787541696e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.350126343941869 y[1] (closed_form) = 5.995735419951404 y[1] (numeric) = 5.995735419950758 absolute error = 6.465938895416912e-13 relative error = 1.07842298609456e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.360130899283948 y[1] (closed_form) = 6.015112788067318 y[1] (numeric) = 6.015112788066667 absolute error = 6.510347816401918e-13 relative error = 1.082331794229534e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.370135454626026 y[1] (closed_form) = 6.034524689146986 y[1] (numeric) = 6.034524689146332 absolute error = 6.536993168992922e-13 relative error = 1.08326562666147e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.380140009968104 y[1] (closed_form) = 6.053970181606417 y[1] (numeric) = 6.053970181605757 absolute error = 6.59916565837193e-13 relative error = 1.090055857629092e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.390144565310183 y[1] (closed_form) = 6.073448320499454 y[1] (numeric) = 6.073448320498787 absolute error = 6.67021993194794e-13 relative error = 1.098259107504748e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.399987756856421 y[1] (closed_form) = 6.092643236300216 y[1] (numeric) = 6.092643236299542 absolute error = 6.732392421326949e-13 relative error = 1.105003552680564e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.4099923121985 y[1] (closed_form) = 6.112183331894852 y[1] (numeric) = 6.112183331894173 absolute error = 6.785683126508957e-13 relative error = 1.110189724038482e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.419996867540578 y[1] (closed_form) = 6.131753235277508 y[1] (numeric) = 6.131753235276826 absolute error = 6.821210263296962e-13 relative error = 1.11244043939225e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.430001422882657 y[1] (closed_form) = 6.1513519890497 y[1] (numeric) = 6.151351989049013 absolute error = 6.865619184281968e-13 relative error = 1.116115481036326e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.440005978224735 y[1] (closed_form) = 6.170978632925296 y[1] (numeric) = 6.170978632924605 absolute error = 6.910028105266974e-13 relative error = 1.119762118183083e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.450010533566814 y[1] (closed_form) = 6.190632203826638 y[1] (numeric) = 6.190632203825944 absolute error = 6.945555242054979e-13 relative error = 1.121946032872329e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.460015088908892 y[1] (closed_form) = 6.210311735980936 y[1] (numeric) = 6.210311735980237 absolute error = 6.989964163039986e-13 relative error = 1.125541592790253e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.470019644250971 y[1] (closed_form) = 6.230016261016927 y[1] (numeric) = 6.230016261016221 absolute error = 7.061018436615996e-13 relative error = 1.133386838939554e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.480024199593049 y[1] (closed_form) = 6.249744808061805 y[1] (numeric) = 6.249744808061095 absolute error = 7.096545573404001e-13 relative error = 1.135493654756891e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.490028754935127 y[1] (closed_form) = 6.269496403838394 y[1] (numeric) = 6.269496403837679 absolute error = 7.149836278586008e-13 relative error = 1.140416361704688e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.500033310277206 y[1] (closed_form) = 6.289270072762563 y[1] (numeric) = 6.289270072761843 absolute error = 7.203126983768016e-13 relative error = 1.145304129164871e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.510037865619284 y[1] (closed_form) = 6.309064837040875 y[1] (numeric) = 6.309064837040148 absolute error = 7.274181257344026e-13 relative error = 1.152972975430035e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.520042420961363 y[1] (closed_form) = 6.328879716768451 y[1] (numeric) = 6.32887971676772 absolute error = 7.318590178329032e-13 relative error = 1.156380039730938e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.530046976303441 y[1] (closed_form) = 6.34871373002705 y[1] (numeric) = 6.348713730026314 absolute error = 7.362999099314038e-13 relative error = 1.159762341226664e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.54005153164552 y[1] (closed_form) = 6.368565892983354 y[1] (numeric) = 6.368565892982611 absolute error = 7.434053372890048e-13 relative error = 1.167304146304054e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.550056086987598 y[1] (closed_form) = 6.388435219987432 y[1] (numeric) = 6.388435219986688 absolute error = 7.442935157087049e-13 relative error = 1.165063885096684e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.560060642329677 y[1] (closed_form) = 6.408320723671402 y[1] (numeric) = 6.408320723670646 absolute error = 7.558398351648066e-13 relative error = 1.179466302884693e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.570065197671755 y[1] (closed_form) = 6.428221415048251 y[1] (numeric) = 6.428221415047489 absolute error = 7.611689056830073e-13 relative error = 1.1841049903806e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.580069753013833 y[1] (closed_form) = 6.448136303610827 y[1] (numeric) = 6.448136303610062 absolute error = 7.647216193618078e-13 relative error = 1.185957590464673e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.590074308355912 y[1] (closed_form) = 6.468064397430975 y[1] (numeric) = 6.468064397430203 absolute error = 7.718270467194088e-13 relative error = 1.193289057273406e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.60007886369799 y[1] (closed_form) = 6.488004703258826 y[1] (numeric) = 6.48800470325805 absolute error = 7.762679388179095e-13 relative error = 1.196466362652299e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.610083419040069 y[1] (closed_form) = 6.507956226622204 y[1] (numeric) = 6.507956226621421 absolute error = 7.824851877558103e-13 relative error = 1.202351645444211e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.620087974382147 y[1] (closed_form) = 6.527917971926168 y[1] (numeric) = 6.527917971925378 absolute error = 7.904787935331115e-13 relative error = 1.210920230512437e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.630092529724226 y[1] (closed_form) = 6.54788894255266 y[1] (numeric) = 6.547888942551864 absolute error = 7.966960424710123e-13 relative error = 1.216721983926051e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.640097085066304 y[1] (closed_form) = 6.567868140960258 y[1] (numeric) = 6.567868140959456 absolute error = 8.01136934569513e-13 relative error = 1.219782305879823e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.650101640408383 y[1] (closed_form) = 6.587854568784014 y[1] (numeric) = 6.587854568783207 absolute error = 8.064660050877137e-13 relative error = 1.224170929499695e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.660106195750461 y[1] (closed_form) = 6.607847226935391 y[1] (numeric) = 6.607847226934576 absolute error = 8.15347789284715e-13 relative error = 1.233908353633139e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.670110751092539 y[1] (closed_form) = 6.627845115702256 y[1] (numeric) = 6.627845115701438 absolute error = 8.180123245438153e-13 relative error = 1.234205552881485e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.680115306434618 y[1] (closed_form) = 6.647847234848941 y[1] (numeric) = 6.647847234848116 absolute error = 8.251177519014163e-13 relative error = 1.241180374266175e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.690119861776696 y[1] (closed_form) = 6.667852583716356 y[1] (numeric) = 6.667852583715521 absolute error = 8.348877145181177e-13 relative error = 1.252108837194462e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.700124417118775 y[1] (closed_form) = 6.687860161322151 y[1] (numeric) = 6.68786016132131 absolute error = 8.411049634560186e-13 relative error = 1.257659315785899e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.710128972460853 y[1] (closed_form) = 6.707868966460899 y[1] (numeric) = 6.707868966460054 absolute error = 8.455458555545192e-13 relative error = 1.260528283695191e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.720133527802932 y[1] (closed_form) = 6.72787799780431 y[1] (numeric) = 6.727877997803462 absolute error = 8.482103908136196e-13 relative error = 1.260739851540767e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.73013808314501 y[1] (closed_form) = 6.74788625400145 y[1] (numeric) = 6.747886254000595 absolute error = 8.553158181712206e-13 relative error = 1.267531469819937e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.740142638487089 y[1] (closed_form) = 6.767892733778973 y[1] (numeric) = 6.767892733778115 absolute error = 8.588685318500211e-13 relative error = 1.269033901148218e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.749985830033327 y[1] (closed_form) = 6.787573822972012 y[1] (numeric) = 6.787573822971146 absolute error = 8.668621376273222e-13 relative error = 1.277131063670343e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.759990385375406 y[1] (closed_form) = 6.8075738157816 y[1] (numeric) = 6.807573815780726 absolute error = 8.739675649849232e-13 relative error = 1.283816508840279e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.769994940717484 y[1] (closed_form) = 6.82756904595171 y[1] (numeric) = 6.827569045950828 absolute error = 8.810729923425242e-13 relative error = 1.290463686873941e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.779999496059562 y[1] (closed_form) = 6.847558513512771 y[1] (numeric) = 6.847558513511888 absolute error = 8.828493491819245e-13 relative error = 1.289290697464995e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.790004051401641 y[1] (closed_form) = 6.867541219071999 y[1] (numeric) = 6.867541219071106 absolute error = 8.926193117986259e-13 relative error = 1.299765495865847e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.800008606743719 y[1] (closed_form) = 6.887516163913416 y[1] (numeric) = 6.887516163912519 absolute error = 8.970602038971265e-13 relative error = 1.302443700382441e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.810013162085798 y[1] (closed_form) = 6.907482350097818 y[1] (numeric) = 6.90748235009691 absolute error = 9.07718344933528e-13 relative error = 1.31410881552332e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.820017717427876 y[1] (closed_form) = 6.927438780562658 y[1] (numeric) = 6.927438780561746 absolute error = 9.121592370320286e-13 relative error = 1.316733739446978e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.830022272769955 y[1] (closed_form) = 6.947384459221844 y[1] (numeric) = 6.947384459220921 absolute error = 9.228173780684301e-13 relative error = 1.328294674758495e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.840026828112033 y[1] (closed_form) = 6.96731839106543 y[1] (numeric) = 6.967318391064503 absolute error = 9.272582701669307e-13 relative error = 1.330868230962438e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.850031383454112 y[1] (closed_form) = 6.987239582259217 y[1] (numeric) = 6.987239582258284 absolute error = 9.325873406851315e-13 relative error = 1.334700677865684e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.86003593879619 y[1] (closed_form) = 7.007147040244218 y[1] (numeric) = 7.007147040243282 absolute error = 9.36140054363932e-13 relative error = 1.33597889267542e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.870040494138268 y[1] (closed_form) = 7.02703977383601 y[1] (numeric) = 7.027039773835067 absolute error = 9.423573033018329e-13 relative error = 1.34104449900873e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.880045049480347 y[1] (closed_form) = 7.046916793323936 y[1] (numeric) = 7.046916793322991 absolute error = 9.450218385609332e-13 relative error = 1.341042992669109e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.890049604822425 y[1] (closed_form) = 7.066777110570171 y[1] (numeric) = 7.06677711056922 absolute error = 9.512390874988341e-13 relative error = 1.346072010784114e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.900054160164504 y[1] (closed_form) = 7.086619739108619 y[1] (numeric) = 7.086619739107665 absolute error = 9.547918011776346e-13 relative error = 1.347316261247188e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.910058715506582 y[1] (closed_form) = 7.106443694243656 y[1] (numeric) = 7.106443694242698 absolute error = 9.583445148564351e-13 relative error = 1.348557106886967e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.920063270848661 y[1] (closed_form) = 7.126247993148681 y[1] (numeric) = 7.12624799314772 absolute error = 9.610090501155355e-13 relative error = 1.348548424134929e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.930067826190739 y[1] (closed_form) = 7.14603165496449 y[1] (numeric) = 7.146031654963526 absolute error = 9.64561763794336e-13 relative error = 1.349786581373783e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.940072381532818 y[1] (closed_form) = 7.165793700897457 y[1] (numeric) = 7.165793700896488 absolute error = 9.690026558928366e-13 relative error = 1.352261447006878e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.950076936874896 y[1] (closed_form) = 7.18553315431749 y[1] (numeric) = 7.185533154316518 absolute error = 9.71667191151937e-13 relative error = 1.352254829647682e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.960081492216974 y[1] (closed_form) = 7.205249040855792 y[1] (numeric) = 7.205249040854816 absolute error = 9.761080832504376e-13 relative error = 1.354718036414328e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.970086047559053 y[1] (closed_form) = 7.224940388502379 y[1] (numeric) = 7.224940388501397 absolute error = 9.814371537686384e-13 relative error = 1.358401732048166e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.980090602901131 y[1] (closed_form) = 7.244606227703374 y[1] (numeric) = 7.244606227702384 absolute error = 9.894307595459395e-13 relative error = 1.365748155865748e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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] = 4.99009515824321 y[1] (closed_form) = 7.264245591458047 y[1] (numeric) = 7.264245591457053 absolute error = 9.938716516444401e-13 relative error = 1.368169122493771e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613637958399319 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 , 1 ) = 1.0 - sin ( x ) ; Iterations = 22740 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100 %