##############ECHO OF PROBLEM################# ##############temp/tanpostode.ode################# diff ( y , x , 1 ) = tan ( x ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=20; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=0.1; x_end=1.5; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_iter=10000; glob_max_h=0.5; // # Not Given = 0 // # No Pole = 3 // # Pole = 4 glob_type_given_pole=4; // # Real Part array_given_rad_poles[1][1]=1.570796327; // # Imag Part array_given_rad_poles[1][2]=0.0; // # Order array_given_ord_poles[1][1]=0.0; // # Not Used array_given_ord_poles[1][2]=0.0; // END SECOND INPUT BLOCK // BEGIN OVERRIDE BLOCK glob_desired_digits_correct=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=1000000000; glob_max_minutes=30.0; glob_subiter_method=3; // END OVERRIDE BLOCK ! // BEGIN USER DEF BLOCK double exact_soln_y (double x) { return(-ln(cos(x))); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1.4 estimated_steps = 1400000 step_error = 7.142857142857143e-17 est_needed_step_err = 7.142857142857143e-17 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.472759789521329e-100 estimated_step_error = 1.472759789521329e-100 best_h = 2e-06 opt_iter = 2 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.651880976585251e-96 estimated_step_error = 9.651880976585251e-96 best_h = 4e-06 opt_iter = 3 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.32545988873263e-91 estimated_step_error = 6.32545988873263e-91 best_h = 8e-06 opt_iter = 4 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.145457550185764e-86 estimated_step_error = 4.145457550185764e-86 best_h = 1.6e-05 opt_iter = 5 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.716772509442038e-81 estimated_step_error = 2.716772509442038e-81 best_h = 3.2e-05 opt_iter = 6 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.780471174431389e-76 estimated_step_error = 1.780471174431389e-76 best_h = 6.4e-05 opt_iter = 7 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.166858951060336e-71 estimated_step_error = 1.166858951060336e-71 best_h = 0.000128 opt_iter = 8 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.647249538401683e-67 estimated_step_error = 7.647249538401683e-67 best_h = 0.000256 opt_iter = 9 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.011862317088712e-62 estimated_step_error = 5.011862317088712e-62 best_h = 0.000512 opt_iter = 10 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.284784962340086e-57 estimated_step_error = 3.284784962340086e-57 best_h = 0.001024 opt_iter = 11 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.152993154701019e-52 estimated_step_error = 2.152993154701019e-52 best_h = 0.002048 opt_iter = 12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.411348206296005e-47 estimated_step_error = 1.411348206296005e-47 best_h = 0.004096 opt_iter = 13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.254170269628698e-43 estimated_step_error = 9.254170269628698e-43 best_h = 0.008192 opt_iter = 14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.071065620364792e-38 estimated_step_error = 6.071065620364792e-38 best_h = 0.016384 opt_iter = 15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.986969263894856e-33 estimated_step_error = 3.986969263894856e-33 best_h = 0.032768 opt_iter = 16 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.623801320095617e-28 estimated_step_error = 2.623801320095617e-28 best_h = 0.065536 opt_iter = 17 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.734106028935758e-23 estimated_step_error = 1.734106028935758e-23 best_h = 0.131072 opt_iter = 18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.156327561590421e-18 estimated_step_error = 1.156327561590421e-18 best_h = 0.262144 opt_iter = 19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.859664928848418e-14 estimated_step_error = 7.859664928848418e-14 best_h = 0.131072 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 0.005008355623235254 y[1] (numeric) = 0.005008355623235254 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.471 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (analytic) = 0.006062240346532338 y[1] (numeric) = 0.006062240346532248 absolute error = 9.020562075079397e-17 relative error = 1.487991494800969e-12 % Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 1.461 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (analytic) = 0.007217346646627739 y[1] (numeric) = 0.007217346646627681 absolute error = 5.724587470723463e-17 relative error = 7.931706416510065e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 1.451 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (analytic) = 0.008473908649082243 y[1] (numeric) = 0.008473908649082238 absolute error = 5.204170427930421e-18 relative error = 6.141404921203691e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.441 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (analytic) = 0.009832181658295606 y[1] (numeric) = 0.009832181658295495 absolute error = 1.110223024625157e-16 relative error = 1.129172612152095e-12 % Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 1.431 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (analytic) = 0.01129244236664183 y[1] (numeric) = 0.01129244236664173 absolute error = 1.006139616066548e-16 relative error = 8.909849467451882e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 1.421 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.16 y[1] (analytic) = 0.01285498908200967 y[1] (numeric) = 0.01285498908200959 absolute error = 7.459310946700271e-17 relative error = 5.802658329083644e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 1.411 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.17 y[1] (analytic) = 0.01452014197414718 y[1] (numeric) = 0.01452014197414706 absolute error = 1.144917494144693e-16 relative error = 7.885029610476229e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 1.401 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.18 y[1] (analytic) = 0.01628824334024881 y[1] (numeric) = 0.0162882433402488 absolute error = 1.734723475976807e-17 relative error = 1.065015692447476e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 1.391 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1900000000000001 y[1] (analytic) = 0.01815965789025992 y[1] (numeric) = 0.01815965789025986 absolute error = 6.245004513516506e-17 relative error = 3.438943922432627e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 1.381 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2000000000000001 y[1] (analytic) = 0.02013477305240835 y[1] (numeric) = 0.0201347730524083 absolute error = 5.551115123125783e-17 relative error = 2.756979236208379e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 1.371 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2100000000000001 y[1] (analytic) = 0.02221399929951903 y[1] (numeric) = 0.022213999299519 absolute error = 2.42861286636753e-17 relative error = 1.093280338052461e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 1.361 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2200000000000001 y[1] (analytic) = 0.02439777049670313 y[1] (numeric) = 0.0243977704967031 absolute error = 2.42861286636753e-17 relative error = 9.954240969254584e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.351 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2300000000000001 y[1] (analytic) = 0.02668654427106085 y[1] (numeric) = 0.02668654427106074 absolute error = 1.144917494144693e-16 relative error = 4.290242612589792e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 1.341 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2400000000000001 y[1] (analytic) = 0.02908080240408099 y[1] (numeric) = 0.02908080240408088 absolute error = 1.040834085586084e-16 relative error = 3.579110614361938e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 1.331 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2500000000000001 y[1] (analytic) = 0.03158105124746966 y[1] (numeric) = 0.03158105124746956 absolute error = 1.040834085586084e-16 relative error = 3.295755031807176e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 1.321 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2600000000000001 y[1] (analytic) = 0.03418782216318843 y[1] (numeric) = 0.03418782216318837 absolute error = 6.245004513516506e-17 relative error = 1.82667514874369e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 1.311 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2700000000000001 y[1] (analytic) = 0.03690167198853801 y[1] (numeric) = 0.03690167198853797 absolute error = 3.469446951953614e-17 relative error = 9.401869251429193e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.301 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2800000000000001 y[1] (analytic) = 0.03972318352717689 y[1] (numeric) = 0.03972318352717678 absolute error = 1.110223024625157e-16 relative error = 2.794899416522318e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 1.291 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2900000000000001 y[1] (analytic) = 0.04265296606702416 y[1] (numeric) = 0.04265296606702402 absolute error = 1.457167719820518e-16 relative error = 3.416333854791596e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 1.281 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3000000000000002 y[1] (analytic) = 0.04569165592605806 y[1] (numeric) = 0.04569165592605797 absolute error = 9.020562075079397e-17 relative error = 1.974225247970264e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 1.271 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3100000000000002 y[1] (analytic) = 0.04883991702708585 y[1] (numeric) = 0.04883991702708579 absolute error = 6.245004513516506e-17 relative error = 1.278668125102081e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 1.261 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3200000000000002 y[1] (analytic) = 0.05209844150263039 y[1] (numeric) = 0.05209844150263031 absolute error = 8.326672684688674e-17 relative error = 1.598257537947324e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 1.251 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3300000000000002 y[1] (analytic) = 0.05546795033115276 y[1] (numeric) = 0.05546795033115264 absolute error = 1.179611963664229e-16 relative error = 2.126655044258445e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 1.241 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3400000000000002 y[1] (analytic) = 0.05894919400590685 y[1] (numeric) = 0.05894919400590678 absolute error = 7.632783294297951e-17 relative error = 1.294807066154819e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 1.231 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3500000000000002 y[1] (analytic) = 0.06254295323780479 y[1] (numeric) = 0.06254295323780472 absolute error = 6.938893903907228e-17 relative error = 1.109460545862573e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 1.221 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3600000000000002 y[1] (analytic) = 0.0662500396937582 y[1] (numeric) = 0.06625003969375812 absolute error = 8.326672684688674e-17 relative error = 1.256855501246315e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 1.211 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.3 Order of pole (ratio test) = 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3700000000000002 y[1] (analytic) = 0.07007129677205522 y[1] (numeric) = 0.07007129677205513 absolute error = 8.326672684688674e-17 relative error = 1.188314341002662e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 1.201 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.289 Order of pole (ratio test) = 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3800000000000002 y[1] (analytic) = 0.07400760041643002 y[1] (numeric) = 0.07400760041642987 absolute error = 1.52655665885959e-16 relative error = 2.062702547130129e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 1.191 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.278 Order of pole (ratio test) = 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3900000000000002 y[1] (analytic) = 0.07805985997058702 y[1] (numeric) = 0.07805985997058694 absolute error = 8.326672684688674e-17 relative error = 1.066703512897175e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 1.181 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.267 Order of pole (ratio test) = 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4000000000000002 y[1] (analytic) = 0.08222901907505553 y[1] (numeric) = 0.08222901907505542 absolute error = 1.110223024625157e-16 relative error = 1.350159635993939e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 1.171 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.256 Order of pole (ratio test) = 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4100000000000003 y[1] (analytic) = 0.08651605660836616 y[1] (numeric) = 0.08651605660836603 absolute error = 1.249000902703301e-16 relative error = 1.443663698586237e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 1.161 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.245 Order of pole (ratio test) = 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4200000000000003 y[1] (analytic) = 0.09092198767467256 y[1] (numeric) = 0.0909219876746724 absolute error = 1.665334536937735e-16 relative error = 1.831608150600995e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 1.151 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.234 Order of pole (ratio test) = 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4300000000000003 y[1] (analytic) = 0.09544786464007339 y[1] (numeric) = 0.09544786464007321 absolute error = 1.804112415015879e-16 relative error = 1.890154820979023e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 1.141 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.223 Order of pole (ratio test) = 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4400000000000003 y[1] (analytic) = 0.1000947782200377 y[1] (numeric) = 0.1000947782200375 absolute error = 1.804112415015879e-16 relative error = 1.802404128465035e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 1.131 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.212 Order of pole (ratio test) = 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4500000000000003 y[1] (analytic) = 0.1048638586204904 y[1] (numeric) = 0.1048638586204902 absolute error = 1.52655665885959e-16 relative error = 1.455750988893424e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 1.121 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.201 Order of pole (ratio test) = 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4600000000000003 y[1] (analytic) = 0.1097562767352823 y[1] (numeric) = 0.1097562767352821 absolute error = 1.804112415015879e-16 relative error = 1.643744183639868e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 1.111 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.191 Order of pole (ratio test) = 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4700000000000003 y[1] (analytic) = 0.1147732454029447 y[1] (numeric) = 0.1147732454029447 absolute error = 6.938893903907228e-17 relative error = 6.045741653071001e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.101 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.18 Order of pole (ratio test) = 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4800000000000003 y[1] (analytic) = 0.1199160207258237 y[1] (numeric) = 0.1199160207258236 absolute error = 1.387778780781446e-16 relative error = 1.15729222199131e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 1.091 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.169 Order of pole (ratio test) = 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4900000000000003 y[1] (analytic) = 0.1251859034548867 y[1] (numeric) = 0.1251859034548866 absolute error = 1.387778780781446e-16 relative error = 1.108574322253112e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 1.081 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.158 Order of pole (ratio test) = 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5000000000000003 y[1] (analytic) = 0.1305842404437229 y[1] (numeric) = 0.1305842404437227 absolute error = 1.665334536937735e-16 relative error = 1.275295189740322e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 1.071 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.147 Order of pole (ratio test) = 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5100000000000003 y[1] (analytic) = 0.1361124261754862 y[1] (numeric) = 0.136112426175486 absolute error = 1.942890293094024e-16 relative error = 1.427415811829778e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 1.061 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.137 Order of pole (ratio test) = 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5200000000000004 y[1] (analytic) = 0.1417719043667884 y[1] (numeric) = 0.1417719043667883 absolute error = 1.110223024625157e-16 relative error = 7.831051078730083e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.051 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.126 Order of pole (ratio test) = 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5300000000000004 y[1] (analytic) = 0.1475641696528218 y[1] (numeric) = 0.1475641696528216 absolute error = 1.942890293094024e-16 relative error = 1.316640955365462e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 1.041 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.115 Order of pole (ratio test) = 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5400000000000004 y[1] (analytic) = 0.1534907693582817 y[1] (numeric) = 0.1534907693582815 absolute error = 1.942890293094024e-16 relative error = 1.26580269368439e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 1.031 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.104 Order of pole (ratio test) = 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5500000000000004 y[1] (analytic) = 0.159553305358981 y[1] (numeric) = 0.1595533053589808 absolute error = 1.665334536937735e-16 relative error = 1.043748064755461e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 1.021 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.094 Order of pole (ratio test) = 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5600000000000004 y[1] (analytic) = 0.1657534360393848 y[1] (numeric) = 0.1657534360393846 absolute error = 2.220446049250313e-16 relative error = 1.339607855081032e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 1.011 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.083 Order of pole (ratio test) = 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5700000000000004 y[1] (analytic) = 0.1720928783516632 y[1] (numeric) = 0.1720928783516629 absolute error = 2.498001805406602e-16 relative error = 1.451542811842603e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 1.001 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.072 Order of pole (ratio test) = 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5800000000000004 y[1] (analytic) = 0.1785734099822599 y[1] (numeric) = 0.1785734099822597 absolute error = 1.942890293094024e-16 relative error = 1.088006491720709e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 0.9908 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.062 Order of pole (ratio test) = 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5900000000000004 y[1] (analytic) = 0.1851968716324019 y[1] (numeric) = 0.1851968716324016 absolute error = 2.498001805406602e-16 relative error = 1.34883585418489e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 0.9808 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.051 Order of pole (ratio test) = 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6000000000000004 y[1] (analytic) = 0.1919651694194379 y[1] (numeric) = 0.1919651694194378 absolute error = 1.387778780781446e-16 relative error = 7.229325950007067e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.9708 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.04 Order of pole (ratio test) = 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6100000000000004 y[1] (analytic) = 0.1988802774064051 y[1] (numeric) = 0.1988802774064048 absolute error = 2.220446049250313e-16 relative error = 1.116473728922304e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 0.9608 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.029 Order of pole (ratio test) = 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6200000000000004 y[1] (analytic) = 0.2059442402677548 y[1] (numeric) = 0.2059442402677546 absolute error = 2.220446049250313e-16 relative error = 1.078178271149239e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 0.9508 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.019 Order of pole (ratio test) = 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6300000000000004 y[1] (analytic) = 0.2131591760997758 y[1] (numeric) = 0.2131591760997756 absolute error = 1.665334536937735e-16 relative error = 7.812633579322071e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.9408 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.008 Order of pole (ratio test) = 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6400000000000005 y[1] (analytic) = 0.220527279384879 y[1] (numeric) = 0.2205272793848788 absolute error = 2.498001805406602e-16 relative error = 1.132740499213669e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 0.9308 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.9973 Order of pole (ratio test) = 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6500000000000005 y[1] (analytic) = 0.2280508241196166 y[1] (numeric) = 0.2280508241196163 absolute error = 2.775557561562891e-16 relative error = 1.217078505319088e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 0.9208 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.9866 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.9202 Order of pole (three term test) = 0.008055 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6600000000000005 y[1] (analytic) = 0.2357321671170591 y[1] (numeric) = 0.2357321671170588 absolute error = 3.05311331771918e-16 relative error = 1.295161943767766e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 0.9108 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.9759 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.9103 Order of pole (three term test) = 0.006636 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6700000000000005 y[1] (analytic) = 0.2435737514949815 y[1] (numeric) = 0.2435737514949813 absolute error = 2.220446049250313e-16 relative error = 9.116113848975481e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.9008 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.9651 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.9004 Order of pole (three term test) = 0.005461 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6800000000000005 y[1] (analytic) = 0.2515781103622067 y[1] (numeric) = 0.2515781103622064 absolute error = 2.775557561562891e-16 relative error = 1.103258768247688e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 0.8908 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.9544 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.8905 Order of pole (three term test) = 0.004488 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6900000000000005 y[1] (analytic) = 0.259747870716431 y[1] (numeric) = 0.2597478707164309 absolute error = 1.665334536937735e-16 relative error = 6.411350100173852e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.8808 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.9437 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.8805 Order of pole (three term test) = 0.003684 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7000000000000005 y[1] (analytic) = 0.2680857575679316 y[1] (numeric) = 0.2680857575679313 absolute error = 2.775557561562891e-16 relative error = 1.035324512104892e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 0.8708 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.933 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.8706 Order of pole (three term test) = 0.00302 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7100000000000005 y[1] (analytic) = 0.2765945983047113 y[1] (numeric) = 0.2765945983047111 absolute error = 1.665334536937735e-16 relative error = 6.020849818271266e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.8608 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.9223 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.8606 Order of pole (three term test) = 0.002472 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7200000000000005 y[1] (analytic) = 0.285277327315926 y[1] (numeric) = 0.2852773273159258 absolute error = 2.220446049250313e-16 relative error = 7.783464848544778e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.8508 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.9116 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.8507 Order of pole (three term test) = 0.002021 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7300000000000005 y[1] (analytic) = 0.2941369908918218 y[1] (numeric) = 0.2941369908918215 absolute error = 2.775557561562891e-16 relative error = 9.436275094633341e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.8408 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.9009 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.8407 Order of pole (three term test) = 0.00165 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7400000000000005 y[1] (analytic) = 0.3031767524199507 y[1] (numeric) = 0.3031767524199504 absolute error = 2.775557561562891e-16 relative error = 9.154915538241132e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.8308 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.8901 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.8307 Order of pole (three term test) = 0.001345 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7500000000000006 y[1] (analytic) = 0.3123998978991059 y[1] (numeric) = 0.3123998978991056 absolute error = 2.775557561562891e-16 relative error = 8.884630181471117e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.8208 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.8794 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.8207 Order of pole (three term test) = 0.001095 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7600000000000006 y[1] (analytic) = 0.32180984179426 y[1] (numeric) = 0.3218098417942598 absolute error = 2.775557561562891e-16 relative error = 8.624837407357371e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.8108 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.8687 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.8107 Order of pole (three term test) = 0.0008903 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7700000000000006 y[1] (analytic) = 0.3314101332578185 y[1] (numeric) = 0.3314101332578183 absolute error = 2.220446049250313e-16 relative error = 6.699994437173503e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.8008 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.858 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.8008 Order of pole (three term test) = 0.0007226 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7800000000000006 y[1] (analytic) = 0.3412044627447259 y[1] (numeric) = 0.3412044627447257 absolute error = 2.220446049250313e-16 relative error = 6.507670009320929e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.7908 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.8473 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.7908 Order of pole (three term test) = 0.0005855 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7900000000000006 y[1] (analytic) = 0.351196669051421 y[1] (numeric) = 0.3511966690514207 absolute error = 3.33066907387547e-16 relative error = 9.483771821844371e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.7808 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.8366 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.7808 Order of pole (three term test) = 0.0004736 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8000000000000006 y[1] (analytic) = 0.3613907468113444 y[1] (numeric) = 0.361390746811344 absolute error = 3.33066907387547e-16 relative error = 9.2162544372343e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.7708 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.8259 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.7708 Order of pole (three term test) = 0.0003824 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8100000000000006 y[1] (analytic) = 0.3717908544826952 y[1] (numeric) = 0.3717908544826949 absolute error = 2.220446049250313e-16 relative error = 5.972298733221429e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.7608 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.8151 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.7608 Order of pole (three term test) = 0.0003083 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8200000000000006 y[1] (analytic) = 0.3824013228674413 y[1] (numeric) = 0.3824013228674411 absolute error = 2.220446049250313e-16 relative error = 5.806585690133783e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.7508 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.8044 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.7508 Order of pole (three term test) = 0.0002481 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8300000000000006 y[1] (analytic) = 0.3932266642042512 y[1] (numeric) = 0.3932266642042508 absolute error = 3.885780586188048e-16 relative error = 9.881783052661155e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.7408 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.7937 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.7408 Order of pole (three term test) = 0.0001992 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8400000000000006 y[1] (analytic) = 0.4042715818820776 y[1] (numeric) = 0.4042715818820773 absolute error = 2.775557561562891e-16 relative error = 6.865576721077804e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.7308 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.783 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.7308 Order of pole (three term test) = 0.0001597 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8500000000000006 y[1] (analytic) = 0.4155409808256353 y[1] (numeric) = 0.415540980825635 absolute error = 3.33066907387547e-16 relative error = 8.015260173034649e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.7208 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.7723 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.7208 Order of pole (three term test) = 0.0001278 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8600000000000007 y[1] (analytic) = 0.4270399786090209 y[1] (numeric) = 0.4270399786090205 absolute error = 3.33066907387547e-16 relative error = 7.799431530331928e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.7108 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.7616 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.7108 Order of pole (three term test) = 0.000102 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8700000000000007 y[1] (analytic) = 0.4387739173593156 y[1] (numeric) = 0.4387739173593153 absolute error = 3.33066907387547e-16 relative error = 7.590854747977093e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.7008 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.7509 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.7008 Order of pole (three term test) = 8.126e-05 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8800000000000007 y[1] (analytic) = 0.4507483765182265 y[1] (numeric) = 0.4507483765182262 absolute error = 3.33066907387547e-16 relative error = 7.389198158855244e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.6908 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.7401 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.6908 Order of pole (three term test) = 6.459e-05 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8900000000000007 y[1] (analytic) = 0.4629691865367751 y[1] (numeric) = 0.4629691865367747 absolute error = 3.885780586188048e-16 relative error = 8.393173237414555e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.6808 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.7294 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.6808 Order of pole (three term test) = 5.123e-05 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9000000000000007 y[1] (analytic) = 0.4754424435858151 y[1] (numeric) = 0.4754424435858148 absolute error = 2.775557561562891e-16 relative error = 5.837841360206446e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.6708 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.7187 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.6708 Order of pole (three term test) = 4.053e-05 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9100000000000007 y[1] (analytic) = 0.488174525373867 y[1] (numeric) = 0.4881745253738666 absolute error = 3.33066907387547e-16 relative error = 6.822701515046666e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.6608 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.708 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.6608 Order of pole (three term test) = 3.199e-05 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9200000000000007 y[1] (analytic) = 0.5011721081735231 y[1] (numeric) = 0.5011721081735226 absolute error = 4.440892098500626e-16 relative error = 8.861012067660868e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.6508 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.6973 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.6508 Order of pole (three term test) = 2.519e-05 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9300000000000007 y[1] (analytic) = 0.5144421851686615 y[1] (numeric) = 0.5144421851686611 absolute error = 3.33066907387547e-16 relative error = 6.474331168590888e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.6408 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.6866 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.6408 Order of pole (three term test) = 1.978e-05 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9400000000000007 y[1] (analytic) = 0.5279920862470625 y[1] (numeric) = 0.5279920862470622 absolute error = 3.33066907387547e-16 relative error = 6.308179915251523e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.6308 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.6759 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.6308 Order of pole (three term test) = 1.55e-05 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9500000000000007 y[1] (analytic) = 0.5418294993769632 y[1] (numeric) = 0.541829499376963 absolute error = 2.220446049250313e-16 relative error = 4.098053080911155e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.6208 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.6651 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.6208 Order of pole (three term test) = 1.21e-05 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9600000000000007 y[1] (analytic) = 0.5559624937218419 y[1] (numeric) = 0.5559624937218415 absolute error = 4.440892098500626e-16 relative error = 7.987754837150012e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.6108 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.6544 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.6108 Order of pole (three term test) = 9.426e-06 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9700000000000008 y[1] (analytic) = 0.5703995446655491 y[1] (numeric) = 0.5703995446655488 absolute error = 3.33066907387547e-16 relative error = 5.83918606707232e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.6008 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.6437 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.6008 Order of pole (three term test) = 7.32e-06 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9800000000000008 y[1] (analytic) = 0.5851495609401413 y[1] (numeric) = 0.5851495609401408 absolute error = 4.440892098500626e-16 relative error = 7.589328258856736e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.5908 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.633 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.5908 Order of pole (three term test) = 5.667e-06 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9900000000000008 y[1] (analytic) = 0.6002219140717494 y[1] (numeric) = 0.6002219140717491 absolute error = 3.33066907387547e-16 relative error = 5.549062764604972e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.5808 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.6223 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.5808 Order of pole (three term test) = 4.373e-06 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.000000000000001 y[1] (analytic) = 0.6156264703860153 y[1] (numeric) = 0.615626470386015 absolute error = 2.220446049250313e-16 relative error = 3.606807302905657e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.5708 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.6116 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.5708 Order of pole (three term test) = 3.364e-06 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.010000000000001 y[1] (analytic) = 0.6313736258445042 y[1] (numeric) = 0.631373625844504 absolute error = 2.220446049250313e-16 relative error = 3.516849545750852e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.5608 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.6009 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.5608 Order of pole (three term test) = 2.578e-06 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.020000000000001 y[1] (analytic) = 0.647474344017704 y[1] (numeric) = 0.6474743440177037 absolute error = 3.33066907387547e-16 relative error = 5.144094286745049e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.5508 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.5901 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.5508 Order of pole (three term test) = 1.969e-06 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.030000000000001 y[1] (analytic) = 0.6639401975394195 y[1] (numeric) = 0.6639401975394192 absolute error = 2.220446049250313e-16 relative error = 3.344346459936222e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.5408 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.5794 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.5408 Order of pole (three term test) = 1.499e-06 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.040000000000001 y[1] (analytic) = 0.6807834134324346 y[1] (numeric) = 0.6807834134324342 absolute error = 4.440892098500626e-16 relative error = 6.523208425584489e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.5308 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.5687 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.5308 Order of pole (three term test) = 1.136e-06 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.050000000000001 y[1] (analytic) = 0.6980169227472273 y[1] (numeric) = 0.6980169227472268 absolute error = 4.440892098500626e-16 relative error = 6.362155348644471e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.5208 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.558 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.5208 Order of pole (three term test) = 8.578e-07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.060000000000001 y[1] (analytic) = 0.7156544150154999 y[1] (numeric) = 0.7156544150154995 absolute error = 3.33066907387547e-16 relative error = 4.654018761001192e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.5108 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.5473 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.5108 Order of pole (three term test) = 6.45e-07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.070000000000001 y[1] (analytic) = 0.7337103980897428 y[1] (numeric) = 0.7337103980897425 absolute error = 3.33066907387547e-16 relative error = 4.539487354339066e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.5008 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.5366 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.5008 Order of pole (three term test) = 4.829e-07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.080000000000001 y[1] (analytic) = 0.7522002640207198 y[1] (numeric) = 0.7522002640207195 absolute error = 3.33066907387547e-16 relative error = 4.42790202714383e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.4908 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.5259 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.4908 Order of pole (three term test) = 3.6e-07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.090000000000001 y[1] (analytic) = 0.7711403617187269 y[1] (numeric) = 0.7711403617187266 absolute error = 3.33066907387547e-16 relative error = 4.319147640582623e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.4808 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.5151 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.4808 Order of pole (three term test) = 2.67e-07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.100000000000001 y[1] (analytic) = 0.790548077254233 y[1] (numeric) = 0.7905480772542327 absolute error = 3.33066907387547e-16 relative error = 4.213113875937437e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.4708 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.5044 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.4708 Order of pole (three term test) = 1.971e-07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.110000000000001 y[1] (analytic) = 0.8104419227821352 y[1] (numeric) = 0.8104419227821348 absolute error = 4.440892098500626e-16 relative error = 5.479593260989827e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.4608 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.4937 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.4608 Order of pole (three term test) = 1.448e-07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.120000000000001 y[1] (analytic) = 0.8308416352250594 y[1] (numeric) = 0.8308416352250589 absolute error = 4.440892098500626e-16 relative error = 5.345052426624807e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.4508 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.483 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.4508 Order of pole (three term test) = 1.058e-07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.130000000000001 y[1] (analytic) = 0.8517682860294862 y[1] (numeric) = 0.8517682860294857 absolute error = 4.440892098500626e-16 relative error = 5.213732621112044e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.4408 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.4723 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.4408 Order of pole (three term test) = 7.686e-08 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.140000000000001 y[1] (analytic) = 0.8732444035195741 y[1] (numeric) = 0.8732444035195738 absolute error = 3.33066907387547e-16 relative error = 3.814131599872098e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.4308 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.4616 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.4308 Order of pole (three term test) = 5.551e-08 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.150000000000001 y[1] (analytic) = 0.8952941096243293 y[1] (numeric) = 0.8952941096243289 absolute error = 4.440892098500626e-16 relative error = 4.960260601249851e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.4208 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.4509 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.4208 Order of pole (three term test) = 3.985e-08 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.160000000000001 y[1] (analytic) = 0.9179432730528062 y[1] (numeric) = 0.9179432730528058 absolute error = 4.440892098500626e-16 relative error = 4.83787204380456e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.4108 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.4401 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.4108 Order of pole (three term test) = 2.843e-08 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.170000000000001 y[1] (analytic) = 0.9412196813500504 y[1] (numeric) = 0.9412196813500499 absolute error = 5.551115123125783e-16 relative error = 5.897789042366253e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.4008 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.4294 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.4008 Order of pole (three term test) = 2.014e-08 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.180000000000001 y[1] (analytic) = 0.9651532346969017 y[1] (numeric) = 0.9651532346969012 absolute error = 5.551115123125783e-16 relative error = 5.751537604149525e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.3908 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.4187 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.3908 Order of pole (three term test) = 1.417e-08 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.190000000000001 y[1] (analytic) = 0.989776164836492 y[1] (numeric) = 0.9897761648364913 absolute error = 6.661338147750939e-16 relative error = 6.730146051608923e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.3808 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.408 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.3808 Order of pole (three term test) = 9.895e-09 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.200000000000001 y[1] (analytic) = 1.015123283140662 y[1] (numeric) = 1.015123283140661 absolute error = 6.661338147750939e-16 relative error = 6.562097686442192e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.3708 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.3973 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.3708 Order of pole (three term test) = 6.856e-09 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.210000000000001 y[1] (analytic) = 1.041232262597865 y[1] (numeric) = 1.041232262597864 absolute error = 4.440892098500626e-16 relative error = 4.265035053198065e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.3608 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.3866 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.3608 Order of pole (three term test) = 4.711e-09 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.220000000000001 y[1] (analytic) = 1.06814395944531 y[1] (numeric) = 1.068143959445309 absolute error = 6.661338147750939e-16 relative error = 6.236367381799538e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.3508 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.3759 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.3508 Order of pole (three term test) = 3.209e-09 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.230000000000001 y[1] (analytic) = 1.095902781327143 y[1] (numeric) = 1.095902781327142 absolute error = 6.661338147750939e-16 relative error = 6.078402447052857e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.3408 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.3651 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.3408 Order of pole (three term test) = 2.166e-09 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.240000000000001 y[1] (analytic) = 1.124557110295836 y[1] (numeric) = 1.124557110295836 absolute error = 6.661338147750939e-16 relative error = 5.923521435028361e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.3308 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.3544 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.3308 Order of pole (three term test) = 1.447e-09 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.250000000000001 y[1] (analytic) = 1.154159790761956 y[1] (numeric) = 1.154159790761955 absolute error = 6.661338147750939e-16 relative error = 5.771590901943691e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.3208 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.3437 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.3208 Order of pole (three term test) = 9.572e-10 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.260000000000001 y[1] (analytic) = 1.184768694738796 y[1] (numeric) = 1.184768694738795 absolute error = 6.661338147750939e-16 relative error = 5.622479879264157e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.3108 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.333 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.3108 Order of pole (three term test) = 6.261e-10 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.270000000000001 y[1] (analytic) = 1.216447379556395 y[1] (numeric) = 1.216447379556395 absolute error = 6.661338147750939e-16 relative error = 5.476059433150445e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.3008 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.3223 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.3008 Order of pole (three term test) = 4.046e-10 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.280000000000001 y[1] (analytic) = 1.24926585681298 y[1] (numeric) = 1.249265856812979 absolute error = 6.661338147750939e-16 relative error = 5.332202198133211e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.2908 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.3116 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.2908 Order of pole (three term test) = 2.583e-10 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.290000000000001 y[1] (analytic) = 1.283301495932059 y[1] (numeric) = 1.283301495932059 absolute error = 4.440892098500626e-16 relative error = 3.460521251302069e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.2808 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.3009 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.2808 Order of pole (three term test) = 1.626e-10 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.300000000000001 y[1] (analytic) = 1.318640091629172 y[1] (numeric) = 1.318640091629171 absolute error = 4.440892098500626e-16 relative error = 3.367781797847456e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.2708 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.2901 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.2708 Order of pole (three term test) = 1.009e-10 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.310000000000001 y[1] (analytic) = 1.355377132316208 y[1] (numeric) = 1.355377132316207 absolute error = 4.440892098500626e-16 relative error = 3.276499206469253e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.2608 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.2794 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.2608 Order of pole (three term test) = 6.166e-11 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.320000000000001 y[1] (analytic) = 1.393619316613288 y[1] (numeric) = 1.393619316613287 absolute error = 6.661338147750939e-16 relative error = 4.779883622694775e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.2508 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.2687 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.2508 Order of pole (three term test) = 3.696e-11 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.330000000000001 y[1] (analytic) = 1.433486378584703 y[1] (numeric) = 1.433486378584702 absolute error = 6.661338147750939e-16 relative error = 4.646949037860934e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.2408 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.258 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.2408 Order of pole (three term test) = 2.186e-11 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.340000000000001 y[1] (analytic) = 1.475113300329342 y[1] (numeric) = 1.475113300329341 absolute error = 6.661338147750939e-16 relative error = 4.515814579302954e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.2308 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.2473 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.2308 Order of pole (three term test) = 1.269e-11 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.350000000000001 y[1] (analytic) = 1.518653014960391 y[1] (numeric) = 1.518653014960391 absolute error = 6.661338147750939e-16 relative error = 4.3863463754587e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.2208 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.2366 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.2208 Order of pole (three term test) = 7.07e-12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.360000000000001 y[1] (analytic) = 1.564279736473011 y[1] (numeric) = 1.56427973647301 absolute error = 6.661338147750939e-16 relative error = 4.258405956705858e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.2108 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.2259 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.2108 Order of pole (three term test) = 3.908e-12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.370000000000001 y[1] (analytic) = 1.612193099490702 y[1] (numeric) = 1.612193099490701 absolute error = 6.661338147750939e-16 relative error = 4.131848815042864e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.2008 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.2151 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.2008 Order of pole (three term test) = 2.085e-12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.380000000000001 y[1] (analytic) = 1.662623357400385 y[1] (numeric) = 1.662623357400384 absolute error = 6.661338147750939e-16 relative error = 4.006522654755889e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.1908 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.2044 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.1908 Order of pole (three term test) = 1.105e-12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.390000000000001 y[1] (analytic) = 1.715837981167825 y[1] (numeric) = 1.715837981167824 absolute error = 6.661338147750939e-16 relative error = 3.882265237663718e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.1808 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.1937 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.1808 Order of pole (three term test) = 5.451e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.400000000000001 y[1] (analytic) = 1.772150137669705 y[1] (numeric) = 1.772150137669704 absolute error = 8.881784197001252e-16 relative error = 5.011868920248701e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.1708 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.183 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.1708 Order of pole (three term test) = 3.074e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.410000000000001 y[1] (analytic) = 1.831929728955887 y[1] (numeric) = 1.831929728955886 absolute error = 6.661338147750939e-16 relative error = 3.636241086358474e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.1608 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.1723 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.1608 Order of pole (three term test) = 7.882e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.420000000000001 y[1] (analytic) = 1.895617980714551 y[1] (numeric) = 1.895617980714551 absolute error = 6.661338147750939e-16 relative error = 3.51407204168846e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.1508 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.1616 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.1508 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.430000000000001 y[1] (analytic) = 1.963747043924376 y[1] (numeric) = 1.963747043924376 absolute error = 6.661338147750939e-16 relative error = 3.392156932004256e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.1408 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.1509 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.1408 Order of pole (three term test) = 3.99e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.440000000000001 y[1] (analytic) = 2.036966830539447 y[1] (numeric) = 2.036966830539447 absolute error = 8.881784197001252e-16 relative error = 4.360298883536115e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.1308 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.1401 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.1308 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.450000000000001 y[1] (analytic) = 2.116082544013728 y[1] (numeric) = 2.116082544013727 absolute error = 4.440892098500626e-16 relative error = 2.098638406646114e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.1208 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.1294 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.1208 Order of pole (three term test) = 4.755e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.460000000000001 y[1] (analytic) = 2.202108465746907 y[1] (numeric) = 2.202108465746907 absolute error = 4.440892098500626e-16 relative error = 2.016654568826778e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.1108 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.1187 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.1108 Order of pole (three term test) = 4.023e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.470000000000001 y[1] (analytic) = 2.296347254952646 y[1] (numeric) = 2.296347254952646 absolute error = 8.881784197001252e-16 relative error = 3.867787930525519e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.1008 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.108 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.1008 Order of pole (three term test) = 2.751e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.480000000000001 y[1] (analytic) = 2.400510821257595 y[1] (numeric) = 2.400510821257594 absolute error = 8.881784197001252e-16 relative error = 3.69995590869622e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.0908 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.09728 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.0908 Order of pole (three term test) = 2.91e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.490000000000001 y[1] (analytic) = 2.516912019535261 y[1] (numeric) = 2.51691201953526 absolute error = 1.332267629550188e-15 relative error = 5.293262613908079e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.0808 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.08657 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.0808 Order of pole (three term test) = 8.963e-14 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = tan ( x ) ; Iterations = 140 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 30 Minutes 0.0 Seconds Percent Done = 100.7 %