##############ECHO OF PROBLEM################# ##############temp/arctan_sqrt_sm_hpostode.ode################# diff ( y , x , 1 ) = arctan ( sqrt ( 0.1 * x + 0.2 ) ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=40; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=-1.0; x_end=0.5; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_h=0.000001; glob_type_given_pole=1; array_given_rad_poles[1][1]=-2.0; array_given_rad_poles[1][2]=0.0; array_given_ord_poles[1][1]=0.5; 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=100000000; glob_max_minutes=10.0; glob_subiter_method=3; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(10.0 * (0.1 * x + 0.2) * arctan(sqrt ( 0.1 * x + 0.2)) - 10.0 * sqrt( 0.1 * x + 0.2) + 10.0 * arctan(sqrt( 0.1 * x + 0.2))); } /* 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 = 1.5 estimated_steps = 1500000 step_error = 2.041241452319315e-15 est_needed_step_err = 2.041241452319315e-15 opt_iter = 1 SETTING H FOR MAX H Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] = -1 y[1] (analytic) = 0.2067734006979847 y[1] (numeric) = 0.2067734006979847 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 16 h = 1e-06 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9899999999997124 y[1] (analytic) = 0.2098433472793522 y[1] (numeric) = 0.2098433472792638 absolute error = 8.837375276016246e-14 relative error = 4.211415510948539e-11 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 13 h = 1e-06 Radius of convergence (given) for eq 1 = 1.01 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9799999999994249 y[1] (analytic) = 0.2129275836243343 y[1] (numeric) = 0.2129275836241575 absolute error = 1.767752610959406e-13 relative error = 8.302130615816462e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 1e-06 Radius of convergence (given) for eq 1 = 1.02 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9699999999991373 y[1] (analytic) = 0.2160260266073237 y[1] (numeric) = 0.2160260266070567 absolute error = 2.670086374223501e-13 relative error = 1.236002168885413e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.03 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9599999999988498 y[1] (analytic) = 0.2191385942767754 y[1] (numeric) = 0.2191385942764194 absolute error = 3.560207684216721e-13 relative error = 1.624637456476573e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.04 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9499999999985622 y[1] (analytic) = 0.2222652058273793 y[1] (numeric) = 0.2222652058269345 absolute error = 4.447553436648377e-13 relative error = 2.001011998298347e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.05 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9399999999982747 y[1] (analytic) = 0.2254057815731536 y[1] (numeric) = 0.2254057815726174 absolute error = 5.361822097427194e-13 relative error = 2.378742044683117e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.06 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9299999999979871 y[1] (analytic) = 0.2285602429214202 y[1] (numeric) = 0.2285602429207945 absolute error = 6.25666185527507e-13 relative error = 2.737423523576728e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.07 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9199999999976995 y[1] (analytic) = 0.2317285123476394 y[1] (numeric) = 0.2317285123469214 absolute error = 7.179257188738575e-13 relative error = 3.098132860736725e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.08 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.909999999997412 y[1] (analytic) = 0.2349105133710374 y[1] (numeric) = 0.2349105133702291 absolute error = 8.082978730783452e-13 relative error = 3.440875682739885e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.09 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8999999999971244 y[1] (analytic) = 0.2381061705310308 y[1] (numeric) = 0.2381061705301314 absolute error = 8.993916722488393e-13 relative error = 3.777271585372995e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8899999999968369 y[1] (analytic) = 0.2413154093643843 y[1] (numeric) = 0.241315409363393 absolute error = 9.913736498390335e-13 relative error = 4.108206982928584e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.11 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8799999999965493 y[1] (analytic) = 0.2445381563830926 y[1] (numeric) = 0.2445381563820076 absolute error = 1.085020961966165e-12 relative error = 4.43702110956613e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.12 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8699999999962618 y[1] (analytic) = 0.2477743390529419 y[1] (numeric) = 0.2477743390517627 absolute error = 1.179195630029994e-12 relative error = 4.759151551113757e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.13 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8599999999959742 y[1] (analytic) = 0.2510238857727414 y[1] (numeric) = 0.251023885771471 absolute error = 1.270372695927335e-12 relative error = 5.060764205831144e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.14 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8499999999956867 y[1] (analytic) = 0.2542867258541857 y[1] (numeric) = 0.2542867258528226 absolute error = 1.363020807332305e-12 relative error = 5.36017286295115e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.15 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8399999999953991 y[1] (analytic) = 0.2575627895023165 y[1] (numeric) = 0.2575627895008587 absolute error = 1.457778342484062e-12 relative error = 5.659894992211019e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.16 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8299999999951115 y[1] (analytic) = 0.2608520077965881 y[1] (numeric) = 0.2608520077950348 absolute error = 1.553368544904288e-12 relative error = 5.954980212824743e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.17 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.819999999994824 y[1] (analytic) = 0.2641543126724804 y[1] (numeric) = 0.2641543126708341 absolute error = 1.646294212065413e-12 relative error = 6.232320023132163e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.18 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8099999999945364 y[1] (analytic) = 0.2674696369036642 y[1] (numeric) = 0.2674696369019235 absolute error = 1.740718680309783e-12 relative error = 6.508098266633329e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.19 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7999999999942489 y[1] (analytic) = 0.2707979140846826 y[1] (numeric) = 0.2707979140828473 absolute error = 1.835309682007846e-12 relative error = 6.777414398524198e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7899999999939613 y[1] (analytic) = 0.2741390786141351 y[1] (numeric) = 0.2741390786122023 absolute error = 1.932787263569935e-12 relative error = 7.050389434956965e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.21 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7799999999936738 y[1] (analytic) = 0.2774930656783452 y[1] (numeric) = 0.2774930656763153 absolute error = 2.029931778224636e-12 relative error = 7.315252268601271e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.22 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7699999999933862 y[1] (analytic) = 0.280859811235497 y[1] (numeric) = 0.2808598112333715 absolute error = 2.125466469493631e-12 relative error = 7.567713088404298e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.23 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7599999999930986 y[1] (analytic) = 0.2842392520002144 y[1] (numeric) = 0.2842392519979925 absolute error = 2.221889339182326e-12 relative error = 7.816968710502552e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.24 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7499999999928111 y[1] (analytic) = 0.2876313254285772 y[1] (numeric) = 0.2876313254262574 absolute error = 2.319755498803033e-12 relative error = 8.065030800614451e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.25 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7399999999925235 y[1] (analytic) = 0.2910359697035507 y[1] (numeric) = 0.2910359697011315 absolute error = 2.419175970658216e-12 relative error = 8.312292027416368e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.26 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.729999999992236 y[1] (analytic) = 0.2944531237208201 y[1] (numeric) = 0.2944531237183021 absolute error = 2.517985819849855e-12 relative error = 8.551397886467095e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.27 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7199999999919484 y[1] (analytic) = 0.2978827270750117 y[1] (numeric) = 0.2978827270723961 absolute error = 2.615629934865638e-12 relative error = 8.780737173145924e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.28 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7099999999916609 y[1] (analytic) = 0.3013247200462863 y[1] (numeric) = 0.3013247200435736 absolute error = 2.712718938369107e-12 relative error = 9.002643188227002e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.29 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.6999999999913733 y[1] (analytic) = 0.3047790435872972 y[1] (numeric) = 0.3047790435844854 absolute error = 2.811861854468134e-12 relative error = 9.225902874987985e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.3 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.6899999999910857 y[1] (analytic) = 0.3082456393104933 y[1] (numeric) = 0.3082456393075813 absolute error = 2.912003971289323e-12 relative error = 9.447024061080342e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.31 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.6799999999907982 y[1] (analytic) = 0.3117244494757609 y[1] (numeric) = 0.3117244494727489 absolute error = 3.012090576959281e-12 relative error = 9.6626702911011e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.32 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.6699999999905106 y[1] (analytic) = 0.3152154169783934 y[1] (numeric) = 0.3152154169752788 absolute error = 3.114564162132183e-12 relative error = 9.880748194323478e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.33 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.6599999999902231 y[1] (analytic) = 0.318718485337365 y[1] (numeric) = 0.3187184853341499 absolute error = 3.215150368163222e-12 relative error = 1.008774362353025e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 Radius of convergence (given) for eq 1 = 1.34 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.6499999999899355 y[1] (analytic) = 0.3222335986839227 y[1] (numeric) = 0.322233598680609 absolute error = 3.313682661598705e-12 relative error = 1.028347967168091e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 Radius of convergence (given) for eq 1 = 1.35 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.639999999989648 y[1] (analytic) = 0.3257607017504629 y[1] (numeric) = 0.3257607017470485 absolute error = 3.414435401083438e-12 relative error = 1.04814220461096e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 Radius of convergence (given) for eq 1 = 1.36 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.6299999999893604 y[1] (analytic) = 0.329299739859692 y[1] (numeric) = 0.3292997398561773 absolute error = 3.514688540207089e-12 relative error = 1.067321991115033e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 Radius of convergence (given) for eq 1 = 1.37 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.6199999999890728 y[1] (analytic) = 0.332850658914063 y[1] (numeric) = 0.3328506589104472 absolute error = 3.61577434659921e-12 relative error = 1.086305299318259e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 Radius of convergence (given) for eq 1 = 1.38 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.6099999999887853 y[1] (analytic) = 0.3364134053854815 y[1] (numeric) = 0.3364134053817613 absolute error = 3.720135310913975e-12 relative error = 1.105822553845984e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 Radius of convergence (given) for eq 1 = 1.39 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.5999999999884977 y[1] (analytic) = 0.3399879263052621 y[1] (numeric) = 0.3399879263014396 absolute error = 3.822442362633183e-12 relative error = 1.124287678145711e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 Radius of convergence (given) for eq 1 = 1.4 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.5899999999882102 y[1] (analytic) = 0.3435741692543415 y[1] (numeric) = 0.3435741692504176 absolute error = 3.923861235932691e-12 relative error = 1.142071083064434e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 Radius of convergence (given) for eq 1 = 1.41 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.5799999999879226 y[1] (analytic) = 0.3471720823537243 y[1] (numeric) = 0.3471720823496951 absolute error = 4.029221400969618e-12 relative error = 1.160583354990034e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 Radius of convergence (given) for eq 1 = 1.42 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.5699999999876351 y[1] (analytic) = 0.3507816142551676 y[1] (numeric) = 0.3507816142510342 absolute error = 4.133415831830689e-12 relative error = 1.178344492372378e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 Radius of convergence (given) for eq 1 = 1.43 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.5599999999873475 y[1] (analytic) = 0.3544027141320929 y[1] (numeric) = 0.3544027141278558 absolute error = 4.237110662330679e-12 relative error = 1.195563829895339e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 Radius of convergence (given) for eq 1 = 1.44 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.54999999998706 y[1] (analytic) = 0.3580353316707101 y[1] (numeric) = 0.35803533166637 absolute error = 4.340139359015893e-12 relative error = 1.212209794704724e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 Radius of convergence (given) for eq 1 = 1.45 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.5399999999867724 y[1] (analytic) = 0.361679417061362 y[1] (numeric) = 0.3616794170569202 absolute error = 4.441780276920326e-12 relative error = 1.228098715987131e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 Radius of convergence (given) for eq 1 = 1.46 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.5299999999864848 y[1] (analytic) = 0.3653349209900698 y[1] (numeric) = 0.3653349209855218 absolute error = 4.547973109225723e-12 relative error = 1.244877740376026e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 Radius of convergence (given) for eq 1 = 1.47 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.5199999999861973 y[1] (analytic) = 0.3690017946302784 y[1] (numeric) = 0.3690017946256234 absolute error = 4.654943097648356e-12 relative error = 1.261496059202742e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 Radius of convergence (given) for eq 1 = 1.48 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.5099999999859097 y[1] (analytic) = 0.3726799896347956 y[1] (numeric) = 0.3726799896300358 absolute error = 4.759859173475434e-12 relative error = 1.277197409536212e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 Radius of convergence (given) for eq 1 = 1.49 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.4999999999856222 y[1] (analytic) = 0.3763694581279218 y[1] (numeric) = 0.3763694581230567 absolute error = 4.865052805058667e-12 relative error = 1.292626885629257e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 Radius of convergence (given) for eq 1 = 1.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.4899999999858898 y[1] (analytic) = 0.3800701526975496 y[1] (numeric) = 0.3800701526927848 absolute error = 4.764799665935016e-12 relative error = 1.253663207204467e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 Radius of convergence (given) for eq 1 = 1.51 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.4799999999861573 y[1] (analytic) = 0.3837820263882676 y[1] (numeric) = 0.3837820263836021 absolute error = 4.665545727533527e-12 relative error = 1.215675932362046e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 Radius of convergence (given) for eq 1 = 1.52 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.4699999999864249 y[1] (analytic) = 0.3875050326934018 y[1] (numeric) = 0.3875050326888383 absolute error = 4.563405209268012e-12 relative error = 1.177637662548406e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 Radius of convergence (given) for eq 1 = 1.53 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.4599999999866924 y[1] (analytic) = 0.3912391255480445 y[1] (numeric) = 0.39123912554358 absolute error = 4.464484337773911e-12 relative error = 1.141113975122017e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 Radius of convergence (given) for eq 1 = 1.54 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.44999999998696 y[1] (analytic) = 0.3949842593220394 y[1] (numeric) = 0.3949842593176722 absolute error = 4.367228800816747e-12 relative error = 1.105671605322391e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 Radius of convergence (given) for eq 1 = 1.55 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.4399999999872276 y[1] (analytic) = 0.3987403888131222 y[1] (numeric) = 0.3987403888088557 absolute error = 4.266531572483245e-12 relative error = 1.070002360478924e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 Radius of convergence (given) for eq 1 = 1.56 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.4299999999874951 y[1] (analytic) = 0.402507469240216 y[1] (numeric) = 0.4025074692360475 absolute error = 4.168443368257613e-12 relative error = 1.035618885812499e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 Radius of convergence (given) for eq 1 = 1.57 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.4199999999877627 y[1] (analytic) = 0.4062854562368727 y[1] (numeric) = 0.4062854562328027 absolute error = 4.070022097124593e-12 relative error = 1.001764162276999e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 Radius of convergence (given) for eq 1 = 1.58 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.4099999999880302 y[1] (analytic) = 0.4100743058448595 y[1] (numeric) = 0.4100743058408926 absolute error = 3.966882378136916e-12 relative error = 9.673569696019135e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.59 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.3999999999882978 y[1] (analytic) = 0.4138739745078848 y[1] (numeric) = 0.4138739745040192 absolute error = 3.86557452713987e-12 relative error = 9.339979716618366e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.6 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.3899999999885653 y[1] (analytic) = 0.4176844190654618 y[1] (numeric) = 0.4176844190616988 absolute error = 3.762989919664506e-12 relative error = 9.009169956791586e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.61 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.3799999999888329 y[1] (analytic) = 0.4215055967468939 y[1] (numeric) = 0.4215055967432341 absolute error = 3.659794689525597e-12 relative error = 8.682671636560105e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.62 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.3699999999891004 y[1] (analytic) = 0.4253374651654123 y[1] (numeric) = 0.4253374651618562 absolute error = 3.556099859025608e-12 relative error = 8.360655127435465e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.63 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.359999999989368 y[1] (analytic) = 0.4291799823124061 y[1] (numeric) = 0.4291799823089526 absolute error = 3.453459740399012e-12 relative error = 8.046646821205166e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.64 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.3499999999896355 y[1] (analytic) = 0.4330331065518029 y[1] (numeric) = 0.4330331065484507 absolute error = 3.352262911704429e-12 relative error = 7.741354785545488e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.65 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.3399999999899031 y[1] (analytic) = 0.4368967966145503 y[1] (numeric) = 0.4368967966113027 absolute error = 3.247568880482277e-12 relative error = 7.433263200021642e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.66 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.3299999999901707 y[1] (analytic) = 0.4407710115932191 y[1] (numeric) = 0.4407710115900757 absolute error = 3.143374449621206e-12 relative error = 7.131536255660521e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.67 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.3199999999904382 y[1] (analytic) = 0.4446557109367144 y[1] (numeric) = 0.4446557109336741 absolute error = 3.040345752935991e-12 relative error = 6.837527727983479e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.68 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.3099999999907058 y[1] (analytic) = 0.4485508544451036 y[1] (numeric) = 0.448550854442166 absolute error = 2.937539100855702e-12 relative error = 6.548954420095116e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.69 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.2999999999909733 y[1] (analytic) = 0.4524564022645392 y[1] (numeric) = 0.4524564022617057 absolute error = 2.833511203448325e-12 relative error = 6.262506595699901e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.7 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.2899999999912409 y[1] (analytic) = 0.4563723148822967 y[1] (numeric) = 0.4563723148795659 absolute error = 2.730760062519266e-12 relative error = 5.983623400169572e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.71 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.2799999999915084 y[1] (analytic) = 0.4602985531218979 y[1] (numeric) = 0.4602985531192725 absolute error = 2.62545540863357e-12 relative error = 5.703809822618077e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.72 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.269999999991776 y[1] (analytic) = 0.4642350781383517 y[1] (numeric) = 0.4642350781358323 absolute error = 2.519484620933099e-12 relative error = 5.427174161497206e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.73 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.2599999999920435 y[1] (analytic) = 0.4681818514134721 y[1] (numeric) = 0.4681818514110602 absolute error = 2.411959520998153e-12 relative error = 5.151757834517264e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.74 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.2499999999923111 y[1] (analytic) = 0.472138834751302 y[1] (numeric) = 0.472138834748992 absolute error = 2.310041047337563e-12 relative error = 4.892715610979918e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.75 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.2399999999923011 y[1] (analytic) = 0.4761059902737292 y[1] (numeric) = 0.4761059902714138 absolute error = 2.315425629006995e-12 relative error = 4.863256661979362e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.76 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.2299999999922911 y[1] (analytic) = 0.4800832804157547 y[1] (numeric) = 0.4800832804134344 absolute error = 2.320255099164115e-12 relative error = 4.833026255683725e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.77 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.2199999999922811 y[1] (analytic) = 0.4840706679215074 y[1] (numeric) = 0.4840706679191826 absolute error = 2.324807013565078e-12 relative error = 4.80261905466672e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.78 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.2099999999922711 y[1] (analytic) = 0.4880681158398996 y[1] (numeric) = 0.4880681158375706 absolute error = 2.328970349907422e-12 relative error = 4.771814167576952e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.79 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.1999999999922611 y[1] (analytic) = 0.4920755875204788 y[1] (numeric) = 0.4920755875181451 absolute error = 2.333633286610848e-12 relative error = 4.742428492276563e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.8 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.1899999999922511 y[1] (analytic) = 0.4960930466093516 y[1] (numeric) = 0.496093046607012 absolute error = 2.339572979792592e-12 relative error = 4.715996315172885e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.81 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.1799999999922411 y[1] (analytic) = 0.5001204570451989 y[1] (numeric) = 0.500120457042855 absolute error = 2.34390284958863e-12 relative error = 4.686676612744113e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.82 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.1699999999922311 y[1] (analytic) = 0.5041577830553479 y[1] (numeric) = 0.5041577830529969 absolute error = 2.351008276946231e-12 relative error = 4.663239081024226e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.83 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.1599999999922211 y[1] (analytic) = 0.5082049891519391 y[1] (numeric) = 0.5082049891495816 absolute error = 2.35755859279152e-12 relative error = 4.638991436754029e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.84 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.1499999999922111 y[1] (analytic) = 0.5122620401281459 y[1] (numeric) = 0.512262040125786 absolute error = 2.359890061143233e-12 relative error = 4.606802527380108e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.85 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.1399999999922011 y[1] (analytic) = 0.5163289010544814 y[1] (numeric) = 0.5163289010521176 absolute error = 2.363775841729421e-12 relative error = 4.578042865510646e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.86 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.1299999999921911 y[1] (analytic) = 0.5204055372751619 y[1] (numeric) = 0.5204055372727939 absolute error = 2.367994689222996e-12 relative error = 4.550287265623253e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.87 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.1199999999921811 y[1] (analytic) = 0.5244919144045399 y[1] (numeric) = 0.5244919144021682 absolute error = 2.371658425204259e-12 relative error = 4.521820756563661e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.88 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.1099999999921711 y[1] (analytic) = 0.5285879983236126 y[1] (numeric) = 0.5285879983212396 absolute error = 2.37299069283381e-12 relative error = 4.489301119888491e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.89 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.09999999999216105 y[1] (analytic) = 0.5326937551765791 y[1] (numeric) = 0.5326937551742057 absolute error = 2.37343478204366e-12 relative error = 4.455533332199296e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.9 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.08999999999215105 y[1] (analytic) = 0.5368091513674709 y[1] (numeric) = 0.5368091513650919 absolute error = 2.378985897166785e-12 relative error = 4.431716357864881e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.91 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.07999999999214105 y[1] (analytic) = 0.5409341535568393 y[1] (numeric) = 0.5409341535544592 absolute error = 2.380096120191411e-12 relative error = 4.399973831456954e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.92 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.06999999999213105 y[1] (analytic) = 0.5450687286585012 y[1] (numeric) = 0.5450687286561177 absolute error = 2.383537811567749e-12 relative error = 4.372912416813941e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.93 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.05999999999212105 y[1] (analytic) = 0.5492128438363477 y[1] (numeric) = 0.5492128438339572 absolute error = 2.390532216622887e-12 relative error = 4.352651696789539e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.94 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.04999999999211105 y[1] (analytic) = 0.5533664665012079 y[1] (numeric) = 0.5533664664988132 absolute error = 2.394751064116463e-12 relative error = 4.327604235323203e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.95 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.03999999999210105 y[1] (analytic) = 0.5575295643077594 y[1] (numeric) = 0.5575295643053639 absolute error = 2.395417197931238e-12 relative error = 4.296484619439758e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.96 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.02999999999209105 y[1] (analytic) = 0.561702105151511 y[1] (numeric) = 0.5617021051491139 absolute error = 2.397082532468175e-12 relative error = 4.267533467444629e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.97 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.01999999999208105 y[1] (analytic) = 0.5658840571658241 y[1] (numeric) = 0.5658840571634238 absolute error = 2.400302179239588e-12 relative error = 4.241685463381441e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.98 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.009999999992080805 y[1] (analytic) = 0.5700753887189798 y[1] (numeric) = 0.5700753887165807 absolute error = 2.399080933912501e-12 relative error = 4.208357317974192e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 1.99 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.91830063542152e-12 y[1] (analytic) = 0.5742760684113319 y[1] (numeric) = 0.5742760684089278 absolute error = 2.404187959825776e-12 relative error = 4.186467262124788e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.01000000000791741 y[1] (analytic) = 0.578486065072461 y[1] (numeric) = 0.5784860650700645 absolute error = 2.396527420955863e-12 relative error = 4.142757389766467e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 2.01 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.02000000000791765 y[1] (analytic) = 0.582705347758413 y[1] (numeric) = 0.5827053477560101 absolute error = 2.402855692196226e-12 relative error = 4.123620456616162e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 2.02 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.03000000000792765 y[1] (analytic) = 0.5869338857489659 y[1] (numeric) = 0.5869338857465595 absolute error = 2.406408405875027e-12 relative error = 4.099965028947499e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 2.03 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.04000000000793765 y[1] (analytic) = 0.5911716485449543 y[1] (numeric) = 0.5911716485425418 absolute error = 2.412514632510465e-12 relative error = 4.080903809322329e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 2.04 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.05000000000794765 y[1] (analytic) = 0.5954186058656306 y[1] (numeric) = 0.5954186058632176 absolute error = 2.412958721720315e-12 relative error = 4.052541687393714e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 2.05 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.06000000000795765 y[1] (analytic) = 0.599674727646077 y[1] (numeric) = 0.5996747276436606 absolute error = 2.416400413096653e-12 relative error = 4.029518506777548e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 2.06 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.07000000000796765 y[1] (analytic) = 0.6039399840346604 y[1] (numeric) = 0.6039399840322356 absolute error = 2.424838108083804e-12 relative error = 4.015031579602521e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 2.07 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.08000000000797765 y[1] (analytic) = 0.6082143453905262 y[1] (numeric) = 0.6082143453880987 absolute error = 2.427502643342905e-12 relative error = 3.991195968559798e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 2.08 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.09000000000798765 y[1] (analytic) = 0.6124977822811335 y[1] (numeric) = 0.6124977822787043 absolute error = 2.429167977879843e-12 relative error = 3.96600289528047e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 2.09 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1000000000079976 y[1] (analytic) = 0.6167902654798336 y[1] (numeric) = 0.6167902654774003 absolute error = 2.433275803070956e-12 relative error = 3.945061942859916e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 2.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1100000000080077 y[1] (analytic) = 0.621091765963488 y[1] (numeric) = 0.6210917659610504 absolute error = 2.437605672866994e-12 relative error = 3.924710979037987e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 2.11 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1200000000080177 y[1] (analytic) = 0.6254022549101266 y[1] (numeric) = 0.625402254907685 absolute error = 2.441602475755644e-12 relative error = 3.904051283132189e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 2.12 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1300000000080276 y[1] (analytic) = 0.6297217036966356 y[1] (numeric) = 0.6297217036941917 absolute error = 2.443933944107357e-12 relative error = 3.880974611103299e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 2.13 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1400000000080376 y[1] (analytic) = 0.6340500838964971 y[1] (numeric) = 0.6340500838940495 absolute error = 2.44759768008862e-12 relative error = 3.860259216507206e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 2.14 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1500000000080476 y[1] (analytic) = 0.6383873672775535 y[1] (numeric) = 0.6383873672750991 absolute error = 2.454370040538834e-12 relative error = 3.844640677972157e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 2.15 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1600000000080576 y[1] (analytic) = 0.6427335257998088 y[1] (numeric) = 0.6427335257973514 absolute error = 2.457367642705321e-12 relative error = 3.823307084607741e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 2.16 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1700000000080676 y[1] (analytic) = 0.6470885316132744 y[1] (numeric) = 0.6470885316108098 absolute error = 2.464584092365385e-12 relative error = 3.808727820010752e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 2.17 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1800000000080776 y[1] (analytic) = 0.6514523570558346 y[1] (numeric) = 0.6514523570533659 absolute error = 2.468691917556498e-12 relative error = 3.789520278525774e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 2.18 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1900000000080876 y[1] (analytic) = 0.6558249746511633 y[1] (numeric) = 0.6558249746486873 absolute error = 2.476019389519024e-12 relative error = 3.775427111228925e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 2.19 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2000000000080976 y[1] (analytic) = 0.6602063571066497 y[1] (numeric) = 0.6602063571041719 absolute error = 2.477795746358424e-12 relative error = 3.753062538230242e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 2.2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2100000000081076 y[1] (analytic) = 0.6645964773113908 y[1] (numeric) = 0.664596477308906 absolute error = 2.484790151413563e-12 relative error = 3.738795248307247e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 2.21 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2200000000081176 y[1] (analytic) = 0.6689953083341726 y[1] (numeric) = 0.6689953083316795 absolute error = 2.493116824098252e-12 relative error = 3.726658158943178e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 2.22 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2300000000081276 y[1] (analytic) = 0.6734028234215215 y[1] (numeric) = 0.6734028234190246 absolute error = 2.496891582381977e-12 relative error = 3.707872161413599e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 2.23 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2400000000081376 y[1] (analytic) = 0.6778189959957621 y[1] (numeric) = 0.6778189959932641 absolute error = 2.498001805406602e-12 relative error = 3.685352314059697e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 2.24 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2500000000081476 y[1] (analytic) = 0.6822437996531168 y[1] (numeric) = 0.6822437996506132 absolute error = 2.503552920529728e-12 relative error = 3.66958691570762e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 2.25 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2600000000078801 y[1] (analytic) = 0.686677208161699 y[1] (numeric) = 0.68667720815932 absolute error = 2.378985897166785e-12 relative error = 3.464489382916261e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 2.26 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2700000000076125 y[1] (analytic) = 0.6911191954600415 y[1] (numeric) = 0.691119195457784 absolute error = 2.257527498272793e-12 relative error = 3.26648067815578e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 2.27 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.280000000007345 y[1] (analytic) = 0.6955697356549075 y[1] (numeric) = 0.6955697356527692 absolute error = 2.138289545428051e-12 relative error = 3.074155524341156e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 2.28 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2900000000070774 y[1] (analytic) = 0.7000288030196193 y[1] (numeric) = 0.700028803017603 absolute error = 2.016387057324209e-12 relative error = 2.880434417307394e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 2.29 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3000000000068099 y[1] (analytic) = 0.7044963719922945 y[1] (numeric) = 0.7044963719903926 absolute error = 1.901923063485356e-12 relative error = 2.699691778549227e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 2.3 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3100000000065423 y[1] (analytic) = 0.7089724171741079 y[1] (numeric) = 0.7089724171723265 absolute error = 1.781352843011064e-12 relative error = 2.512584128605956e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 2.31 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3200000000062748 y[1] (analytic) = 0.713456913327577 y[1] (numeric) = 0.7134569133259188 absolute error = 1.658229109580134e-12 relative error = 2.324217592687021e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 2.32 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3300000000060072 y[1] (analytic) = 0.7179498353748799 y[1] (numeric) = 0.7179498353733459 absolute error = 1.533995153124579e-12 relative error = 2.136632780650473e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 2.33 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3400000000057397 y[1] (analytic) = 0.7224511583961855 y[1] (numeric) = 0.722451158394775 absolute error = 1.410427330483799e-12 relative error = 1.952280530098249e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 2.34 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3500000000054721 y[1] (analytic) = 0.7269608576280202 y[1] (numeric) = 0.7269608576267367 absolute error = 1.283528838769143e-12 relative error = 1.765609283224867e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 2.35 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3600000000052045 y[1] (analytic) = 0.7314789084616562 y[1] (numeric) = 0.7314789084604976 absolute error = 1.158628748498813e-12 relative error = 1.583953734134971e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 2.36 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.370000000004937 y[1] (analytic) = 0.7360052864415154 y[1] (numeric) = 0.7360052864404782 absolute error = 1.037170349604821e-12 relative error = 1.409188722841106e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 2.37 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3800000000046694 y[1] (analytic) = 0.7405399672636066 y[1] (numeric) = 0.7405399672626864 absolute error = 9.201528428093297e-13 relative error = 1.242543121891741e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 2.38 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3900000000044019 y[1] (analytic) = 0.7450829267739802 y[1] (numeric) = 0.7450829267731821 absolute error = 7.98139332403025e-13 relative error = 1.07120872552907e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 Radius of convergence (given) for eq 1 = 2.39 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4000000000041343 y[1] (analytic) = 0.7496341409672009 y[1] (numeric) = 0.7496341409665254 absolute error = 6.755707104844078e-13 relative error = 9.012005638013841e-11 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 13 h = 1e-06 Radius of convergence (given) for eq 1 = 2.4 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4100000000038668 y[1] (analytic) = 0.7541935859848592 y[1] (numeric) = 0.7541935859843076 absolute error = 5.515587986337778e-13 relative error = 7.313225793527904e-11 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 13 h = 1e-06 Radius of convergence (given) for eq 1 = 2.41 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4200000000035992 y[1] (analytic) = 0.7587612381140776 y[1] (numeric) = 0.7587612381136472 absolute error = 4.304334666471732e-13 relative error = 5.672844697721087e-11 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 13 h = 1e-06 Radius of convergence (given) for eq 1 = 2.42 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4300000000033317 y[1] (analytic) = 0.7633370737860607 y[1] (numeric) = 0.7633370737857518 absolute error = 3.089750677531811e-13 relative error = 4.047688476870403e-11 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 13 h = 1e-06 Radius of convergence (given) for eq 1 = 2.43 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4400000000030641 y[1] (analytic) = 0.7679210695746592 y[1] (numeric) = 0.7679210695744769 absolute error = 1.822986206434507e-13 relative error = 2.373923933932733e-11 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 13 h = 1e-06 Radius of convergence (given) for eq 1 = 2.44 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4500000000027966 y[1] (analytic) = 0.7725132021949475 y[1] (numeric) = 0.7725132021948847 absolute error = 6.272760089132134e-14 relative error = 8.119939013740212e-12 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 14 h = 1e-06 Radius of convergence (given) for eq 1 = 2.45 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.460000000002529 y[1] (analytic) = 0.7771134485018276 y[1] (numeric) = 0.7771134485018893 absolute error = 6.17284001691587e-14 relative error = 7.943293258939596e-12 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 14 h = 1e-06 Radius of convergence (given) for eq 1 = 2.46 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4700000000022614 y[1] (analytic) = 0.7817217854886582 y[1] (numeric) = 0.7817217854888443 absolute error = 1.860733789271762e-13 relative error = 2.380301820690091e-11 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 13 h = 1e-06 Radius of convergence (given) for eq 1 = 2.47 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4800000000019939 y[1] (analytic) = 0.7863381902858828 y[1] (numeric) = 0.7863381902861952 absolute error = 3.124167591295191e-13 relative error = 3.973058449773833e-11 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 13 h = 1e-06 Radius of convergence (given) for eq 1 = 2.48 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4900000000017263 y[1] (analytic) = 0.7909626401597039 y[1] (numeric) = 0.7909626401601352 absolute error = 4.313216450668733e-13 relative error = 5.453122855205713e-11 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 13 h = 1e-06 Radius of convergence (given) for eq 1 = 2.49 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = arctan ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations = 1500000 Total Elapsed Time = 2 Minutes 6.0 Seconds Elapsed Time(since restart) = 2 Minutes 6.0 Seconds Time to Timeout = 7 Minutes 54.0 Seconds Percent Done = 100 %