##############ECHO OF PROBLEM################# ##############temp/divpostode.ode################# diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=0.0; x_end=1.5; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_iter=10000000; glob_display_interval=0.1; glob_max_minutes=10; glob_max_h=0.001; // # 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=10000000; glob_max_minutes=3; glob_subiter_method=3; // END OVERRIDE BLOCK ! // BEGIN USER DEF BLOCK double exact_soln_y (double x) { return(2.0 - ln(fabs(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 desired_abs_gbl_error = 1e-10 range = 1.5 estimated_steps = 1500000 step_error = 6.666666666666667e-17 est_needed_step_err = 6.666666666666667e-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 = 6.122655795896328e-163 estimated_step_error = 6.122655795896328e-163 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 = 4.108844751257344e-155 estimated_step_error = 4.108844751257344e-155 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 = 2.757399036095543e-147 estimated_step_error = 2.757399036095543e-147 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 = 1.850459169079025e-139 estimated_step_error = 1.850459169079025e-139 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 = 1.241822127175206e-131 estimated_step_error = 1.241822127175206e-131 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 = 8.333727225081322e-124 estimated_step_error = 8.333727225081322e-124 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 = 5.592669671227226e-116 estimated_step_error = 5.592669671227226e-116 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 = 3.753177087972187e-108 estimated_step_error = 3.753177087972187e-108 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 = 2.518714519293996e-100 estimated_step_error = 2.518714519293996e-100 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 = 1.690280732567497e-92 estimated_step_error = 1.690280732567497e-92 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 = 1.134328281966585e-84 estimated_step_error = 1.134328281966585e-84 best_h = 0.001 START of Soultion TOP MAIN SOLVE Loop x[1] = 0 y[1] (analytic) = 2 y[1] (numeric) = 2 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.571 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] = 0.01 y[1] (analytic) = 2.000050000833355 y[1] (numeric) = 2.000050000833355 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.561 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] = 0.02000000000000001 y[1] (analytic) = 2.000200013334756 y[1] (numeric) = 2.000200013334755 absolute error = 4.440892098500626e-16 relative error = 2.220224012046036e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.551 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] = 0.03000000000000002 y[1] (analytic) = 2.000450067516204 y[1] (numeric) = 2.000450067516204 absolute error = 4.440892098500626e-16 relative error = 2.219946486349704e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.541 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] = 0.04000000000000003 y[1] (analytic) = 2.0008002134244 y[1] (numeric) = 2.0008002134244 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.531 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] = 0.05000000000000004 y[1] (analytic) = 2.001250521180819 y[1] (numeric) = 2.00125052118082 absolute error = 4.440892098500626e-16 relative error = 2.219058559385318e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.521 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] = 0.06000000000000005 y[1] (analytic) = 2.001801081037935 y[1] (numeric) = 2.001801081037935 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.511 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] = 0.07000000000000005 y[1] (analytic) = 2.002452003451651 y[1] (numeric) = 2.00245200345165 absolute error = 8.881784197001252e-16 relative error = 4.435454223967223e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.501 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] = 0.08000000000000006 y[1] (analytic) = 2.003203419170097 y[1] (numeric) = 2.003203419170096 absolute error = 4.440892098500626e-16 relative error = 2.216895226916313e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.491 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.188 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.09000000000000007 y[1] (analytic) = 2.004055479338916 y[1] (numeric) = 2.004055479338915 absolute error = 8.881784197001252e-16 relative error = 4.431905348214768e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.481 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.256 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1000000000000001 y[1] (analytic) = 2.005008355623235 y[1] (numeric) = 2.005008355623235 absolute error = 8.881784197001252e-16 relative error = 4.429799093899758e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.471 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.309 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1100000000000001 y[1] (analytic) = 2.006062240346532 y[1] (numeric) = 2.006062240346531 absolute error = 1.332267629550188e-15 relative error = 6.641207848665994e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.461 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.349 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1200000000000001 y[1] (analytic) = 2.007217346646628 y[1] (numeric) = 2.007217346646626 absolute error = 1.332267629550188e-15 relative error = 6.637385989992317e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.451 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.379 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1300000000000001 y[1] (analytic) = 2.008473908649082 y[1] (numeric) = 2.008473908649081 absolute error = 1.332267629550188e-15 relative error = 6.633233440638933e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.441 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.401 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1400000000000001 y[1] (analytic) = 2.009832181658296 y[1] (numeric) = 2.009832181658294 absolute error = 1.77635683940025e-15 relative error = 8.838334143573088e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.431 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.416 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1500000000000001 y[1] (analytic) = 2.011292442366642 y[1] (numeric) = 2.01129244236664 absolute error = 1.332267629550188e-15 relative error = 6.62393792909866e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.421 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.425 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 5.301 Order of pole (three term test) = 2373 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1600000000000001 y[1] (analytic) = 2.01285498908201 y[1] (numeric) = 2.012854989082008 absolute error = 1.332267629550188e-15 relative error = 6.618795873406594e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.411 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.431 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 2.964 Order of pole (three term test) = 1330 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1700000000000001 y[1] (analytic) = 2.014520141974147 y[1] (numeric) = 2.014520141974146 absolute error = 8.881784197001252e-16 relative error = 4.408883292821022e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.401 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.432 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 2.241 Order of pole (three term test) = 1010 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1800000000000001 y[1] (analytic) = 2.016288243340249 y[1] (numeric) = 2.016288243340248 absolute error = 8.881784197001252e-16 relative error = 4.405017103252756e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.391 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.431 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.9 Order of pole (three term test) = 860.3 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1900000000000001 y[1] (analytic) = 2.01815965789026 y[1] (numeric) = 2.01815965789026 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.381 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.428 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.708 Order of pole (three term test) = 777.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2000000000000001 y[1] (analytic) = 2.020134773052408 y[1] (numeric) = 2.020134773052408 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.371 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.423 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.588 Order of pole (three term test) = 727.2 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2100000000000002 y[1] (analytic) = 2.022213999299519 y[1] (numeric) = 2.022213999299519 absolute error = 4.440892098500626e-16 relative error = 2.196054472987983e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.361 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.417 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.507 Order of pole (three term test) = 694.9 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2200000000000002 y[1] (analytic) = 2.024397770496703 y[1] (numeric) = 2.024397770496702 absolute error = 8.881784197001252e-16 relative error = 4.38737106236885e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.351 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.408 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.451 Order of pole (three term test) = 673.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2300000000000002 y[1] (analytic) = 2.026686544271061 y[1] (numeric) = 2.02668654427106 absolute error = 8.881784197001252e-16 relative error = 4.382416324866738e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.341 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.4 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.41 Order of pole (three term test) = 658.9 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2400000000000002 y[1] (analytic) = 2.029080802404081 y[1] (numeric) = 2.029080802404081 absolute error = 4.440892098500626e-16 relative error = 2.188622598587006e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.331 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.39 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.378 Order of pole (three term test) = 648.9 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2500000000000002 y[1] (analytic) = 2.031581051247469 y[1] (numeric) = 2.031581051247469 absolute error = 4.440892098500626e-16 relative error = 2.185929080099338e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.321 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.381 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.354 Order of pole (three term test) = 641.9 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2600000000000002 y[1] (analytic) = 2.034187822163188 y[1] (numeric) = 2.034187822163188 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.311 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.371 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.333 Order of pole (three term test) = 637 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2700000000000002 y[1] (analytic) = 2.036901671988538 y[1] (numeric) = 2.036901671988538 absolute error = 4.440892098500626e-16 relative error = 2.180219182679141e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.301 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.361 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.316 Order of pole (three term test) = 633.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2800000000000002 y[1] (analytic) = 2.039723183527177 y[1] (numeric) = 2.039723183527177 absolute error = 4.440892098500626e-16 relative error = 2.177203325610706e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.291 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.35 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.301 Order of pole (three term test) = 631 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2900000000000002 y[1] (analytic) = 2.042652966067024 y[1] (numeric) = 2.042652966067024 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.281 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.34 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.287 Order of pole (three term test) = 629.3 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3000000000000002 y[1] (analytic) = 2.045691655926058 y[1] (numeric) = 2.045691655926058 absolute error = 4.440892098500626e-16 relative error = 2.170851157180036e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.271 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.329 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.275 Order of pole (three term test) = 628.1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3100000000000002 y[1] (analytic) = 2.048839917027086 y[1] (numeric) = 2.048839917027085 absolute error = 8.881784197001252e-16 relative error = 4.335030825584913e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.261 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.318 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.263 Order of pole (three term test) = 627.2 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3200000000000002 y[1] (analytic) = 2.05209844150263 y[1] (numeric) = 2.05209844150263 absolute error = 4.440892098500626e-16 relative error = 2.164073617856667e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.251 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.308 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.252 Order of pole (three term test) = 626.6 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3300000000000002 y[1] (analytic) = 2.055467950331153 y[1] (numeric) = 2.055467950331152 absolute error = 4.440892098500626e-16 relative error = 2.160526072802625e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.241 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.297 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.241 Order of pole (three term test) = 626.1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3400000000000002 y[1] (analytic) = 2.058949194005907 y[1] (numeric) = 2.058949194005907 absolute error = 4.440892098500626e-16 relative error = 2.156873084303937e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.231 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.287 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.231 Order of pole (three term test) = 625.8 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3500000000000003 y[1] (analytic) = 2.062542953237805 y[1] (numeric) = 2.062542953237805 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.221 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.276 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.22 Order of pole (three term test) = 625.6 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3600000000000003 y[1] (analytic) = 2.066250039693758 y[1] (numeric) = 2.066250039693758 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.211 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.266 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.21 Order of pole (three term test) = 625.4 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3700000000000003 y[1] (analytic) = 2.070071296772055 y[1] (numeric) = 2.070071296772055 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.201 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.255 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.2 Order of pole (three term test) = 625.3 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3800000000000003 y[1] (analytic) = 2.07400760041643 y[1] (numeric) = 2.074007600416431 absolute error = 8.881784197001252e-16 relative error = 4.282426060163869e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.191 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.245 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.189 Order of pole (three term test) = 625.2 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3900000000000003 y[1] (analytic) = 2.078059859970587 y[1] (numeric) = 2.078059859970588 absolute error = 8.881784197001252e-16 relative error = 4.274075241089045e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.181 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.234 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.179 Order of pole (three term test) = 625.2 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4000000000000003 y[1] (analytic) = 2.082229019075056 y[1] (numeric) = 2.082229019075056 absolute error = 4.440892098500626e-16 relative error = 2.132758720495265e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.171 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.224 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.169 Order of pole (three term test) = 625.1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4100000000000003 y[1] (analytic) = 2.086516056608366 y[1] (numeric) = 2.086516056608366 absolute error = 4.440892098500626e-16 relative error = 2.128376670975301e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.161 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.214 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.159 Order of pole (three term test) = 625.1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4200000000000003 y[1] (analytic) = 2.090921987674673 y[1] (numeric) = 2.090921987674673 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.151 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.203 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.149 Order of pole (three term test) = 625.1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4300000000000003 y[1] (analytic) = 2.095447864640073 y[1] (numeric) = 2.095447864640073 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.141 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.193 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.139 Order of pole (three term test) = 625.1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4400000000000003 y[1] (analytic) = 2.100094778220038 y[1] (numeric) = 2.100094778220038 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.131 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.182 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.129 Order of pole (three term test) = 625.1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4500000000000003 y[1] (analytic) = 2.10486385862049 y[1] (numeric) = 2.10486385862049 absolute error = 4.440892098500626e-16 relative error = 2.109823911087128e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.121 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.172 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.119 Order of pole (three term test) = 625.1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4600000000000004 y[1] (analytic) = 2.109756276735282 y[1] (numeric) = 2.109756276735282 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.111 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.161 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.109 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4700000000000004 y[1] (analytic) = 2.114773245402945 y[1] (numeric) = 2.114773245402945 absolute error = 4.440892098500626e-16 relative error = 2.099937715854007e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.101 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.151 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.099 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4800000000000004 y[1] (analytic) = 2.119916020725824 y[1] (numeric) = 2.119916020725823 absolute error = 8.881784197001252e-16 relative error = 4.189686813140965e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.091 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.14 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.089 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4900000000000004 y[1] (analytic) = 2.125185903454887 y[1] (numeric) = 2.125185903454885 absolute error = 1.332267629550188e-15 relative error = 6.268946294930425e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.081 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.13 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.079 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5000000000000003 y[1] (analytic) = 2.130584240443723 y[1] (numeric) = 2.130584240443721 absolute error = 1.77635683940025e-15 relative error = 8.337416590626335e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.071 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.119 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.069 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5100000000000003 y[1] (analytic) = 2.136112426175486 y[1] (numeric) = 2.136112426175484 absolute error = 1.77635683940025e-15 relative error = 8.315839642301294e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.061 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.109 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.059 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5200000000000004 y[1] (analytic) = 2.141771904366788 y[1] (numeric) = 2.141771904366786 absolute error = 2.220446049250313e-15 relative error = 1.036733204279652e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 1.051 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.099 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.049 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5300000000000004 y[1] (analytic) = 2.147564169652822 y[1] (numeric) = 2.147564169652819 absolute error = 2.220446049250313e-15 relative error = 1.033936997379349e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 1.041 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.088 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.039 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5400000000000004 y[1] (analytic) = 2.153490769358282 y[1] (numeric) = 2.153490769358279 absolute error = 2.664535259100376e-15 relative error = 1.237309812056627e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 1.031 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.078 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.029 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5500000000000004 y[1] (analytic) = 2.159553305358981 y[1] (numeric) = 2.159553305358978 absolute error = 2.664535259100376e-15 relative error = 1.233836299612642e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 1.021 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.067 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.019 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5600000000000004 y[1] (analytic) = 2.165753436039385 y[1] (numeric) = 2.165753436039382 absolute error = 2.220446049250313e-15 relative error = 1.025253388636403e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 1.011 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.057 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.009 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5700000000000004 y[1] (analytic) = 2.172092878351663 y[1] (numeric) = 2.172092878351662 absolute error = 1.332267629550188e-15 relative error = 6.133566583769688e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1.001 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.046 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.9994 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5800000000000004 y[1] (analytic) = 2.17857340998226 y[1] (numeric) = 2.178573409982259 absolute error = 8.881784197001252e-16 relative error = 4.076880841519853e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.9908 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.036 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.9894 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5900000000000004 y[1] (analytic) = 2.185196871632402 y[1] (numeric) = 2.185196871632401 absolute error = 8.881784197001252e-16 relative error = 4.064523573277092e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.9808 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.025 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.9794 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6000000000000004 y[1] (analytic) = 2.191965169419438 y[1] (numeric) = 2.191965169419437 absolute error = 4.440892098500626e-16 relative error = 2.025986617149048e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.9708 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.015 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.9694 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6100000000000004 y[1] (analytic) = 2.198880277406405 y[1] (numeric) = 2.198880277406404 absolute error = 8.881784197001252e-16 relative error = 4.039230461186082e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.9608 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.004 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.9594 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6200000000000004 y[1] (analytic) = 2.205944240267755 y[1] (numeric) = 2.205944240267754 absolute error = 8.881784197001252e-16 relative error = 4.026295875875445e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.9508 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.994 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.9494 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6300000000000004 y[1] (analytic) = 2.213159176099776 y[1] (numeric) = 2.213159176099776 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.9408 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.9836 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.9395 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6400000000000005 y[1] (analytic) = 2.220527279384879 y[1] (numeric) = 2.220527279384878 absolute error = 4.440892098500626e-16 relative error = 1.999926837075752e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.9308 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.9731 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.9295 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6500000000000005 y[1] (analytic) = 2.228050824119617 y[1] (numeric) = 2.228050824119616 absolute error = 8.881784197001252e-16 relative error = 3.986347214727818e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.9208 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.9627 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.9195 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6600000000000005 y[1] (analytic) = 2.235732167117059 y[1] (numeric) = 2.235732167117058 absolute error = 8.881784197001252e-16 relative error = 3.972651253863817e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.9108 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.9522 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.9095 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6700000000000005 y[1] (analytic) = 2.243573751494981 y[1] (numeric) = 2.243573751494981 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.9008 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.9417 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.8995 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6800000000000005 y[1] (analytic) = 2.251578110362207 y[1] (numeric) = 2.251578110362207 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.8908 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.9313 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.8895 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6900000000000005 y[1] (analytic) = 2.259747870716431 y[1] (numeric) = 2.259747870716432 absolute error = 8.881784197001252e-16 relative error = 3.930431492866224e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.8808 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.9208 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.8795 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7000000000000005 y[1] (analytic) = 2.268085757567932 y[1] (numeric) = 2.268085757567932 absolute error = 4.440892098500626e-16 relative error = 1.957991263638371e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.8708 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.9104 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.8696 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7100000000000005 y[1] (analytic) = 2.276594598304711 y[1] (numeric) = 2.276594598304712 absolute error = 8.881784197001252e-16 relative error = 3.901346424881778e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.8608 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.8999 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.8596 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7200000000000005 y[1] (analytic) = 2.285277327315926 y[1] (numeric) = 2.285277327315927 absolute error = 8.881784197001252e-16 relative error = 3.886523570175603e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.8508 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.8895 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.8496 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7300000000000005 y[1] (analytic) = 2.294136990891822 y[1] (numeric) = 2.294136990891822 absolute error = 4.440892098500626e-16 relative error = 1.935757156670176e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.8408 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.879 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.8396 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7400000000000005 y[1] (analytic) = 2.30317675241995 y[1] (numeric) = 2.303176752419951 absolute error = 8.881784197001252e-16 relative error = 3.856318967994597e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.8308 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.8686 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.8296 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7500000000000006 y[1] (analytic) = 2.312399897899106 y[1] (numeric) = 2.312399897899106 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.8208 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.8581 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.8196 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7600000000000006 y[1] (analytic) = 2.32180984179426 y[1] (numeric) = 2.32180984179426 absolute error = 4.440892098500626e-16 relative error = 1.912685534603803e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.8108 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.8477 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.8096 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7700000000000006 y[1] (analytic) = 2.331410133257819 y[1] (numeric) = 2.331410133257818 absolute error = 8.881784197001252e-16 relative error = 3.809618938470601e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.8008 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.8372 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.7997 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7800000000000006 y[1] (analytic) = 2.341204462744726 y[1] (numeric) = 2.341204462744725 absolute error = 8.881784197001252e-16 relative error = 3.793681559357971e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.7908 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.8267 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.7897 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7900000000000006 y[1] (analytic) = 2.351196669051421 y[1] (numeric) = 2.35119666905142 absolute error = 1.332267629550188e-15 relative error = 5.666338537676156e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.7808 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.8163 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.7797 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8000000000000006 y[1] (analytic) = 2.361390746811344 y[1] (numeric) = 2.361390746811343 absolute error = 1.77635683940025e-15 relative error = 7.522502753087e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.7708 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.8058 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.7697 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8100000000000006 y[1] (analytic) = 2.371790854482695 y[1] (numeric) = 2.371790854482693 absolute error = 1.77635683940025e-15 relative error = 7.48951719770286e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.7608 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.7954 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.7597 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8200000000000006 y[1] (analytic) = 2.382401322867441 y[1] (numeric) = 2.382401322867439 absolute error = 2.220446049250313e-15 relative error = 9.320201545967075e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.7508 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.7849 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.7497 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8300000000000006 y[1] (analytic) = 2.393226664204251 y[1] (numeric) = 2.393226664204248 absolute error = 2.664535259100376e-15 relative error = 1.11336518974743e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.7408 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.7745 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.7397 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8400000000000006 y[1] (analytic) = 2.404271581882078 y[1] (numeric) = 2.404271581882075 absolute error = 2.664535259100376e-15 relative error = 1.10825053175339e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.7308 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.764 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.7298 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8500000000000006 y[1] (analytic) = 2.415540980825635 y[1] (numeric) = 2.415540980825632 absolute error = 3.108624468950438e-15 relative error = 1.286926818309622e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.7208 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.7536 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.7198 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8600000000000007 y[1] (analytic) = 2.427039978609021 y[1] (numeric) = 2.427039978609018 absolute error = 2.220446049250313e-15 relative error = 9.148782339065094e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.7108 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.7431 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.7098 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8700000000000007 y[1] (analytic) = 2.438773917359315 y[1] (numeric) = 2.438773917359313 absolute error = 2.220446049250313e-15 relative error = 9.104763805472358e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.7008 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.7327 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.6998 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8800000000000007 y[1] (analytic) = 2.450748376518227 y[1] (numeric) = 2.450748376518225 absolute error = 1.77635683940025e-15 relative error = 7.248222038706059e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.6908 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.7222 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.6898 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8900000000000007 y[1] (analytic) = 2.462969186536775 y[1] (numeric) = 2.462969186536772 absolute error = 2.664535259100376e-15 relative error = 1.081838649734399e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.6808 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.7117 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.6798 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9000000000000007 y[1] (analytic) = 2.475442443585815 y[1] (numeric) = 2.475442443585812 absolute error = 3.108624468950438e-15 relative error = 1.255785395861365e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.6708 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.7013 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.6698 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9100000000000007 y[1] (analytic) = 2.488174525373867 y[1] (numeric) = 2.488174525373864 absolute error = 3.108624468950438e-15 relative error = 1.249359495183861e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.6608 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.6908 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.6599 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9200000000000007 y[1] (analytic) = 2.501172108173523 y[1] (numeric) = 2.50117210817352 absolute error = 3.108624468950438e-15 relative error = 1.242867077716018e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.6508 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.6804 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.6499 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9300000000000007 y[1] (analytic) = 2.514442185168662 y[1] (numeric) = 2.514442185168658 absolute error = 3.552713678800501e-15 relative error = 1.412923192172023e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.6408 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.6699 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.6399 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9400000000000007 y[1] (analytic) = 2.527992086247063 y[1] (numeric) = 2.527992086247059 absolute error = 3.996802888650564e-15 relative error = 1.581018750174977e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.6308 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.6595 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.6299 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9500000000000007 y[1] (analytic) = 2.541829499376963 y[1] (numeric) = 2.541829499376959 absolute error = 3.996802888650564e-15 relative error = 1.572411874844569e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.6208 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.649 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.6199 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9600000000000007 y[1] (analytic) = 2.555962493721842 y[1] (numeric) = 2.555962493721838 absolute error = 3.552713678800501e-15 relative error = 1.389970974741202e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.6108 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.6386 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.6099 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9700000000000008 y[1] (analytic) = 2.570399544665549 y[1] (numeric) = 2.570399544665546 absolute error = 3.108624468950438e-15 relative error = 1.209393487250606e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.6008 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.6281 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.5999 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9800000000000008 y[1] (analytic) = 2.585149560940141 y[1] (numeric) = 2.585149560940138 absolute error = 3.108624468950438e-15 relative error = 1.202493084314984e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.5908 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.6177 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.59 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9900000000000008 y[1] (analytic) = 2.600221914071749 y[1] (numeric) = 2.600221914071747 absolute error = 2.664535259100376e-15 relative error = 1.024733790866302e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.5808 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.6072 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.58 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.000000000000001 y[1] (analytic) = 2.615626470386015 y[1] (numeric) = 2.615626470386013 absolute error = 1.77635683940025e-15 relative error = 6.791324600481256e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.5708 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.5967 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.57 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.010999999999999 y[1] (analytic) = 2.632967601307485 y[1] (numeric) = 2.632967601307485 absolute error = 4.440892098500626e-16 relative error = 1.68664897216941e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.5598 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.5852 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.559 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.020999999999998 y[1] (analytic) = 2.649104301818291 y[1] (numeric) = 2.649104301818292 absolute error = 8.881784197001252e-16 relative error = 3.352749905281184e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.5498 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.5748 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.549 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.030999999999997 y[1] (analytic) = 2.665607330148701 y[1] (numeric) = 2.665607330148703 absolute error = 2.220446049250313e-15 relative error = 8.329981779898713e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.5398 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.5643 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.539 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.040999999999996 y[1] (analytic) = 2.682488981415228 y[1] (numeric) = 2.682488981415231 absolute error = 3.552713678800501e-15 relative error = 1.324409421031866e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.5298 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.5539 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.529 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.050999999999995 y[1] (analytic) = 2.699762259981916 y[1] (numeric) = 2.699762259981921 absolute error = 5.329070518200751e-15 relative error = 1.973903627438828e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.5198 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.5434 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.5191 Order of pole (three term test) = 625 Radius of convergence (six term test) for eq 1 = 0.5886 Order of pole (six term test) = -4.429e-11 TOP MAIN SOLVE Loop x[1] = 1.060999999999994 y[1] (analytic) = 2.717440934425537 y[1] (numeric) = 2.717440934425545 absolute error = 7.993605777301127e-15 relative error = 2.941593201175121e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.5098 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.533 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.5091 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.070999999999993 y[1] (analytic) = 2.735539597948169 y[1] (numeric) = 2.735539597948179 absolute error = 9.769962616701378e-15 relative error = 3.571493764531678e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.4998 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.5225 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4991 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.080999999999992 y[1] (analytic) = 2.754073734897819 y[1] (numeric) = 2.754073734897831 absolute error = 1.154631945610163e-14 relative error = 4.192451098819261e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.4898 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.5121 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4891 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.090999999999991 y[1] (analytic) = 2.773059794153156 y[1] (numeric) = 2.773059794153169 absolute error = 1.376676550535194e-14 relative error = 4.96446760159244e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.4798 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.5016 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4791 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.10099999999999 y[1] (analytic) = 2.792515270239913 y[1] (numeric) = 2.792515270239929 absolute error = 1.554312234475219e-14 relative error = 5.565993679746946e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.4698 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.4912 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4691 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.110999999999988 y[1] (analytic) = 2.812458793177247 y[1] (numeric) = 2.812458793177265 absolute error = 1.731947918415244e-14 relative error = 6.158127267915115e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.4598 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.4807 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4591 Order of pole (three term test) = 625 Radius of convergence (six term test) for eq 1 = 1.586 Order of pole (six term test) = -2.935e-10 TOP MAIN SOLVE Loop x[1] = 1.120999999999987 y[1] (analytic) = 2.83291022820599 y[1] (numeric) = 2.832910228206009 absolute error = 1.909583602355269e-14 relative error = 6.740713430811961e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.4498 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.4702 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4492 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.130999999999986 y[1] (analytic) = 2.853890786732123 y[1] (numeric) = 2.853890786732145 absolute error = 2.176037128265307e-14 relative error = 7.624808694088117e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.4398 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.4598 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4392 Order of pole (three term test) = 625 Radius of convergence (six term test) for eq 1 = 2.983 Order of pole (six term test) = -1.27e-09 TOP MAIN SOLVE Loop x[1] = 1.140999999999985 y[1] (analytic) = 2.875423150033514 y[1] (numeric) = 2.875423150033538 absolute error = 2.442490654175344e-14 relative error = 8.494369443143965e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.4298 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.4493 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4292 Order of pole (three term test) = 625 Radius of convergence (six term test) for eq 1 = 0.5963 Order of pole (six term test) = -8.091e-11 TOP MAIN SOLVE Loop x[1] = 1.150999999999984 y[1] (analytic) = 2.897531607533112 y[1] (numeric) = 2.897531607533139 absolute error = 2.708944180085382e-14 relative error = 9.349144537517957e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.4198 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.4389 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4192 Order of pole (three term test) = 625 Radius of convergence (six term test) for eq 1 = 0.6272 Order of pole (six term test) = -1.175e-10 TOP MAIN SOLVE Loop x[1] = 1.160999999999983 y[1] (analytic) = 2.920242211746277 y[1] (numeric) = 2.920242211746306 absolute error = 2.97539770599542e-14 relative error = 1.018887301206485e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 0.4098 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.4284 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4092 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.170999999999982 y[1] (analytic) = 2.943582952374446 y[1] (numeric) = 2.943582952374477 absolute error = 3.153033389935445e-14 relative error = 1.071154929536484e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 0.3998 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.418 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.3992 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.180999999999981 y[1] (analytic) = 2.967583952455929 y[1] (numeric) = 2.967583952455963 absolute error = 3.419486915845482e-14 relative error = 1.152279757078335e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 0.3898 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.4075 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.3892 Order of pole (three term test) = 625 Radius of convergence (six term test) for eq 1 = 0.215 Order of pole (six term test) = -1.254e-11 TOP MAIN SOLVE Loop x[1] = 1.19099999999998 y[1] (analytic) = 2.992277690014306 y[1] (numeric) = 2.992277690014344 absolute error = 3.730349362740526e-14 relative error = 1.246658816188511e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 0.3798 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.3971 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.3793 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.200999999999979 y[1] (analytic) = 3.017699249287779 y[1] (numeric) = 3.017699249287819 absolute error = 3.996802888650564e-14 relative error = 1.324453684241021e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 0.3698 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.3866 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.3693 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.210999999999977 y[1] (analytic) = 3.043886606406725 y[1] (numeric) = 3.043886606406768 absolute error = 4.307665335545607e-14 relative error = 1.415185876661404e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 0.3598 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.3762 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.3593 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.220999999999976 y[1] (analytic) = 3.070880955347464 y[1] (numeric) = 3.07088095534751 absolute error = 4.618527782440651e-14 relative error = 1.503974868969831e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 0.3498 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.3657 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.3493 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.230999999999975 y[1] (analytic) = 3.098727081174039 y[1] (numeric) = 3.098727081174088 absolute error = 4.884981308350689e-14 relative error = 1.576447741406087e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 0.3398 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.3552 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.3393 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.240999999999974 y[1] (analytic) = 3.12747378904666 y[1] (numeric) = 3.127473789046711 absolute error = 5.10702591327572e-14 relative error = 1.632955624172467e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 0.3298 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.3448 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.3293 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.250999999999973 y[1] (analytic) = 3.157174399303809 y[1] (numeric) = 3.157174399303863 absolute error = 5.417888360170764e-14 relative error = 1.716056091600599e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 0.3198 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.3343 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.3193 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.260999999999972 y[1] (analytic) = 3.187887321218344 y[1] (numeric) = 3.187887321218402 absolute error = 5.773159728050814e-14 relative error = 1.810967310426905e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 0.3098 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.3239 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.3094 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.270999999999971 y[1] (analytic) = 3.219676720923608 y[1] (numeric) = 3.219676720923669 absolute error = 6.128431095930864e-14 relative error = 1.903430569940215e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 0.2998 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.3134 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.2994 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.28099999999997 y[1] (analytic) = 3.252613302687652 y[1] (numeric) = 3.252613302687717 absolute error = 6.483702463810914e-14 relative error = 1.993382508290609e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 0.2898 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.303 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.2894 Order of pole (three term test) = 625 Radius of convergence (six term test) for eq 1 = 0.1775 Order of pole (six term test) = -1.052e-11 TOP MAIN SOLVE Loop x[1] = 1.290999999999969 y[1] (analytic) = 3.286775227430942 y[1] (numeric) = 3.286775227431011 absolute error = 6.883382752675971e-14 relative error = 2.094266348130006e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 0.2798 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.2925 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.2794 Order of pole (three term test) = 625 Radius of convergence (six term test) for eq 1 = 0.1741 Order of pole (six term test) = -2.819e-11 TOP MAIN SOLVE Loop x[1] = 1.300999999999968 y[1] (analytic) = 3.322249198474641 y[1] (numeric) = 3.322249198474714 absolute error = 7.327471962526033e-14 relative error = 2.205575658168667e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 0.2698 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.2821 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.2694 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.310999999999966 y[1] (analytic) = 3.359131752440537 y[1] (numeric) = 3.359131752440614 absolute error = 7.682743330406083e-14 relative error = 2.287121761396908e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 0.2598 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.2716 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.2594 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.320999999999965 y[1] (analytic) = 3.397530803651099 y[1] (numeric) = 3.39753080365118 absolute error = 8.126832540256146e-14 relative error = 2.391982003966758e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 0.2498 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.2612 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.2494 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.330999999999964 y[1] (analytic) = 3.437567504217098 y[1] (numeric) = 3.437567504217184 absolute error = 8.615330671091215e-14 relative error = 2.506228797113716e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 0.2398 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.2507 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.2395 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.340999999999963 y[1] (analytic) = 3.479378500559851 y[1] (numeric) = 3.479378500559941 absolute error = 9.059419880941277e-14 relative error = 2.603746582754238e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 0.2298 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.2402 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.2295 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.350999999999962 y[1] (analytic) = 3.523118692288129 y[1] (numeric) = 3.523118692288224 absolute error = 9.547918011776346e-14 relative error = 2.710075602243007e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 0.2198 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.2298 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.2195 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.360999999999961 y[1] (analytic) = 3.56896463391136 y[1] (numeric) = 3.568964633911461 absolute error = 1.016964290556643e-13 relative error = 2.849465867197778e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 0.2098 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.2193 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.2095 Order of pole (three term test) = 625 Radius of convergence (six term test) for eq 1 = 0.287 Order of pole (six term test) = 1.982e-11 TOP MAIN SOLVE Loop x[1] = 1.37099999999996 y[1] (analytic) = 3.61711876795355 y[1] (numeric) = 3.617118767953657 absolute error = 1.06581410364015e-13 relative error = 2.946583101121542e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 0.1998 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.2089 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1995 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.380999999999959 y[1] (analytic) = 3.6678147458949 y[1] (numeric) = 3.667814745895011 absolute error = 1.119104808822158e-13 relative error = 3.051148671220882e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 0.1898 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.1984 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1895 Order of pole (three term test) = 625 Radius of convergence (six term test) for eq 1 = 0.2945 Order of pole (six term test) = -1.848e-11 TOP MAIN SOLVE Loop x[1] = 1.390999999999958 y[1] (analytic) = 3.721324190662625 y[1] (numeric) = 3.721324190662744 absolute error = 1.190159082398168e-13 relative error = 3.198213919078752e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 0.1798 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.188 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1795 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.400999999999957 y[1] (analytic) = 3.777965396306684 y[1] (numeric) = 3.777965396306809 absolute error = 1.247890679678676e-13 relative error = 3.303075991375163e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 0.1698 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.1775 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1696 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.410999999999955 y[1] (analytic) = 3.838114671457698 y[1] (numeric) = 3.83811467145783 absolute error = 1.318944953254686e-13 relative error = 3.436439674570111e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 0.1598 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.1671 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1596 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.420999999999954 y[1] (analytic) = 3.902221353428768 y[1] (numeric) = 3.902221353428907 absolute error = 1.385558334732195e-13 relative error = 3.550691283862577e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 0.1498 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.1566 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1496 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.430999999999953 y[1] (analytic) = 3.970828017539234 y[1] (numeric) = 3.97082801753938 absolute error = 1.456612608308205e-13 relative error = 3.668284302101012e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 0.1398 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.1462 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1396 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.440999999999952 y[1] (analytic) = 4.044598200305071 y[1] (numeric) = 4.044598200305225 absolute error = 1.536548666081217e-13 relative error = 3.799014364307732e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 0.1298 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.1357 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1296 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.450999999999951 y[1] (analytic) = 4.124355260143009 y[1] (numeric) = 4.124355260143171 absolute error = 1.625366508051229e-13 relative error = 3.940898408433591e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 0.1198 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.1252 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1196 Order of pole (three term test) = 625 Radius of convergence (six term test) for eq 1 = 0.2039 Order of pole (six term test) = -6.492e-11 TOP MAIN SOLVE Loop x[1] = 1.46099999999995 y[1] (analytic) = 4.211138217627107 y[1] (numeric) = 4.211138217627281 absolute error = 1.731947918415244e-13 relative error = 4.112778609748797e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 0.1098 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.1148 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1096 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.470999999999949 y[1] (analytic) = 4.306284337869535 y[1] (numeric) = 4.30628433786972 absolute error = 1.84741111297626e-13 relative error = 4.290035139412641e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 0.0998 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.1043 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.09965 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.480999999999948 y[1] (analytic) = 4.41155546691282 y[1] (numeric) = 4.411555466913015 absolute error = 1.945110739143274e-13 relative error = 4.409126789251164e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 0.0898 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.09388 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.08967 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.490999999999947 y[1] (analytic) = 4.529339273357407 y[1] (numeric) = 4.529339273357615 absolute error = 2.078337502098293e-13 relative error = 4.588610781099004e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 0.0798 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.08342 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.07968 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ; Iterations = 1501 Total Elapsed Time = 0 Seconds Elapsed Time(since restart) = 0 Seconds Time to Timeout = 3 Minutes 0 Seconds Percent Done = 100.1 %