##############ECHO OF PROBLEM################# ##############temp/tanpostode.ode################# diff ( y , x , 1 ) = tan ( x ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=0.1; x_end=1.5; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_iter=10000; glob_max_h=0.001; // # 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(-ln(cos(x))); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1e-10 range = 1.4 estimated_steps = 1400000 step_error = 7.142857142857143e-17 est_needed_step_err = 7.142857142857143e-17 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.754534988133388e-162 estimated_step_error = 1.754534988133388e-162 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 = 1.177448859057355e-154 estimated_step_error = 1.177448859057355e-154 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 = 7.901730367303554e-147 estimated_step_error = 7.901730367303554e-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 = 5.302767971737841e-139 estimated_step_error = 5.302767971737841e-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 = 3.558636051649607e-131 estimated_step_error = 3.558636051649607e-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 = 2.388171912256999e-123 estimated_step_error = 2.388171912256999e-123 best_h = 6.4e-05 opt_iter = 7 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.602690723079055e-115 estimated_step_error = 1.602690723079055e-115 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 = 1.075568586951286e-107 estimated_step_error = 1.075568586951286e-107 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 = 7.218301139703027e-100 estimated_step_error = 7.218301139703027e-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 = 4.844499160745373e-92 estimated_step_error = 4.844499160745373e-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 = 3.251597531276495e-84 estimated_step_error = 3.251597531276495e-84 best_h = 0.001 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 0.005008355623235254 y[1] (numeric) = 0.005008355623235254 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 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] = 0.11 y[1] (analytic) = 0.006062240346532338 y[1] (numeric) = 0.006062240346532249 absolute error = 8.933825901280557e-17 relative error = 1.473683884274036e-12 % Correct digits = 14 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] = 0.12 y[1] (analytic) = 0.007217346646627739 y[1] (numeric) = 0.007217346646627682 absolute error = 5.637851296924623e-17 relative error = 7.811529046562943e-13 % Correct digits = 15 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] = 0.13 y[1] (analytic) = 0.008473908649082243 y[1] (numeric) = 0.00847390864908224 absolute error = 3.469446951953614e-18 relative error = 4.094269947469128e-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] = 0.14 y[1] (analytic) = 0.009832181658295606 y[1] (numeric) = 0.009832181658295499 absolute error = 1.07552855510562e-16 relative error = 1.093885968022342e-12 % Correct digits = 14 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] = 0.15 y[1] (analytic) = 0.01129244236664183 y[1] (numeric) = 0.01129244236664174 absolute error = 9.71445146547012e-17 relative error = 8.602613278919059e-13 % Correct digits = 15 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) = 0.01285498908200967 y[1] (numeric) = 0.0128549890820096 absolute error = 6.938893903907228e-17 relative error = 5.397821701473156e-13 % Correct digits = 15 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) = 0.01452014197414718 y[1] (numeric) = 0.01452014197414707 absolute error = 1.110223024625157e-16 relative error = 7.646089319249677e-13 % Correct digits = 15 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) = 0.01628824334024881 y[1] (numeric) = 0.0162882433402488 absolute error = 1.734723475976807e-17 relative error = 1.065015692447476e-13 % Correct digits = 15 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) = 0.01815965789025992 y[1] (numeric) = 0.01815965789025985 absolute error = 6.591949208711867e-17 relative error = 3.629996362567773e-13 % Correct digits = 15 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) = 0.02013477305240835 y[1] (numeric) = 0.0201347730524083 absolute error = 5.551115123125783e-17 relative error = 2.756979236208379e-13 % Correct digits = 15 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] = 0.2100000000000001 y[1] (analytic) = 0.02221399929951903 y[1] (numeric) = 0.02221399929951901 absolute error = 2.081668171172169e-17 relative error = 9.370974326163953e-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] = 0.2200000000000001 y[1] (analytic) = 0.02439777049670313 y[1] (numeric) = 0.0243977704967031 absolute error = 2.081668171172169e-17 relative error = 8.532206545075357e-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] = 0.2300000000000001 y[1] (analytic) = 0.02668654427106085 y[1] (numeric) = 0.02668654427106075 absolute error = 1.07552855510562e-16 relative error = 4.030227908796472e-13 % Correct digits = 15 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] = 0.2400000000000001 y[1] (analytic) = 0.02908080240408099 y[1] (numeric) = 0.02908080240408089 absolute error = 9.367506770274758e-17 relative error = 3.221199552925744e-13 % Correct digits = 15 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] = 0.2500000000000001 y[1] (analytic) = 0.03158105124746966 y[1] (numeric) = 0.03158105124746956 absolute error = 9.71445146547012e-17 relative error = 3.076038029686697e-13 % Correct digits = 15 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] = 0.2600000000000001 y[1] (analytic) = 0.03418782216318843 y[1] (numeric) = 0.03418782216318839 absolute error = 4.85722573273506e-17 relative error = 1.420747337911759e-13 % Correct digits = 15 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] = 0.2700000000000001 y[1] (analytic) = 0.03690167198853801 y[1] (numeric) = 0.03690167198853799 absolute error = 1.387778780781446e-17 relative error = 3.760747700571677e-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] = 0.2800000000000001 y[1] (analytic) = 0.03972318352717689 y[1] (numeric) = 0.0397231835271768 absolute error = 9.020562075079397e-17 relative error = 2.270855775924384e-13 % Correct digits = 15 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] = 0.2900000000000001 y[1] (analytic) = 0.04265296606702416 y[1] (numeric) = 0.04265296606702404 absolute error = 1.249000902703301e-16 relative error = 2.928286161249939e-13 % Correct digits = 15 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) = 0.04569165592605806 y[1] (numeric) = 0.045691655926058 absolute error = 6.245004513516506e-17 relative error = 1.366771325517875e-13 % Correct digits = 15 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) = 0.04883991702708585 y[1] (numeric) = 0.04883991702708582 absolute error = 3.469446951953614e-17 relative error = 7.103711806122671e-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) = 0.05209844150263039 y[1] (numeric) = 0.05209844150263034 absolute error = 4.85722573273506e-17 relative error = 9.323168971359391e-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) = 0.05546795033115276 y[1] (numeric) = 0.05546795033115269 absolute error = 6.938893903907228e-17 relative error = 1.250973555446144e-13 % Correct digits = 15 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) = 0.05894919400590685 y[1] (numeric) = 0.05894919400590681 absolute error = 4.163336342344337e-17 relative error = 7.062583997208105e-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] = 0.3500000000000002 y[1] (analytic) = 0.06254295323780479 y[1] (numeric) = 0.06254295323780475 absolute error = 4.163336342344337e-17 relative error = 6.656763275175439e-14 % 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] = 0.3600000000000002 y[1] (analytic) = 0.0662500396937582 y[1] (numeric) = 0.06625003969375816 absolute error = 4.163336342344337e-17 relative error = 6.284277506231576e-14 % 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] = 0.3700000000000002 y[1] (analytic) = 0.07007129677205522 y[1] (numeric) = 0.07007129677205519 absolute error = 2.775557561562891e-17 relative error = 3.961047803342206e-14 % 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] = 0.3800000000000002 y[1] (analytic) = 0.07400760041643002 y[1] (numeric) = 0.07400760041642994 absolute error = 8.326672684688674e-17 relative error = 1.125110480252798e-13 % Correct digits = 15 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] = 0.3900000000000002 y[1] (analytic) = 0.07805985997058702 y[1] (numeric) = 0.07805985997058701 absolute error = 1.387778780781446e-17 relative error = 1.777839188161958e-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] = 0.4000000000000002 y[1] (analytic) = 0.08222901907505553 y[1] (numeric) = 0.08222901907505546 absolute error = 6.938893903907228e-17 relative error = 8.43849772496212e-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) = 0.08651605660836616 y[1] (numeric) = 0.08651605660836607 absolute error = 8.326672684688674e-17 relative error = 9.624424657241578e-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) = 0.09092198767467256 y[1] (numeric) = 0.09092198767467245 absolute error = 1.110223024625157e-16 relative error = 1.221072100400663e-13 % Correct digits = 15 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) = 0.09544786464007339 y[1] (numeric) = 0.09544786464007325 absolute error = 1.387778780781446e-16 relative error = 1.453965246906941e-13 % Correct digits = 15 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) = 0.1000947782200377 y[1] (numeric) = 0.1000947782200375 absolute error = 1.52655665885959e-16 relative error = 1.52511118562426e-13 % Correct digits = 15 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) = 0.1048638586204904 y[1] (numeric) = 0.1048638586204902 absolute error = 1.387778780781446e-16 relative error = 1.323409989903112e-13 % Correct digits = 15 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] = 0.4600000000000003 y[1] (analytic) = 0.1097562767352823 y[1] (numeric) = 0.1097562767352821 absolute error = 1.52655665885959e-16 relative error = 1.390860463079888e-13 % Correct digits = 15 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] = 0.4700000000000003 y[1] (analytic) = 0.1147732454029447 y[1] (numeric) = 0.1147732454029447 absolute error = 5.551115123125783e-17 relative error = 4.836593322456801e-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] = 0.4800000000000003 y[1] (analytic) = 0.1199160207258237 y[1] (numeric) = 0.1199160207258236 absolute error = 1.249000902703301e-16 relative error = 1.041562999792179e-13 % Correct digits = 15 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] = 0.4900000000000003 y[1] (analytic) = 0.1251859034548867 y[1] (numeric) = 0.1251859034548866 absolute error = 1.110223024625157e-16 relative error = 8.868594578024896e-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) = 0.1305842404437229 y[1] (numeric) = 0.1305842404437228 absolute error = 1.387778780781446e-16 relative error = 1.062745991450269e-13 % Correct digits = 15 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) = 0.1361124261754862 y[1] (numeric) = 0.1361124261754861 absolute error = 1.665334536937735e-16 relative error = 1.223499267282667e-13 % Correct digits = 15 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) = 0.1417719043667884 y[1] (numeric) = 0.1417719043667884 absolute error = 5.551115123125783e-17 relative error = 3.915525539365042e-14 % Correct digits = 16 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) = 0.1475641696528218 y[1] (numeric) = 0.1475641696528217 absolute error = 1.387778780781446e-16 relative error = 9.404578252610443e-14 % Correct digits = 16 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) = 0.1534907693582817 y[1] (numeric) = 0.1534907693582815 absolute error = 1.665334536937735e-16 relative error = 1.084973737443763e-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) = 0.159553305358981 y[1] (numeric) = 0.1595533053589809 absolute error = 1.387778780781446e-16 relative error = 8.697900539628839e-14 % Correct digits = 16 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) = 0.1657534360393848 y[1] (numeric) = 0.1657534360393846 absolute error = 1.942890293094024e-16 relative error = 1.172156873195903e-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) = 0.1720928783516632 y[1] (numeric) = 0.1720928783516629 absolute error = 2.498001805406602e-16 relative error = 1.451542811842603e-13 % Correct digits = 15 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) = 0.1785734099822599 y[1] (numeric) = 0.1785734099822597 absolute error = 1.942890293094024e-16 relative error = 1.088006491720709e-13 % Correct digits = 15 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) = 0.1851968716324019 y[1] (numeric) = 0.1851968716324016 absolute error = 3.05311331771918e-16 relative error = 1.648577155114866e-13 % Correct digits = 15 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) = 0.1919651694194379 y[1] (numeric) = 0.1919651694194377 absolute error = 2.220446049250313e-16 relative error = 1.156692152001131e-13 % Correct digits = 15 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) = 0.1988802774064051 y[1] (numeric) = 0.1988802774064047 absolute error = 3.33066907387547e-16 relative error = 1.674710593383456e-13 % Correct digits = 15 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) = 0.2059442402677548 y[1] (numeric) = 0.2059442402677545 absolute error = 3.33066907387547e-16 relative error = 1.617267406723858e-13 % Correct digits = 15 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) = 0.2131591760997758 y[1] (numeric) = 0.2131591760997755 absolute error = 3.05311331771918e-16 relative error = 1.432316156209046e-13 % Correct digits = 15 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) = 0.220527279384879 y[1] (numeric) = 0.2205272793848786 absolute error = 3.885780586188048e-16 relative error = 1.762040776554597e-13 % Correct digits = 15 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) = 0.2280508241196166 y[1] (numeric) = 0.2280508241196162 absolute error = 4.163336342344337e-16 relative error = 1.825617757978632e-13 % Correct digits = 15 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) = 0.2357321671170591 y[1] (numeric) = 0.2357321671170586 absolute error = 4.996003610813204e-16 relative error = 2.119355907983617e-13 % Correct digits = 15 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) = 0.2435737514949815 y[1] (numeric) = 0.2435737514949811 absolute error = 4.440892098500626e-16 relative error = 1.823222769795096e-13 % Correct digits = 15 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) = 0.2515781103622067 y[1] (numeric) = 0.2515781103622062 absolute error = 4.996003610813204e-16 relative error = 1.985865782845839e-13 % Correct digits = 15 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) = 0.259747870716431 y[1] (numeric) = 0.2597478707164306 absolute error = 3.885780586188048e-16 relative error = 1.495981690040565e-13 % Correct digits = 15 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) = 0.2680857575679316 y[1] (numeric) = 0.2680857575679311 absolute error = 4.440892098500626e-16 relative error = 1.656519219367827e-13 % Correct digits = 15 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) = 0.2765945983047113 y[1] (numeric) = 0.2765945983047109 absolute error = 3.33066907387547e-16 relative error = 1.204169963654253e-13 % Correct digits = 15 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) = 0.285277327315926 y[1] (numeric) = 0.2852773273159257 absolute error = 3.33066907387547e-16 relative error = 1.167519727281717e-13 % Correct digits = 15 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) = 0.2941369908918218 y[1] (numeric) = 0.2941369908918214 absolute error = 3.885780586188048e-16 relative error = 1.321078513248667e-13 % Correct digits = 15 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) = 0.3031767524199507 y[1] (numeric) = 0.3031767524199502 absolute error = 4.440892098500626e-16 relative error = 1.464786486118581e-13 % Correct digits = 15 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) = 0.3123998978991059 y[1] (numeric) = 0.3123998978991054 absolute error = 4.996003610813204e-16 relative error = 1.599233432664801e-13 % Correct digits = 15 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) = 0.32180984179426 y[1] (numeric) = 0.3218098417942596 absolute error = 4.440892098500626e-16 relative error = 1.379973985177179e-13 % Correct digits = 15 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) = 0.3314101332578185 y[1] (numeric) = 0.3314101332578181 absolute error = 3.885780586188048e-16 relative error = 1.172499026505363e-13 % Correct digits = 15 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) = 0.3412044627447259 y[1] (numeric) = 0.3412044627447255 absolute error = 3.885780586188048e-16 relative error = 1.138842251631163e-13 % Correct digits = 15 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) = 0.351196669051421 y[1] (numeric) = 0.3511966690514206 absolute error = 3.885780586188048e-16 relative error = 1.106440045881843e-13 % Correct digits = 15 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) = 0.3613907468113444 y[1] (numeric) = 0.3613907468113441 absolute error = 2.775557561562891e-16 relative error = 7.680212031028582e-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) = 0.3717908544826952 y[1] (numeric) = 0.371790854482695 absolute error = 1.665334536937735e-16 relative error = 4.479224049916072e-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) = 0.3824013228674413 y[1] (numeric) = 0.3824013228674412 absolute error = 1.110223024625157e-16 relative error = 2.903292845066891e-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) = 0.3932266642042512 y[1] (numeric) = 0.393226664204251 absolute error = 2.220446049250313e-16 relative error = 5.646733172949231e-14 % Correct digits = 16 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) = 0.4042715818820776 y[1] (numeric) = 0.4042715818820775 absolute error = 1.665334536937735e-16 relative error = 4.119346032646682e-14 % Correct digits = 16 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) = 0.4155409808256353 y[1] (numeric) = 0.4155409808256351 absolute error = 2.775557561562891e-16 relative error = 6.679383477528874e-14 % Correct digits = 16 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) = 0.4270399786090209 y[1] (numeric) = 0.4270399786090207 absolute error = 2.220446049250313e-16 relative error = 5.199621020221286e-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) = 0.4387739173593156 y[1] (numeric) = 0.4387739173593153 absolute error = 3.33066907387547e-16 relative error = 7.590854747977093e-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) = 0.4507483765182265 y[1] (numeric) = 0.4507483765182262 absolute error = 3.33066907387547e-16 relative error = 7.389198158855244e-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) = 0.4629691865367751 y[1] (numeric) = 0.4629691865367748 absolute error = 3.33066907387547e-16 relative error = 7.194148489212476e-14 % Correct digits = 16 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) = 0.4754424435858151 y[1] (numeric) = 0.4754424435858149 absolute error = 2.220446049250313e-16 relative error = 4.670273088165157e-14 % Correct digits = 16 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) = 0.488174525373867 y[1] (numeric) = 0.4881745253738667 absolute error = 2.775557561562891e-16 relative error = 5.685584595872223e-14 % Correct digits = 16 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) = 0.5011721081735231 y[1] (numeric) = 0.5011721081735228 absolute error = 3.33066907387547e-16 relative error = 6.645759050745651e-14 % Correct digits = 16 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) = 0.5144421851686615 y[1] (numeric) = 0.5144421851686614 absolute error = 1.110223024625157e-16 relative error = 2.158110389530296e-14 % Correct digits = 16 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) = 0.5279920862470625 y[1] (numeric) = 0.5279920862470624 absolute error = 1.110223024625157e-16 relative error = 2.102726638417174e-14 % Correct digits = 16 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) = 0.5418294993769632 y[1] (numeric) = 0.5418294993769632 absolute error = 0 relative error = 0 % Correct digits = 16 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) = 0.5559624937218419 y[1] (numeric) = 0.5559624937218417 absolute error = 2.220446049250313e-16 relative error = 3.993877418575006e-14 % Correct digits = 16 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) = 0.5703995446655491 y[1] (numeric) = 0.570399544665549 absolute error = 1.110223024625157e-16 relative error = 1.946395355690773e-14 % Correct digits = 16 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) = 0.5851495609401413 y[1] (numeric) = 0.5851495609401413 absolute error = 0 relative error = 0 % Correct digits = 16 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) = 0.6002219140717494 y[1] (numeric) = 0.6002219140717494 absolute error = 0 relative error = 0 % Correct digits = 16 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) = 0.6156264703860153 y[1] (numeric) = 0.6156264703860154 absolute error = 1.110223024625157e-16 relative error = 1.803403651452829e-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) = 0.6329676013074854 y[1] (numeric) = 0.6329676013074875 absolute error = 2.109423746787797e-15 relative error = 3.332593552071986e-13 % Correct digits = 15 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) = 0.6491043018182907 y[1] (numeric) = 0.6491043018182945 absolute error = 3.774758283725532e-15 relative error = 5.81533395041685e-13 % Correct digits = 15 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) = 0.665607330148701 y[1] (numeric) = 0.6656073301487067 absolute error = 5.662137425588298e-15 relative error = 8.506723362441546e-13 % Correct digits = 15 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) = 0.6824889814152276 y[1] (numeric) = 0.682488981415235 absolute error = 7.327471962526033e-15 relative error = 1.073639598888701e-12 % Correct digits = 14 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) = 0.6997622599819159 y[1] (numeric) = 0.6997622599819251 absolute error = 9.214851104388799e-15 relative error = 1.3168545420879e-12 % Correct digits = 14 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) = 0.7174409344255369 y[1] (numeric) = 0.717440934425548 absolute error = 1.110223024625157e-14 relative error = 1.547476553612214e-12 % Correct digits = 14 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) = 0.7355395979481689 y[1] (numeric) = 0.7355395979481821 absolute error = 1.321165399303936e-14 relative error = 1.796185280832473e-12 % Correct digits = 14 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) = 0.7540737348978194 y[1] (numeric) = 0.7540737348978346 absolute error = 1.521005543736464e-14 relative error = 2.017051480970316e-12 % Correct digits = 14 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) = 0.7730597941531558 y[1] (numeric) = 0.7730597941531731 absolute error = 1.720845688168993e-14 relative error = 2.226018868377554e-12 % Correct digits = 14 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) = 0.7925152702399136 y[1] (numeric) = 0.7925152702399328 absolute error = 1.920685832601521e-14 relative error = 2.423531639989829e-12 % Correct digits = 14 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) = 0.8124587931772475 y[1] (numeric) = 0.812458793177269 absolute error = 2.153832667772804e-14 relative error = 2.65100542434885e-12 % Correct digits = 14 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) = 0.8329102282059896 y[1] (numeric) = 0.8329102282060132 absolute error = 2.364775042451583e-14 relative error = 2.839171572601632e-12 % Correct digits = 14 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) = 0.8538907867321232 y[1] (numeric) = 0.8538907867321494 absolute error = 2.620126338115369e-14 relative error = 3.06845603539383e-12 % Correct digits = 14 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) = 0.8754231500335135 y[1] (numeric) = 0.8754231500335419 absolute error = 2.842170943040401e-14 relative error = 3.246625295357559e-12 % Correct digits = 14 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) = 0.8975316075331121 y[1] (numeric) = 0.8975316075331429 absolute error = 3.075317778211684e-14 relative error = 3.426417245253647e-12 % Correct digits = 14 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) = 0.9202422117462766 y[1] (numeric) = 0.92024221174631 absolute error = 3.341771304121721e-14 relative error = 3.631404060220499e-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) = 0.9435829523744456 y[1] (numeric) = 0.9435829523744814 absolute error = 3.586020369539256e-14 relative error = 3.800429374561445e-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) = 0.9675839524559287 y[1] (numeric) = 0.967583952455967 absolute error = 3.83026943495679e-14 relative error = 3.958591319373138e-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) = 0.9922776900143061 y[1] (numeric) = 0.992277690014347 absolute error = 4.085620730620576e-14 relative error = 4.117416698708274e-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) = 1.017699249287779 y[1] (numeric) = 1.017699249287823 absolute error = 4.39648317751562e-14 relative error = 4.320022030666163e-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) = 1.043886606406725 y[1] (numeric) = 1.043886606406772 absolute error = 4.685141163918161e-14 relative error = 4.488170587843245e-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) = 1.070880955347464 y[1] (numeric) = 1.070880955347514 absolute error = 5.018208071305708e-14 relative error = 4.686055948840246e-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) = 1.098727081174039 y[1] (numeric) = 1.098727081174092 absolute error = 5.306866057708248e-14 relative error = 4.830012974684873e-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) = 1.12747378904666 y[1] (numeric) = 1.127473789046716 absolute error = 5.617728504603292e-14 relative error = 4.982580135502206e-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) = 1.157174399303809 y[1] (numeric) = 1.157174399303868 absolute error = 5.950795411990839e-14 relative error = 5.142522523459746e-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) = 1.187887321218344 y[1] (numeric) = 1.187887321218407 absolute error = 6.306066779870889e-14 relative error = 5.308640531160094e-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) = 1.219676720923607 y[1] (numeric) = 1.219676720923674 absolute error = 6.639133687258436e-14 relative error = 5.443355254194663e-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) = 1.252613302687653 y[1] (numeric) = 1.252613302687723 absolute error = 7.016609515630989e-14 relative error = 5.601576720106594e-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) = 1.286775227430942 y[1] (numeric) = 1.286775227431016 absolute error = 7.371880883511039e-14 relative error = 5.728957728094489e-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) = 1.322249198474641 y[1] (numeric) = 1.322249198474719 absolute error = 7.749356711883593e-14 relative error = 5.860738445387845e-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) = 1.359131752440537 y[1] (numeric) = 1.359131752440619 absolute error = 8.193445921733655e-14 relative error = 6.028441250836073e-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) = 1.397530803651098 y[1] (numeric) = 1.397530803651184 absolute error = 8.593126210598712e-14 relative error = 6.148791989520994e-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) = 1.437567504217098 y[1] (numeric) = 1.437567504217188 absolute error = 9.037215420448774e-14 relative error = 6.286463344460794e-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) = 1.479378500559851 y[1] (numeric) = 1.479378500559946 absolute error = 9.547918011776346e-14 relative error = 6.454006197983185e-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) = 1.523118692288129 y[1] (numeric) = 1.523118692288229 absolute error = 1.003641614261142e-13 relative error = 6.589385445420575e-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) = 1.56896463391136 y[1] (numeric) = 1.568964633911465 absolute error = 1.052491427344648e-13 relative error = 6.708190896061396e-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) = 1.61711876795355 y[1] (numeric) = 1.617118767953661 absolute error = 1.105782132526656e-13 relative error = 6.837977237293546e-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) = 1.667814745894899 y[1] (numeric) = 1.667814745895016 absolute error = 1.165734175856414e-13 relative error = 6.989590293080881e-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) = 1.721324190662625 y[1] (numeric) = 1.721324190662747 absolute error = 1.223465773136923e-13 relative error = 7.107701034898884e-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) = 1.777965396306684 y[1] (numeric) = 1.777965396306812 absolute error = 1.285638262515931e-13 relative error = 7.230952105066559e-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) = 1.838114671457699 y[1] (numeric) = 1.838114671457834 absolute error = 1.352251643993441e-13 relative error = 7.356731682692304e-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) = 1.902221353428768 y[1] (numeric) = 1.902221353428911 absolute error = 1.425526363618701e-13 relative error = 7.494008838924971e-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) = 1.970828017539234 y[1] (numeric) = 1.970828017539384 absolute error = 1.498801083243961e-13 relative error = 7.604930871215017e-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) = 2.044598200305071 y[1] (numeric) = 2.044598200305229 absolute error = 1.585398479164724e-13 relative error = 7.754083315382793e-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) = 2.124355260143009 y[1] (numeric) = 2.124355260143175 absolute error = 1.665334536937735e-13 relative error = 7.839246891433905e-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) = 2.211138217627107 y[1] (numeric) = 2.211138217627283 absolute error = 1.758593271006248e-13 relative error = 7.95333940224456e-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) = 2.306284337869535 y[1] (numeric) = 2.306284337869722 absolute error = 1.865174681370263e-13 relative error = 8.087357880135656e-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) = 2.41155546691282 y[1] (numeric) = 2.411555466913019 absolute error = 1.989519660128281e-13 relative error = 8.249943604553234e-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) = 2.529339273357407 y[1] (numeric) = 2.529339273357619 absolute error = 2.118305530984799e-13 relative error = 8.374936305689791e-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 ) = tan ( x ) ; Iterations = 1401 Total Elapsed Time = 0 Seconds Elapsed Time(since restart) = 0 Seconds Time to Timeout = 3 Minutes 0 Seconds Percent Done = 100.1 %