##############ECHO OF PROBLEM################# ##############temp/sinh_sqrtpostode.ode################# diff ( y , x , 1 ) = sinh ( sqrt ( 0.1 * x + 0.2 ) ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=40; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=2.0; x_end=3.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_min_h=0.001; glob_type_given_pole=1; array_given_rad_poles[1][1]=-2.0; array_given_rad_poles[1][2]=0.0; array_given_ord_poles[1][1]=0.5; array_given_ord_poles[1][2]=0.0; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=100000000; glob_max_minutes=10.0; glob_subiter_method=3; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(20.0 * sqrt(0.1 * x + 0.2) * cosh( sqrt(0.1 * x + 0.2)) - 20.0 * sinh( sqrt(0.1 * x + 0.2))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.001 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1 estimated_steps = 1000 step_error = 7.905694150420948e-14 est_needed_step_err = 7.905694150420948e-14 opt_iter = 1 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 1.504 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1.754980921980319 glob_desired_digits_correct = 10 estimated_h = 0.001 estimated_answer = 1.754980921980319 desired_abs_gbl_error = 1.754980921980319e-10 range = 1 estimated_steps = 1000 step_error = 1.387434240900017e-13 est_needed_step_err = 1.387434240900017e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.15567147663814e-134 estimated_step_error = 2.15567147663814e-134 Double H and LOOP opt_iter = 2 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 1.504 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1.754980921980319 glob_desired_digits_correct = 10 estimated_h = 0.002 estimated_answer = 1.754980921980319 desired_abs_gbl_error = 1.754980921980319e-10 range = 1 estimated_steps = 500 step_error = 1.962128320381625e-13 est_needed_step_err = 1.962128320381625e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.481193548289166e-123 estimated_step_error = 1.481193548289166e-123 Double H and LOOP opt_iter = 3 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 1.504 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1.754980921980319 glob_desired_digits_correct = 10 estimated_h = 0.004 estimated_answer = 1.754980921980319 desired_abs_gbl_error = 1.754980921980319e-10 range = 1 estimated_steps = 250 step_error = 2.774868481800035e-13 est_needed_step_err = 2.774868481800035e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.017631304691615e-112 estimated_step_error = 1.017631304691615e-112 Double H and LOOP opt_iter = 4 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 1.504 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1.754980921980319 glob_desired_digits_correct = 10 estimated_h = 0.008 estimated_answer = 1.754980921980319 desired_abs_gbl_error = 1.754980921980319e-10 range = 1 estimated_steps = 125 step_error = 3.924256640763249e-13 est_needed_step_err = 3.924256640763249e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.98985197787268e-102 estimated_step_error = 6.98985197787268e-102 Double H and LOOP opt_iter = 5 SETTING H FOR DISPLAY INTERVAL Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.5 Order of pole (three term test) = 1.504 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] = 2 y[1] (analytic) = 1.754980921980319 y[1] (numeric) = 1.754980921980319 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 1.504 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.01 y[1] (analytic) = 1.76174039666226 y[1] (numeric) = 1.761735625836366 absolute error = 4.770825893896102e-06 relative error = 0.0002708018674564519 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 6 h = 0.01 Radius of convergence (given) for eq 1 = 4.01 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.01 Order of pole (three term test) = 1.504 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.02 y[1] (analytic) = 1.768509403906236 y[1] (numeric) = 1.768499866098326 absolute error = 9.53780791057568e-06 relative error = 0.0005393133838875171 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 6 h = 0.01 Radius of convergence (given) for eq 1 = 4.02 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.02 Order of pole (three term test) = 1.504 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.029999999999999 y[1] (analytic) = 1.775287936060634 y[1] (numeric) = 1.775273635097265 absolute error = 1.430096336907383e-05 relative error = 0.0008055574016239688 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 6 h = 0.01 Radius of convergence (given) for eq 1 = 4.03 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.03 Order of pole (three term test) = 1.504 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.039999999999999 y[1] (analytic) = 1.78207598550825 y[1] (numeric) = 1.78205692519877 absolute error = 1.906030947984583e-05 relative error = 0.001069556496739942 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.04 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.04 Order of pole (three term test) = 1.504 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.049999999999999 y[1] (analytic) = 1.788873544666071 y[1] (numeric) = 1.788849728802729 absolute error = 2.381586334165853e-05 relative error = 0.001331332972790105 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.05 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.05 Order of pole (three term test) = 1.504 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.059999999999999 y[1] (analytic) = 1.795680605985053 y[1] (numeric) = 1.795652038343115 absolute error = 2.856764193825967e-05 relative error = 0.001590908864474168 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.06 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.06 Order of pole (three term test) = 1.504 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.069999999999999 y[1] (analytic) = 1.802497161949931 y[1] (numeric) = 1.802463846287769 absolute error = 3.331566216258075e-05 relative error = 0.001848305942769976 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.07 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.07 Order of pole (three term test) = 1.504 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.079999999999998 y[1] (analytic) = 1.809323205078979 y[1] (numeric) = 1.809285145138189 absolute error = 3.805994078920349e-05 relative error = 0.002103545717114822 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.08 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.08 Order of pole (three term test) = 1.504 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.089999999999998 y[1] (analytic) = 1.816158727923812 y[1] (numeric) = 1.81611592742932 absolute error = 4.280049449123524e-05 relative error = 0.002356649440005925 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.09 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.09 Order of pole (three term test) = 1.504 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.099999999999998 y[1] (analytic) = 1.823003723069178 y[1] (numeric) = 1.822956185729341 absolute error = 4.753733983675623e-05 relative error = 0.002607638110399642 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.1 Order of pole (three term test) = 1.504 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.109999999999998 y[1] (analytic) = 1.829858183132751 y[1] (numeric) = 1.829805912639459 absolute error = 5.227049329215028e-05 relative error = 0.00285653247743288 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.11 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.11 Order of pole (three term test) = 1.504 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.119999999999997 y[1] (analytic) = 1.836722100764922 y[1] (numeric) = 1.836665100793705 absolute error = 5.69999712163316e-05 relative error = 0.003103353043587453 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.12 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.12 Order of pole (three term test) = 1.504 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.129999999999997 y[1] (analytic) = 1.843595468648605 y[1] (numeric) = 1.843533742858728 absolute error = 6.172578987673205e-05 relative error = 0.003348120068985545 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.13 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.13 Order of pole (three term test) = 1.504 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.139999999999997 y[1] (analytic) = 1.850478279499024 y[1] (numeric) = 1.850411831533593 absolute error = 6.644796543087139e-05 relative error = 0.003590853573750712 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.14 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.14 Order of pole (three term test) = 1.504 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.149999999999997 y[1] (analytic) = 1.857370526063519 y[1] (numeric) = 1.85729935954958 absolute error = 7.11665139392359e-05 relative error = 0.003831573342022662 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.15 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.15 Order of pole (three term test) = 1.504 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.159999999999997 y[1] (analytic) = 1.864272201121349 y[1] (numeric) = 1.864196319669988 absolute error = 7.588145136083746e-05 relative error = 0.004070298924974326 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.16 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.16 Order of pole (three term test) = 1.504 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.169999999999996 y[1] (analytic) = 1.871183297483498 y[1] (numeric) = 1.871102704689933 absolute error = 8.059279356453786e-05 relative error = 0.0043070496446246 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.17 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.17 Order of pole (three term test) = 1.504 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.179999999999996 y[1] (analytic) = 1.878103807992472 y[1] (numeric) = 1.878018507436158 absolute error = 8.530055631417177e-05 relative error = 0.004541844596191441 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.18 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.18 Order of pole (three term test) = 1.504 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.189999999999996 y[1] (analytic) = 1.885033725522113 y[1] (numeric) = 1.884943720766835 absolute error = 9.000475527809471e-05 relative error = 0.004774702651708014 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.19 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.19 Order of pole (three term test) = 1.504 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.199999999999996 y[1] (analytic) = 1.891973042977408 y[1] (numeric) = 1.891878337571375 absolute error = 9.470540603295774e-05 relative error = 0.005005642463273119 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.2 Order of pole (three term test) = 1.504 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.209999999999996 y[1] (analytic) = 1.898921753294289 y[1] (numeric) = 1.898822350770238 absolute error = 9.940252405127303e-05 relative error = 0.005234682465395294 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.21 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.21 Order of pole (three term test) = 1.504 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.219999999999995 y[1] (analytic) = 1.905879849439465 y[1] (numeric) = 1.905775753314739 absolute error = 0.0001040961247258387 relative error = 0.005461840879237705 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.22 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.22 Order of pole (three term test) = 1.504 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.229999999999995 y[1] (analytic) = 1.912847324410214 y[1] (numeric) = 1.91273853818687 absolute error = 0.0001087862233433157 relative error = 0.005687135714130119 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.23 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.23 Order of pole (three term test) = 1.504 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.239999999999995 y[1] (analytic) = 1.919824171234218 y[1] (numeric) = 1.919710698399106 absolute error = 0.000113472835112205 relative error = 0.005910584771898952 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.24 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.24 Order of pole (three term test) = 1.504 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.249999999999995 y[1] (analytic) = 1.926810382969348 y[1] (numeric) = 1.926692226994223 absolute error = 0.0001181559751248784 relative error = 0.00613220564769803 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.25 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.25 Order of pole (three term test) = 1.504 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.259999999999994 y[1] (analytic) = 1.933805952703535 y[1] (numeric) = 1.933683117045119 absolute error = 0.0001228356584159762 relative error = 0.00635201573582123 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.26 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.26 Order of pole (three term test) = 1.504 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.269999999999994 y[1] (analytic) = 1.940810873554522 y[1] (numeric) = 1.940683361654627 absolute error = 0.0001275118998946834 relative error = 0.006570032228908019 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.27 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.27 Order of pole (three term test) = 1.504 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.279999999999994 y[1] (analytic) = 1.947825138669753 y[1] (numeric) = 1.94769295395534 absolute error = 0.0001321847144128974 relative error = 0.006786272124158514 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.28 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.28 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.289999999999994 y[1] (analytic) = 1.954848741226135 y[1] (numeric) = 1.95471188710943 absolute error = 0.000136854116704388 relative error = 0.007000752222831793 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.29 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.29 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.299999999999994 y[1] (analytic) = 1.961881674429913 y[1] (numeric) = 1.961740154308474 absolute error = 0.000141520121438532 relative error = 0.007213489135610341 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.3 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.3 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.309999999999993 y[1] (analytic) = 1.968923931516464 y[1] (numeric) = 1.968777748773276 absolute error = 0.0001461827431881169 relative error = 0.007424499283500861 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.31 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.31 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.319999999999993 y[1] (analytic) = 1.975975505750128 y[1] (numeric) = 1.975824663753695 absolute error = 0.0001508419964333374 relative error = 0.007633798900562492 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.32 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.32 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.329999999999993 y[1] (analytic) = 1.983036390424051 y[1] (numeric) = 1.982880892528471 absolute error = 0.0001554978955795594 relative error = 0.007841404037285865 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.33 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.33 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.339999999999993 y[1] (analytic) = 1.990106578860004 y[1] (numeric) = 1.989946428405057 absolute error = 0.0001601504549468835 relative error = 0.008047330562497951 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.34 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.34 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.349999999999993 y[1] (analytic) = 1.997186064408202 y[1] (numeric) = 1.997021264719448 absolute error = 0.0001647996887548242 relative error = 0.008251594164996186 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.35 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.35 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.359999999999992 y[1] (analytic) = 2.004274840447167 y[1] (numeric) = 2.004105394836009 absolute error = 0.0001694456111578369 relative error = 0.008454210357698869 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.36 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.36 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.369999999999992 y[1] (analytic) = 2.01137290038354 y[1] (numeric) = 2.011198812147315 absolute error = 0.0001740882362244456 relative error = 0.00865519447891783 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.37 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.37 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.379999999999992 y[1] (analytic) = 2.018480237651914 y[1] (numeric) = 2.018301510073983 absolute error = 0.0001787275779316921 relative error = 0.008854561694376796 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.38 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.38 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.389999999999992 y[1] (analytic) = 2.025596845714677 y[1] (numeric) = 2.025413482064503 absolute error = 0.0001833636501737956 relative error = 0.009052326999902131 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.39 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.39 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.399999999999991 y[1] (analytic) = 2.032722718061864 y[1] (numeric) = 2.032534721595085 absolute error = 0.00018799646677925 relative error = 0.009248505224485245 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.4 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.4 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.409999999999991 y[1] (analytic) = 2.039857848210962 y[1] (numeric) = 2.039665222169486 absolute error = 0.0001926260414761849 relative error = 0.009443111030757644 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.41 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.41 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.419999999999991 y[1] (analytic) = 2.047002229706798 y[1] (numeric) = 2.046804977318861 absolute error = 0.000197252387937219 relative error = 0.00963615891935166 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.42 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.42 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.429999999999991 y[1] (analytic) = 2.05415585612133 y[1] (numeric) = 2.053953980601596 absolute error = 0.0002018755197337185 relative error = 0.009827663228772775 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.43 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.43 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.439999999999991 y[1] (analytic) = 2.061318721053521 y[1] (numeric) = 2.061112225603154 absolute error = 0.0002064954503664396 relative error = 0.010017638138992 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.44 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.44 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.44999999999999 y[1] (analytic) = 2.068490818129183 y[1] (numeric) = 2.068279705935919 absolute error = 0.0002111121932633075 relative error = 0.01020609767338706 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.45 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.45 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.45999999999999 y[1] (analytic) = 2.075672141000801 y[1] (numeric) = 2.075456415239039 absolute error = 0.0002157257617620978 relative error = 0.01039305569992783 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.46 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.46 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.46999999999999 y[1] (analytic) = 2.082862683347418 y[1] (numeric) = 2.082642347178273 absolute error = 0.0002203361691450745 relative error = 0.01057852593484305 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.47 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.47 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.47999999999999 y[1] (analytic) = 2.09006243887443 y[1] (numeric) = 2.089837495445839 absolute error = 0.0002249434285905849 relative error = 0.01076252194224995 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.48 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.48 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.48999999999999 y[1] (analytic) = 2.097271401313492 y[1] (numeric) = 2.097041853760262 absolute error = 0.0002295475532299029 relative error = 0.01094505713882049 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.49 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.49 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.499999999999989 y[1] (analytic) = 2.10448956442232 y[1] (numeric) = 2.104255415866223 absolute error = 0.0002341485560966028 relative error = 0.01112614479325662 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.5 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.509999999999989 y[1] (analytic) = 2.111716921984584 y[1] (numeric) = 2.111478175534412 absolute error = 0.0002387464501718561 relative error = 0.01130579803032894 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.51 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.51 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.519999999999989 y[1] (analytic) = 2.11895346780971 y[1] (numeric) = 2.118710126561379 absolute error = 0.0002433412483315855 relative error = 0.01148402983021232 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.52 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.52 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.529999999999989 y[1] (analytic) = 2.126199195732804 y[1] (numeric) = 2.125951262769385 absolute error = 0.000247932963418851 relative error = 0.01166085303373468 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.53 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.53 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.539999999999988 y[1] (analytic) = 2.133454099614429 y[1] (numeric) = 2.133201578006261 absolute error = 0.0002525216081679105 relative error = 0.01183628034057765 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.54 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.54 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.549999999999988 y[1] (analytic) = 2.140718173340524 y[1] (numeric) = 2.140461066145261 absolute error = 0.0002571071952628401 relative error = 0.01201032431380878 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.55 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.55 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.559999999999988 y[1] (analytic) = 2.147991410822232 y[1] (numeric) = 2.147729721084918 absolute error = 0.0002616897373148852 relative error = 0.01218299738054877 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.56 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.56 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.569999999999988 y[1] (analytic) = 2.155273805995753 y[1] (numeric) = 2.155007536748903 absolute error = 0.0002662692468504702 relative error = 0.01235431183312933 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.57 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.57 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.579999999999988 y[1] (analytic) = 2.162565352822227 y[1] (numeric) = 2.162294507085883 absolute error = 0.0002708457363440608 relative error = 0.01252427983231106 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.58 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.58 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.589999999999987 y[1] (analytic) = 2.169866045287561 y[1] (numeric) = 2.169590626069384 absolute error = 0.0002754192181768644 relative error = 0.01269291340702852 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.59 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.59 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.599999999999987 y[1] (analytic) = 2.177175877402341 y[1] (numeric) = 2.176895887697648 absolute error = 0.0002799897046927846 relative error = 0.01286022445861606 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.6 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.6 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.609999999999987 y[1] (analytic) = 2.184494843201637 y[1] (numeric) = 2.184210285993498 absolute error = 0.0002845572081398018 relative error = 0.01302622475971375 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.61 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.61 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.619999999999987 y[1] (analytic) = 2.191822936744908 y[1] (numeric) = 2.191533815004198 absolute error = 0.0002891217407099411 relative error = 0.01319092595770158 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.62 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.62 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.629999999999987 y[1] (analytic) = 2.199160152115844 y[1] (numeric) = 2.198866468801322 absolute error = 0.0002936833145223972 relative error = 0.01335433957548931 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.63 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.63 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.639999999999986 y[1] (analytic) = 2.206506483422253 y[1] (numeric) = 2.206208241480616 absolute error = 0.0002982419416364124 relative error = 0.01351647701364758 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.64 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.64 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.649999999999986 y[1] (analytic) = 2.2138619247959 y[1] (numeric) = 2.213559127161866 absolute error = 0.0003027976340344019 relative error = 0.01367734955116125 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.65 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.65 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.659999999999986 y[1] (analytic) = 2.221226470392409 y[1] (numeric) = 2.220919119988762 absolute error = 0.0003073504036472663 relative error = 0.01383696834807523 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.66 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.66 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.669999999999986 y[1] (analytic) = 2.228600114391098 y[1] (numeric) = 2.228288214128772 absolute error = 0.0003119002623255263 relative error = 0.01399534444566536 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.67 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.67 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.679999999999986 y[1] (analytic) = 2.235982850994867 y[1] (numeric) = 2.235666403773007 absolute error = 0.0003164472218601944 relative error = 0.01415248876883809 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.68 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.68 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.689999999999985 y[1] (analytic) = 2.243374674430074 y[1] (numeric) = 2.243053683136093 absolute error = 0.0003209912939809989 relative error = 0.01430841212748139 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.69 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.69 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.699999999999985 y[1] (analytic) = 2.25077557894639 y[1] (numeric) = 2.250450046456042 absolute error = 0.0003255324903488344 relative error = 0.01446312521754031 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.7 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.7 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.709999999999985 y[1] (analytic) = 2.25818555881669 y[1] (numeric) = 2.257855487994124 absolute error = 0.0003300708225664195 relative error = 0.01461663862288534 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.71 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.71 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.719999999999985 y[1] (analytic) = 2.265604608336909 y[1] (numeric) = 2.265270002034741 absolute error = 0.0003346063021685275 relative error = 0.01476896281625013 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.72 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.72 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.729999999999984 y[1] (analytic) = 2.273032721825935 y[1] (numeric) = 2.272693582885302 absolute error = 0.0003391389406326439 relative error = 0.01492010816105685 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.73 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.73 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.739999999999984 y[1] (analytic) = 2.280469893625455 y[1] (numeric) = 2.280126224876097 absolute error = 0.0003436687493576507 relative error = 0.01507008491181138 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.74 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.74 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.749999999999984 y[1] (analytic) = 2.287916118099881 y[1] (numeric) = 2.287567922360172 absolute error = 0.0003481957397091229 relative error = 0.01521890321740904 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.75 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.75 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.759999999999984 y[1] (analytic) = 2.29537138963617 y[1] (numeric) = 2.295018669713208 absolute error = 0.0003527199229620415 relative error = 0.01536657311991458 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.76 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.76 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.769999999999984 y[1] (analytic) = 2.302835702643753 y[1] (numeric) = 2.302478461333399 absolute error = 0.0003572413103540839 relative error = 0.0155131045581739 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.77 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.77 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.779999999999983 y[1] (analytic) = 2.310309051554377 y[1] (numeric) = 2.30994729164133 absolute error = 0.0003617599130474325 relative error = 0.01565850736740352 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.78 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.78 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.789999999999983 y[1] (analytic) = 2.317791430822005 y[1] (numeric) = 2.317425155079856 absolute error = 0.0003662757421496465 relative error = 0.01580279128134263 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.79 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.79 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.799999999999983 y[1] (analytic) = 2.325282834922696 y[1] (numeric) = 2.324912046113985 absolute error = 0.0003707888087109978 relative error = 0.01594596593335815 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.8 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.8 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.809999999999983 y[1] (analytic) = 2.332783258354484 y[1] (numeric) = 2.332407959230758 absolute error = 0.0003752991237253589 relative error = 0.01608804085768732 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.81 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.81 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.819999999999983 y[1] (analytic) = 2.340292695637237 y[1] (numeric) = 2.339912888939132 absolute error = 0.0003798066981048898 relative error = 0.01622902548954341 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.82 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.82 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.829999999999982 y[1] (analytic) = 2.347811141312608 y[1] (numeric) = 2.347426829769861 absolute error = 0.0003843115427466515 relative error = 0.01636892916914056 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.83 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.83 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.839999999999982 y[1] (analytic) = 2.355338589943832 y[1] (numeric) = 2.354949776275386 absolute error = 0.0003888136684464527 relative error = 0.01650776113916279 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.84 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.84 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.849999999999982 y[1] (analytic) = 2.362875036115685 y[1] (numeric) = 2.362481723029711 absolute error = 0.0003933130859739009 relative error = 0.01664553054910875 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.85 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.85 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.859999999999982 y[1] (analytic) = 2.370420474434313 y[1] (numeric) = 2.3700226646283 absolute error = 0.0003978098060137825 relative error = 0.01678224645392153 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.86 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.86 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.869999999999981 y[1] (analytic) = 2.377974899527178 y[1] (numeric) = 2.377572595687952 absolute error = 0.0004023038392264588 relative error = 0.01691791781765445 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.87 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.87 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.879999999999981 y[1] (analytic) = 2.385538306042891 y[1] (numeric) = 2.385131510846697 absolute error = 0.0004067951961936878 relative error = 0.01705255351227103 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.88 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.88 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.889999999999981 y[1] (analytic) = 2.393110688651124 y[1] (numeric) = 2.392699404763683 absolute error = 0.0004112838874408276 relative error = 0.01718616231966469 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.89 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.89 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.899999999999981 y[1] (analytic) = 2.400692042042522 y[1] (numeric) = 2.400276272119061 absolute error = 0.0004157699234608181 relative error = 0.01731875293371984 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.9 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.9 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.909999999999981 y[1] (analytic) = 2.408282360928533 y[1] (numeric) = 2.407862107613878 absolute error = 0.0004202533146546727 relative error = 0.01745033395887352 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.91 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.91 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.91999999999998 y[1] (analytic) = 2.415881640041379 y[1] (numeric) = 2.41545690596997 absolute error = 0.0004247340714091941 relative error = 0.01758091391438859 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.92 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.92 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.92999999999998 y[1] (analytic) = 2.423489874133875 y[1] (numeric) = 2.423060661929846 absolute error = 0.000429212204028584 relative error = 0.0177105012325244 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.93 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.93 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.93999999999998 y[1] (analytic) = 2.431107057979368 y[1] (numeric) = 2.43067337025659 absolute error = 0.0004336877227779645 relative error = 0.01783910426134944 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.94 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.94 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.94999999999998 y[1] (analytic) = 2.438733186371602 y[1] (numeric) = 2.438295025733747 absolute error = 0.0004381606378549563 relative error = 0.01796673126455711 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.95 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.95 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.95999999999998 y[1] (analytic) = 2.446368254124643 y[1] (numeric) = 2.445925623165219 absolute error = 0.000442630959423429 relative error = 0.01809339042383097 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.96 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.96 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.969999999999979 y[1] (analytic) = 2.45401225607274 y[1] (numeric) = 2.453565157375162 absolute error = 0.0004470986975788627 relative error = 0.01821908983838465 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.97 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.97 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.979999999999979 y[1] (analytic) = 2.461665187070253 y[1] (numeric) = 2.461213623207875 absolute error = 0.0004515638623776574 relative error = 0.01834383752711251 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.98 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.98 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.989999999999979 y[1] (analytic) = 2.469327041991507 y[1] (numeric) = 2.468871015527704 absolute error = 0.0004560264638029388 relative error = 0.01846764142813397 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.99 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.99 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.999999999999979 y[1] (analytic) = 2.47699781573075 y[1] (numeric) = 2.476537329218934 absolute error = 0.0004604865118156276 relative error = 0.01859050940179281 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = sinh ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations = 101 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 10 Minutes 0.0 Seconds Percent Done = 102 %