##############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=30; ! /* 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_max_iter=1000000; glob_max_h=0.00001; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=1000000000; glob_max_minutes=30.0; glob_subiter_method=3; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(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 = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1 estimated_steps = 1000000 step_error = 1e-16 est_needed_step_err = 1e-16 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.211685631110643e-176 estimated_step_error = 5.211685631110643e-176 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 = 3.497502625623425e-168 estimated_step_error = 3.497502625623425e-168 best_h = 4e-06 opt_iter = 3 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.34713374802993e-160 estimated_step_error = 2.34713374802993e-160 best_h = 8e-06 opt_iter = 4 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.575134080294016e-152 estimated_step_error = 1.575134080294016e-152 best_h = 1.6e-05 opt_iter = 5 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.057053628684534e-144 estimated_step_error = 1.057053628684534e-144 best_h = 1e-05 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 % Correct digits = 16 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.999 Order of pole (three term test) = 1.507 Radius of convergence (six term test) for eq 1 = 6.943 Order of pole (six term test) = -0.7206 TOP MAIN SOLVE Loop x[1] = 2.010000000000066 y[1] (analytic) = 1.761740396662304 y[1] (numeric) = 1.761740391894056 absolute error = 4.768248018649501e-09 relative error = 2.706555419676565e-07 % Correct digits = 9 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.009 Order of pole (three term test) = 1.507 Radius of convergence (six term test) for eq 1 = 6.961 Order of pole (six term test) = -0.7206 TOP MAIN SOLVE Loop x[1] = 2.020000000000131 y[1] (analytic) = 1.768509403906323 y[1] (numeric) = 1.768509394373666 absolute error = 9.532657330169059e-09 relative error = 5.390221453792166e-07 % Correct digits = 9 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.019 Order of pole (three term test) = 1.507 Radius of convergence (six term test) for eq 1 = 6.979 Order of pole (six term test) = -0.7205 TOP MAIN SOLVE Loop x[1] = 2.030000000000197 y[1] (analytic) = 1.775287936060764 y[1] (numeric) = 1.775287921767514 absolute error = 1.429324947288535e-08 relative error = 8.05122886409122e-07 % Correct digits = 9 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.029 Order of pole (three term test) = 1.507 Radius of convergence (six term test) for eq 1 = 6.996 Order of pole (six term test) = -0.7204 TOP MAIN SOLVE Loop x[1] = 2.040000000000262 y[1] (analytic) = 1.782075985508431 y[1] (numeric) = 1.78207596645838 absolute error = 1.905005087010636e-08 relative error = 1.068980841727202e-06 % Correct digits = 8 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.039 Order of pole (three term test) = 1.507 Radius of convergence (six term test) for eq 1 = 7.014 Order of pole (six term test) = -0.7203 TOP MAIN SOLVE Loop x[1] = 2.050000000000328 y[1] (analytic) = 1.78887354466629 y[1] (numeric) = 1.788873520863231 absolute error = 2.380305819116302e-08 relative error = 1.330617150783759e-06 % Correct digits = 8 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.049 Order of pole (three term test) = 1.507 Radius of convergence (six term test) for eq 1 = 7.032 Order of pole (six term test) = -0.7203 TOP MAIN SOLVE Loop x[1] = 2.060000000000393 y[1] (analytic) = 1.795680605985325 y[1] (numeric) = 1.795680577433017 absolute error = 2.855230785137053e-08 relative error = 1.590054921582411e-06 % Correct digits = 8 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.059 Order of pole (three term test) = 1.507 Radius of convergence (six term test) for eq 1 = 7.049 Order of pole (six term test) = -0.7202 TOP MAIN SOLVE Loop x[1] = 2.070000000000459 y[1] (analytic) = 1.802497161950244 y[1] (numeric) = 1.80249712865244 absolute error = 3.329780362548718e-08 relative error = 1.847315176322387e-06 % Correct digits = 8 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.069 Order of pole (three term test) = 1.507 Radius of convergence (six term test) for eq 1 = 7.067 Order of pole (six term test) = -0.7201 TOP MAIN SOLVE Loop x[1] = 2.080000000000524 y[1] (analytic) = 1.809323205079338 y[1] (numeric) = 1.809323167039768 absolute error = 3.803956905024108e-08 relative error = 2.10241978566638e-06 % Correct digits = 8 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.079 Order of pole (three term test) = 1.507 Radius of convergence (six term test) for eq 1 = 7.085 Order of pole (six term test) = -0.7201 TOP MAIN SOLVE Loop x[1] = 2.09000000000059 y[1] (analytic) = 1.816158727924215 y[1] (numeric) = 1.816158685146597 absolute error = 4.277761744830855e-08 relative error = 2.355389801044613e-06 % Correct digits = 8 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.089 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.102 Order of pole (six term test) = -0.72 TOP MAIN SOLVE Loop x[1] = 2.100000000000655 y[1] (analytic) = 1.823003723069625 y[1] (numeric) = 1.823003675557661 absolute error = 4.751196436281191e-08 relative error = 2.606246150875102e-06 % Correct digits = 8 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.099 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.12 Order of pole (six term test) = -0.7199 TOP MAIN SOLVE Loop x[1] = 2.110000000000721 y[1] (analytic) = 1.829858183133245 y[1] (numeric) = 1.829858130890612 absolute error = 5.224263310843469e-08 relative error = 2.855009945031927e-06 % Correct digits = 8 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.109 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.138 Order of pole (six term test) = -0.7199 TOP MAIN SOLVE Loop x[1] = 2.120000000000786 y[1] (analytic) = 1.836722100765465 y[1] (numeric) = 1.836722043795833 absolute error = 5.696963234491648e-08 relative error = 3.101701249262152e-06 % Correct digits = 8 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.119 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.156 Order of pole (six term test) = -0.7198 TOP MAIN SOLVE Loop x[1] = 2.130000000000852 y[1] (analytic) = 1.843595468649193 y[1] (numeric) = 1.84359540695621 absolute error = 6.169298250036093e-08 relative error = 3.346340536710233e-06 % Correct digits = 8 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.129 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.173 Order of pole (six term test) = -0.7197 TOP MAIN SOLVE Loop x[1] = 2.140000000000917 y[1] (analytic) = 1.850478279499656 y[1] (numeric) = 1.850478213086959 absolute error = 6.641269711948894e-08 relative error = 3.58894767127156e-06 % Correct digits = 8 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.139 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.191 Order of pole (six term test) = -0.7197 TOP MAIN SOLVE Loop x[1] = 2.150000000000983 y[1] (analytic) = 1.857370526064196 y[1] (numeric) = 1.8573704549354 absolute error = 7.112879596427035e-08 relative error = 3.829542623086285e-06 % Correct digits = 8 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.149 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.209 Order of pole (six term test) = -0.7196 TOP MAIN SOLVE Loop x[1] = 2.160000000001048 y[1] (analytic) = 1.864272201122079 y[1] (numeric) = 1.864272125280783 absolute error = 7.584129613213975e-08 relative error = 4.068144989046769e-06 % Correct digits = 8 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.159 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.226 Order of pole (six term test) = -0.7195 TOP MAIN SOLVE Loop x[1] = 2.170000000001114 y[1] (analytic) = 1.871183297484269 y[1] (numeric) = 1.871183216934067 absolute error = 8.05502013978554e-08 relative error = 4.30477342899287e-06 % Correct digits = 8 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.169 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.244 Order of pole (six term test) = -0.7194 TOP MAIN SOLVE Loop x[1] = 2.180000000001179 y[1] (analytic) = 1.878103807993289 y[1] (numeric) = 1.878103722737749 absolute error = 8.525554084926057e-08 relative error = 4.539447739065826e-06 % Correct digits = 8 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.179 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.262 Order of pole (six term test) = -0.7194 TOP MAIN SOLVE Loop x[1] = 2.190000000001245 y[1] (analytic) = 1.885033725522979 y[1] (numeric) = 1.885033635565652 absolute error = 8.995732669880852e-08 relative error = 4.77218659172005e-06 % Correct digits = 8 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.189 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.279 Order of pole (six term test) = -0.7193 TOP MAIN SOLVE Loop x[1] = 2.20000000000131 y[1] (analytic) = 1.89197304297832 y[1] (numeric) = 1.891972948322749 absolute error = 9.46555704928187e-08 relative error = 5.003008411991596e-06 % Correct digits = 8 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.199 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.297 Order of pole (six term test) = -0.7192 TOP MAIN SOLVE Loop x[1] = 2.210000000001376 y[1] (analytic) = 1.898921753295248 y[1] (numeric) = 1.898921653944964 absolute error = 9.935028355556597e-08 relative error = 5.23193140439625e-06 % Correct digits = 8 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.209 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.315 Order of pole (six term test) = -0.7192 TOP MAIN SOLVE Loop x[1] = 2.220000000001441 y[1] (analytic) = 1.905879849440472 y[1] (numeric) = 1.905879745398979 absolute error = 1.040414931985367e-07 relative error = 5.458974406444415e-06 % Correct digits = 8 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.219 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.333 Order of pole (six term test) = -0.7191 TOP MAIN SOLVE Loop x[1] = 2.230000000001507 y[1] (analytic) = 1.912847324411274 y[1] (numeric) = 1.912847215682062 absolute error = 1.087292123003181e-07 relative error = 5.684155285826702e-06 % Correct digits = 8 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.229 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.35 Order of pole (six term test) = -0.719 TOP MAIN SOLVE Loop x[1] = 2.240000000001572 y[1] (analytic) = 1.919824171235319 y[1] (numeric) = 1.919824057821872 absolute error = 1.134134473002035e-07 relative error = 5.90749137340151e-06 % Correct digits = 8 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.239 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.368 Order of pole (six term test) = -0.719 TOP MAIN SOLVE Loop x[1] = 2.250000000001638 y[1] (analytic) = 1.926810382970503 y[1] (numeric) = 1.926810264876281 absolute error = 1.18094222401055e-07 relative error = 6.129000728083731e-06 % Correct digits = 8 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.249 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.386 Order of pole (six term test) = -0.7189 TOP MAIN SOLVE Loop x[1] = 2.260000000001703 y[1] (analytic) = 1.933805952704731 y[1] (numeric) = 1.933805829933185 absolute error = 1.227715460405676e-07 relative error = 6.348700388932632e-06 % Correct digits = 8 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.259 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.404 Order of pole (six term test) = -0.7188 TOP MAIN SOLVE Loop x[1] = 2.270000000001769 y[1] (analytic) = 1.940810873555767 y[1] (numeric) = 1.940810746110334 absolute error = 1.274454328736851e-07 relative error = 6.566607525244944e-06 % Correct digits = 8 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.269 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.421 Order of pole (six term test) = -0.7188 TOP MAIN SOLVE Loop x[1] = 2.280000000001834 y[1] (analytic) = 1.947825138671041 y[1] (numeric) = 1.947825006555136 absolute error = 1.321159046607789e-07 relative error = 6.782739478910247e-06 % Correct digits = 8 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.279 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.439 Order of pole (six term test) = -0.7187 TOP MAIN SOLVE Loop x[1] = 2.2900000000019 y[1] (analytic) = 1.954848741227472 y[1] (numeric) = 1.9548486044445 absolute error = 1.367829725040792e-07 relative error = 6.997112851718215e-06 % Correct digits = 8 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.289 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.457 Order of pole (six term test) = -0.7186 TOP MAIN SOLVE Loop x[1] = 2.300000000001965 y[1] (analytic) = 1.961881674431302 y[1] (numeric) = 1.961881532984648 absolute error = 1.41446654389199e-07 relative error = 7.209744411838736e-06 % Correct digits = 8 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.299 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.474 Order of pole (six term test) = -0.7186 TOP MAIN SOLVE Loop x[1] = 2.310000000002031 y[1] (analytic) = 1.968923931517898 y[1] (numeric) = 1.968923785410939 absolute error = 1.461069587538333e-07 relative error = 7.420650255451738e-06 % Correct digits = 8 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.309 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.492 Order of pole (six term test) = -0.7185 TOP MAIN SOLVE Loop x[1] = 2.320000000002096 y[1] (analytic) = 1.975975505751613 y[1] (numeric) = 1.97597535498771 absolute error = 1.507639029174612e-07 relative error = 7.629846750560518e-06 % Correct digits = 8 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.319 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.51 Order of pole (six term test) = -0.7184 TOP MAIN SOLVE Loop x[1] = 2.330000000002162 y[1] (analytic) = 1.983036390425585 y[1] (numeric) = 1.98303623500809 absolute error = 1.554174953177778e-07 relative error = 7.837349635546689e-06 % Correct digits = 8 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.329 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.528 Order of pole (six term test) = -0.7183 TOP MAIN SOLVE Loop x[1] = 2.340000000002227 y[1] (analytic) = 1.990106578861583 y[1] (numeric) = 1.990106418793822 absolute error = 1.600677617119572e-07 relative error = 8.043175346092373e-06 % Correct digits = 8 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.339 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.545 Order of pole (six term test) = -0.7183 TOP MAIN SOLVE Loop x[1] = 2.350000000002293 y[1] (analytic) = 1.997186064409831 y[1] (numeric) = 1.997185899695124 absolute error = 1.647147076511146e-07 relative error = 8.247339123097067e-06 % Correct digits = 8 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.349 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.563 Order of pole (six term test) = -0.7182 TOP MAIN SOLVE Loop x[1] = 2.360000000002358 y[1] (analytic) = 2.004274840448847 y[1] (numeric) = 2.004274671090502 absolute error = 1.693583446815694e-07 relative error = 8.44985634024336e-06 % Correct digits = 8 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.359 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.581 Order of pole (six term test) = -0.7181 TOP MAIN SOLVE Loop x[1] = 2.370000000002424 y[1] (analytic) = 2.01137290038527 y[1] (numeric) = 2.011372726386567 absolute error = 1.739987034454771e-07 relative error = 8.650743152209536e-06 % Correct digits = 8 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.369 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.599 Order of pole (six term test) = -0.7181 TOP MAIN SOLVE Loop x[1] = 2.380000000002489 y[1] (analytic) = 2.018480237653685 y[1] (numeric) = 2.01848005901791 absolute error = 1.786357759492319e-07 relative error = 8.850013619993674e-06 % Correct digits = 8 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.379 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.616 Order of pole (six term test) = -0.718 TOP MAIN SOLVE Loop x[1] = 2.390000000002555 y[1] (analytic) = 2.025596845716505 y[1] (numeric) = 2.025596662446904 absolute error = 1.832696012726842e-07 relative error = 9.047683978193455e-06 % Correct digits = 8 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.389 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.634 Order of pole (six term test) = -0.7179 TOP MAIN SOLVE Loop x[1] = 2.40000000000262 y[1] (analytic) = 2.032722718063738 y[1] (numeric) = 2.032722530163574 absolute error = 1.879001638727118e-07 relative error = 9.243767593235509e-06 % Correct digits = 8 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.399 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.652 Order of pole (six term test) = -0.7179 TOP MAIN SOLVE Loop x[1] = 2.410000000002686 y[1] (analytic) = 2.03985784821289 y[1] (numeric) = 2.039857655685395 absolute error = 1.925274943914701e-07 relative error = 9.438279954661673e-06 % Correct digits = 8 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.409 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.669 Order of pole (six term test) = -0.7178 TOP MAIN SOLVE Loop x[1] = 2.420000000002752 y[1] (analytic) = 2.047002229708774 y[1] (numeric) = 2.047002032557164 absolute error = 1.971516101484383e-07 relative error = 9.631235730333668e-06 % Correct digits = 8 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.419 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.687 Order of pole (six term test) = -0.7177 TOP MAIN SOLVE Loop x[1] = 2.430000000002817 y[1] (analytic) = 2.054155856123353 y[1] (numeric) = 2.054155654350835 absolute error = 2.017725182490437e-07 relative error = 9.822648931314936e-06 % Correct digits = 8 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.429 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.705 Order of pole (six term test) = -0.7177 TOP MAIN SOLVE Loop x[1] = 2.440000000002883 y[1] (analytic) = 2.061318721055592 y[1] (numeric) = 2.061318514665363 absolute error = 2.063902289073383e-07 relative error = 1.00125335688819e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.439 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.723 Order of pole (six term test) = -0.7176 TOP MAIN SOLVE Loop x[1] = 2.450000000002948 y[1] (analytic) = 2.068490818131302 y[1] (numeric) = 2.068490607126545 absolute error = 2.110047567782658e-07 relative error = 1.020090371824275e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.449 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.74 Order of pole (six term test) = -0.7175 TOP MAIN SOLVE Loop x[1] = 2.460000000003014 y[1] (analytic) = 2.075672141002979 y[1] (numeric) = 2.075671925386859 absolute error = 2.156161196253947e-07 relative error = 1.038777345256499e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.459 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.758 Order of pole (six term test) = -0.7175 TOP MAIN SOLVE Loop x[1] = 2.470000000003079 y[1] (analytic) = 2.082862683349639 y[1] (numeric) = 2.082862463125308 absolute error = 2.202243303273121e-07 relative error = 1.05731564585501e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.469 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.776 Order of pole (six term test) = -0.7174 TOP MAIN SOLVE Loop x[1] = 2.480000000003145 y[1] (analytic) = 2.090062438876704 y[1] (numeric) = 2.090062214047304 absolute error = 2.248293999862483e-07 relative error = 1.075706619114604e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.479 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.794 Order of pole (six term test) = -0.7173 TOP MAIN SOLVE Loop x[1] = 2.49000000000321 y[1] (analytic) = 2.097271401315812 y[1] (numeric) = 2.097271171884475 absolute error = 2.294313370398982e-07 relative error = 1.093951583452455e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.489 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.812 Order of pole (six term test) = -0.7173 TOP MAIN SOLVE Loop x[1] = 2.500000000003276 y[1] (analytic) = 2.104489564424695 y[1] (numeric) = 2.104489330394523 absolute error = 2.34030171686328e-07 relative error = 1.112051946669096e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.499 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.829 Order of pole (six term test) = -0.7172 TOP MAIN SOLVE Loop x[1] = 2.510000000003341 y[1] (analytic) = 2.111716921987005 y[1] (numeric) = 2.111716683361099 absolute error = 2.386259061459839e-07 relative error = 1.130008968822632e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.509 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.847 Order of pole (six term test) = -0.7171 TOP MAIN SOLVE Loop x[1] = 2.520000000003407 y[1] (analytic) = 2.118953467812185 y[1] (numeric) = 2.118953224593637 absolute error = 2.432185479683824e-07 relative error = 1.147823921869814e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.519 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.865 Order of pole (six term test) = -0.717 TOP MAIN SOLVE Loop x[1] = 2.530000000003472 y[1] (analytic) = 2.126199195735325 y[1] (numeric) = 2.126198947927211 absolute error = 2.47808113140735e-07 relative error = 1.165498104024224e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.529 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.883 Order of pole (six term test) = -0.717 TOP MAIN SOLVE Loop x[1] = 2.540000000003538 y[1] (analytic) = 2.133454099617008 y[1] (numeric) = 2.133453847222391 absolute error = 2.523946172061642e-07 relative error = 1.183032797619004e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.539 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.9 Order of pole (six term test) = -0.7169 TOP MAIN SOLVE Loop x[1] = 2.550000000003603 y[1] (analytic) = 2.140718173343153 y[1] (numeric) = 2.140717916365093 absolute error = 2.569780597205806e-07 relative error = 1.200429196708592e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.549 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.918 Order of pole (six term test) = -0.7168 TOP MAIN SOLVE Loop x[1] = 2.560000000003669 y[1] (analytic) = 2.147991410824913 y[1] (numeric) = 2.147991149266435 absolute error = 2.615584775433888e-07 relative error = 1.217688656599144e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.559 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.936 Order of pole (six term test) = -0.7168 TOP MAIN SOLVE Loop x[1] = 2.570000000003734 y[1] (analytic) = 2.155273805998483 y[1] (numeric) = 2.155273539862617 absolute error = 2.661358662336966e-07 relative error = 1.234812326364272e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.569 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.954 Order of pole (six term test) = -0.7167 TOP MAIN SOLVE Loop x[1] = 2.5800000000038 y[1] (analytic) = 2.162565352825006 y[1] (numeric) = 2.162565082114773 absolute error = 2.707102324528421e-07 relative error = 1.251801394576157e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.579 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.971 Order of pole (six term test) = -0.7166 TOP MAIN SOLVE Loop x[1] = 2.590000000003865 y[1] (analytic) = 2.1698660452904 y[1] (numeric) = 2.169865770008793 absolute error = 2.752816068429809e-07 relative error = 1.268657147939928e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.589 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 7.989 Order of pole (six term test) = -0.7166 TOP MAIN SOLVE Loop x[1] = 2.600000000003931 y[1] (analytic) = 2.177175877405229 y[1] (numeric) = 2.177175597555246 absolute error = 2.798499836309531e-07 relative error = 1.285380692185879e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.599 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 8.007 Order of pole (six term test) = -0.7165 TOP MAIN SOLVE Loop x[1] = 2.610000000003996 y[1] (analytic) = 2.184494843204572 y[1] (numeric) = 2.184494558789194 absolute error = 2.844153779157921e-07 relative error = 1.301973217288833e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.609 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 8.025 Order of pole (six term test) = -0.7164 TOP MAIN SOLVE Loop x[1] = 2.620000000004062 y[1] (analytic) = 2.191822936747897 y[1] (numeric) = 2.191822647770079 absolute error = 2.889778181192071e-07 relative error = 1.31843596156529e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.619 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 8.043 Order of pole (six term test) = -0.7164 TOP MAIN SOLVE Loop x[1] = 2.630000000004127 y[1] (analytic) = 2.199160152118884 y[1] (numeric) = 2.199159858581585 absolute error = 2.935372984680384e-07 relative error = 1.33476999474193e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.629 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 8.06 Order of pole (six term test) = -0.7163 TOP MAIN SOLVE Loop x[1] = 2.640000000004193 y[1] (analytic) = 2.206506483425343 y[1] (numeric) = 2.20650618533149 absolute error = 2.980938531571553e-07 relative error = 1.350976556816635e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.639 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 8.078 Order of pole (six term test) = -0.7162 TOP MAIN SOLVE Loop x[1] = 2.650000000004258 y[1] (analytic) = 2.213861924799044 y[1] (numeric) = 2.213861622151577 absolute error = 3.026474675316138e-07 relative error = 1.367056653992031e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.649 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 8.096 Order of pole (six term test) = -0.7162 TOP MAIN SOLVE Loop x[1] = 2.660000000004324 y[1] (analytic) = 2.221226470395601 y[1] (numeric) = 2.221226163197429 absolute error = 3.071981717894801e-07 relative error = 1.38301148434796e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.659 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 8.114 Order of pole (six term test) = -0.7161 TOP MAIN SOLVE Loop x[1] = 2.670000000004389 y[1] (analytic) = 2.228600114394339 y[1] (numeric) = 2.228599802648367 absolute error = 3.117459721480031e-07 relative error = 1.398842125756264e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.669 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 8.131 Order of pole (six term test) = -0.716 TOP MAIN SOLVE Loop x[1] = 2.680000000004455 y[1] (analytic) = 2.235982850998166 y[1] (numeric) = 2.23598253470728 absolute error = 3.162908859266622e-07 relative error = 1.414549694714638e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.679 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 8.149 Order of pole (six term test) = -0.716 TOP MAIN SOLVE Loop x[1] = 2.69000000000452 y[1] (analytic) = 2.243374674433429 y[1] (numeric) = 2.24337435360051 absolute error = 3.208329193427062e-07 relative error = 1.4301352466847e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.689 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 8.167 Order of pole (six term test) = -0.7159 TOP MAIN SOLVE Loop x[1] = 2.700000000004586 y[1] (analytic) = 2.250775578949797 y[1] (numeric) = 2.250775253577723 absolute error = 3.253720746165811e-07 relative error = 1.445599808615297e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.699 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 8.185 Order of pole (six term test) = -0.7158 TOP MAIN SOLVE Loop x[1] = 2.710000000004651 y[1] (analytic) = 2.258185558820148 y[1] (numeric) = 2.258185228911776 absolute error = 3.299083721763907e-07 relative error = 1.460944477692792e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.709 Order of pole (three term test) = 1.508 Radius of convergence (six term test) for eq 1 = 8.203 Order of pole (six term test) = -0.7158 TOP MAIN SOLVE Loop x[1] = 2.720000000004717 y[1] (analytic) = 2.265604608340427 y[1] (numeric) = 2.265604273898593 absolute error = 3.344418333384169e-07 relative error = 1.476170343700873e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.719 Order of pole (three term test) = 1.509 Radius of convergence (six term test) for eq 1 = 8.22 Order of pole (six term test) = -0.7157 TOP MAIN SOLVE Loop x[1] = 2.730000000004782 y[1] (analytic) = 2.273032721829498 y[1] (numeric) = 2.273032382857054 absolute error = 3.389724438918051e-07 relative error = 1.491278328888183e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.729 Order of pole (three term test) = 1.509 Radius of convergence (six term test) for eq 1 = 8.238 Order of pole (six term test) = -0.7156 TOP MAIN SOLVE Loop x[1] = 2.740000000004848 y[1] (analytic) = 2.280469893629073 y[1] (numeric) = 2.280469550128839 absolute error = 3.435002344787108e-07 relative error = 1.506269543125056e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.739 Order of pole (three term test) = 1.509 Radius of convergence (six term test) for eq 1 = 8.256 Order of pole (six term test) = -0.7156 TOP MAIN SOLVE Loop x[1] = 2.750000000004913 y[1] (analytic) = 2.287916118103553 y[1] (numeric) = 2.287915770078329 absolute error = 3.480252237508807e-07 relative error = 1.521145032359656e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.749 Order of pole (three term test) = 1.509 Radius of convergence (six term test) for eq 1 = 8.274 Order of pole (six term test) = -0.7155 TOP MAIN SOLVE Loop x[1] = 2.760000000004979 y[1] (analytic) = 2.295371389639897 y[1] (numeric) = 2.295371037092496 absolute error = 3.525474010501739e-07 relative error = 1.53590570415484e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.759 Order of pole (three term test) = 1.509 Radius of convergence (six term test) for eq 1 = 8.292 Order of pole (six term test) = -0.7154 TOP MAIN SOLVE Loop x[1] = 2.770000000005044 y[1] (analytic) = 2.302835702647529 y[1] (numeric) = 2.302835345580736 absolute error = 3.570667934660321e-07 relative error = 1.550552621081559e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.769 Order of pole (three term test) = 1.509 Radius of convergence (six term test) for eq 1 = 8.309 Order of pole (six term test) = -0.7153 TOP MAIN SOLVE Loop x[1] = 2.78000000000511 y[1] (analytic) = 2.31030905155821 y[1] (numeric) = 2.310308689974799 absolute error = 3.615834116565964e-07 relative error = 1.565086763663601e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.779 Order of pole (three term test) = 1.509 Radius of convergence (six term test) for eq 1 = 8.327 Order of pole (six term test) = -0.7153 TOP MAIN SOLVE Loop x[1] = 2.790000000005175 y[1] (analytic) = 2.317791430825896 y[1] (numeric) = 2.317791064728632 absolute error = 3.660972640595617e-07 relative error = 1.579509092969209e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.789 Order of pole (three term test) = 1.509 Radius of convergence (six term test) for eq 1 = 8.345 Order of pole (six term test) = -0.7152 TOP MAIN SOLVE Loop x[1] = 2.800000000005241 y[1] (analytic) = 2.325282834926636 y[1] (numeric) = 2.325282464318287 absolute error = 3.706083493426604e-07 relative error = 1.593820518416003e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.799 Order of pole (three term test) = 1.509 Radius of convergence (six term test) for eq 1 = 8.363 Order of pole (six term test) = -0.7151 TOP MAIN SOLVE Loop x[1] = 2.810000000005306 y[1] (analytic) = 2.332783258358477 y[1] (numeric) = 2.332782883241778 absolute error = 3.751166990362265e-07 relative error = 1.608022081314948e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.809 Order of pole (three term test) = 1.509 Radius of convergence (six term test) for eq 1 = 8.381 Order of pole (six term test) = -0.7151 TOP MAIN SOLVE Loop x[1] = 2.820000000005372 y[1] (analytic) = 2.340292695641288 y[1] (numeric) = 2.34029231601898 absolute error = 3.796223086993677e-07 relative error = 1.622114658591213e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.819 Order of pole (three term test) = 1.509 Radius of convergence (six term test) for eq 1 = 8.399 Order of pole (six term test) = -0.715 TOP MAIN SOLVE Loop x[1] = 2.830000000005437 y[1] (analytic) = 2.347811141316706 y[1] (numeric) = 2.347810757191513 absolute error = 3.841251929870282e-07 relative error = 1.63609919991947e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.829 Order of pole (three term test) = 1.509 Radius of convergence (six term test) for eq 1 = 8.416 Order of pole (six term test) = -0.7149 TOP MAIN SOLVE Loop x[1] = 2.840000000005503 y[1] (analytic) = 2.355338589947991 y[1] (numeric) = 2.355338201322621 absolute error = 3.886253701068654e-07 relative error = 1.649976660533749e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.839 Order of pole (three term test) = 1.509 Radius of convergence (six term test) for eq 1 = 8.434 Order of pole (six term test) = -0.7149 TOP MAIN SOLVE Loop x[1] = 2.850000000005569 y[1] (analytic) = 2.362875036119895 y[1] (numeric) = 2.36287464299705 absolute error = 3.931228453879498e-07 relative error = 1.663747931560111e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.849 Order of pole (three term test) = 1.509 Radius of convergence (six term test) for eq 1 = 8.452 Order of pole (six term test) = -0.7148 TOP MAIN SOLVE Loop x[1] = 2.860000000005634 y[1] (analytic) = 2.37042047443858 y[1] (numeric) = 2.370420076820956 absolute error = 3.976176237152629e-07 relative error = 1.677413893454646e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.859 Order of pole (three term test) = 1.509 Radius of convergence (six term test) for eq 1 = 8.47 Order of pole (six term test) = -0.7147 TOP MAIN SOLVE Loop x[1] = 2.8700000000057 y[1] (analytic) = 2.377974899531502 y[1] (numeric) = 2.377974497421777 absolute error = 4.021097246287297e-07 relative error = 1.690975479631646e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.869 Order of pole (three term test) = 1.509 Radius of convergence (six term test) for eq 1 = 8.488 Order of pole (six term test) = -0.7147 TOP MAIN SOLVE Loop x[1] = 2.880000000005765 y[1] (analytic) = 2.385538306047266 y[1] (numeric) = 2.385537899448106 absolute error = 4.065991605628483e-07 relative error = 1.704433584370169e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.879 Order of pole (three term test) = 1.509 Radius of convergence (six term test) for eq 1 = 8.505 Order of pole (six term test) = -0.7146 TOP MAIN SOLVE Loop x[1] = 2.890000000005831 y[1] (analytic) = 2.393110688655558 y[1] (numeric) = 2.393110277569631 absolute error = 4.110859266326372e-07 relative error = 1.717789020714224e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.889 Order of pole (three term test) = 1.509 Radius of convergence (six term test) for eq 1 = 8.523 Order of pole (six term test) = -0.7145 TOP MAIN SOLVE Loop x[1] = 2.900000000005896 y[1] (analytic) = 2.400692042047005 y[1] (numeric) = 2.400691626476958 absolute error = 4.155700477070923e-07 relative error = 1.731042717802101e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.899 Order of pole (three term test) = 1.509 Radius of convergence (six term test) for eq 1 = 8.541 Order of pole (six term test) = -0.7145 TOP MAIN SOLVE Loop x[1] = 2.910000000005962 y[1] (analytic) = 2.408282360933079 y[1] (numeric) = 2.408281940881558 absolute error = 4.20051520677589e-07 relative error = 1.744195479282761e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.909 Order of pole (three term test) = 1.509 Radius of convergence (six term test) for eq 1 = 8.559 Order of pole (six term test) = -0.7144 TOP MAIN SOLVE Loop x[1] = 2.920000000006027 y[1] (analytic) = 2.415881640045976 y[1] (numeric) = 2.415881215515612 absolute error = 4.24530363751785e-07 relative error = 1.757248189293354e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.919 Order of pole (three term test) = 1.509 Radius of convergence (six term test) for eq 1 = 8.577 Order of pole (six term test) = -0.7143 TOP MAIN SOLVE Loop x[1] = 2.930000000006093 y[1] (analytic) = 2.423489874138529 y[1] (numeric) = 2.42348944513193 absolute error = 4.290065991341407e-07 relative error = 1.77020173969837e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.929 Order of pole (three term test) = 1.509 Radius of convergence (six term test) for eq 1 = 8.595 Order of pole (six term test) = -0.7143 TOP MAIN SOLVE Loop x[1] = 2.940000000006158 y[1] (analytic) = 2.431107057984068 y[1] (numeric) = 2.431106624503847 absolute error = 4.334802210514965e-07 relative error = 1.78305689841133e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.939 Order of pole (three term test) = 1.509 Radius of convergence (six term test) for eq 1 = 8.612 Order of pole (six term test) = -0.7142 TOP MAIN SOLVE Loop x[1] = 2.950000000006224 y[1] (analytic) = 2.438733186376368 y[1] (numeric) = 2.438732748425112 absolute error = 4.379512557051157e-07 relative error = 1.795814557130183e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.949 Order of pole (three term test) = 1.509 Radius of convergence (six term test) for eq 1 = 8.63 Order of pole (six term test) = -0.7141 TOP MAIN SOLVE Loop x[1] = 2.960000000006289 y[1] (analytic) = 2.446368254129464 y[1] (numeric) = 2.44636781170977 absolute error = 4.424196933250357e-07 relative error = 1.808475451634202e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.959 Order of pole (three term test) = 1.509 Radius of convergence (six term test) for eq 1 = 8.648 Order of pole (six term test) = -0.7141 TOP MAIN SOLVE Loop x[1] = 2.970000000006355 y[1] (analytic) = 2.454012256077617 y[1] (numeric) = 2.454011809192065 absolute error = 4.468855512307357e-07 relative error = 1.821040421146949e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.969 Order of pole (three term test) = 1.509 Radius of convergence (six term test) for eq 1 = 8.666 Order of pole (six term test) = -0.714 TOP MAIN SOLVE Loop x[1] = 2.98000000000642 y[1] (analytic) = 2.461665187075182 y[1] (numeric) = 2.461664735726342 absolute error = 4.513488400803567e-07 relative error = 1.833510269593669e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.979 Order of pole (three term test) = 1.509 Radius of convergence (six term test) for eq 1 = 8.684 Order of pole (six term test) = -0.7139 TOP MAIN SOLVE Loop x[1] = 2.990000000006486 y[1] (analytic) = 2.469327041996499 y[1] (numeric) = 2.469326586186932 absolute error = 4.558095669793261e-07 relative error = 1.845885778705097e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.989 Order of pole (three term test) = 1.509 Radius of convergence (six term test) for eq 1 = 8.702 Order of pole (six term test) = -0.7139 Finished! diff ( y , x , 1 ) = sinh ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations = 100000 Total Elapsed Time = 3.0 Seconds Elapsed Time(since restart) = 3.0 Seconds Time to Timeout = 29 Minutes 57.0 Seconds Percent Done = 100 %