##############ECHO OF PROBLEM################# ##############temp/tanh_sqrt_newpostode.ode################# diff ( y , x , 1 ) = ( 1.0 - ( tanh ( sqrt ( 2.0 * x + 1.0 ) ) * tanh( sqrt ( 2.0 * x + 1.0 ) ) ) ) / sqrt ( 2.0 * x + 1.0 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=0.1; x_end=1.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_iter=1000000; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=10000000; glob_max_minutes=3; glob_subiter_method=3; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(tanh(sqrt(2.0*x + 1.0))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1e-10 range = 0.9 estimated_steps = 900000.0000000001 step_error = 1.111111111111111e-16 est_needed_step_err = 1.111111111111111e-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 = 1.422395301078658e-153 estimated_step_error = 1.422395301078658e-153 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 = 9.545525776602575e-146 estimated_step_error = 9.545525776602575e-146 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 = 6.405883838716534e-138 estimated_step_error = 6.405883838716534e-138 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 = 4.298902353918126e-130 estimated_step_error = 4.298902353918126e-130 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 = 2.884926388918218e-122 estimated_step_error = 2.884926388918218e-122 best_h = 3.2e-05 opt_iter = 6 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.936016973136705e-114 estimated_step_error = 1.936016973136705e-114 best_h = 6.4e-05 opt_iter = 7 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.299206311769296e-106 estimated_step_error = 1.299206311769296e-106 best_h = 0.000128 opt_iter = 8 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.718387300923815e-99 estimated_step_error = 8.718387300923815e-99 best_h = 0.000256 opt_iter = 9 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.850221996271756e-91 estimated_step_error = 5.850221996271756e-91 best_h = 0.000512 opt_iter = 10 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.925227648719573e-83 estimated_step_error = 3.925227648719573e-83 best_h = 0.001024 opt_iter = 11 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.633116174839689e-75 estimated_step_error = 2.633116174839689e-75 best_h = 0.002048 opt_iter = 12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.765634026121937e-67 estimated_step_error = 1.765634026121937e-67 best_h = 0.004096 opt_iter = 13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.182995232736144e-59 estimated_step_error = 1.182995232736144e-59 best_h = 0.008192 opt_iter = 14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.913546536993009e-52 estimated_step_error = 7.913546536993009e-52 best_h = 0.016384 opt_iter = 15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.276933074348221e-44 estimated_step_error = 5.276933074348221e-44 best_h = 0.032768 opt_iter = 16 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.496875179109304e-36 estimated_step_error = 3.496875179109304e-36 best_h = 0.065536 opt_iter = 17 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.289502565761929e-28 estimated_step_error = 2.289502565761929e-28 best_h = 0.131072 opt_iter = 18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.466119370814807e-20 estimated_step_error = 1.466119370814807e-20 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 0.798856925051763 y[1] (numeric) = 0.798856925051763 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.6428 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.015 Order of pole (six term test) = 0.1243 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (analytic) = 0.8021224892873338 y[1] (numeric) = 0.8021224892873338 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.6536 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.027 Order of pole (six term test) = 0.1247 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (analytic) = 0.805314691088346 y[1] (numeric) = 0.805314691088346 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.6643 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.038 Order of pole (six term test) = 0.1251 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (analytic) = 0.8084357793551158 y[1] (numeric) = 0.8084357793551159 absolute error = 1.110223024625157e-16 relative error = 1.373297734930503e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.675 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.05 Order of pole (six term test) = 0.1255 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (analytic) = 0.8114879110711591 y[1] (numeric) = 0.8114879110711591 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.6858 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.062 Order of pole (six term test) = 0.1259 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (analytic) = 0.8144731561650902 y[1] (numeric) = 0.8144731561650902 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.6965 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.073 Order of pole (six term test) = 0.1263 TOP MAIN SOLVE Loop x[1] = 0.16 y[1] (analytic) = 0.8173935020507396 y[1] (numeric) = 0.8173935020507397 absolute error = 1.110223024625157e-16 relative error = 1.358247920786921e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.7072 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.085 Order of pole (six term test) = 0.1267 TOP MAIN SOLVE Loop x[1] = 0.17 y[1] (analytic) = 0.8202508578712564 y[1] (numeric) = 0.8202508578712565 absolute error = 1.110223024625157e-16 relative error = 1.35351644435514e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.718 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.096 Order of pole (six term test) = 0.1271 TOP MAIN SOLVE Loop x[1] = 0.18 y[1] (analytic) = 0.8230470584705385 y[1] (numeric) = 0.8230470584705386 absolute error = 1.110223024625157e-16 relative error = 1.348918039617655e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.7287 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.108 Order of pole (six term test) = 0.1275 TOP MAIN SOLVE Loop x[1] = 0.1900000000000001 y[1] (analytic) = 0.8257838681131744 y[1] (numeric) = 0.8257838681131745 absolute error = 1.110223024625157e-16 relative error = 1.344447460764636e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.7394 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.119 Order of pole (six term test) = 0.1279 TOP MAIN SOLVE Loop x[1] = 0.2000000000000001 y[1] (analytic) = 0.8284629839721465 y[1] (numeric) = 0.8284629839721467 absolute error = 2.220446049250313e-16 relative error = 2.680199468423041e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.7502 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.131 Order of pole (six term test) = 0.1283 TOP MAIN SOLVE Loop x[1] = 0.2100000000000001 y[1] (analytic) = 0.8310860394018158 y[1] (numeric) = 0.8310860394018159 absolute error = 1.110223024625157e-16 relative error = 1.335870140983541e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.7609 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.142 Order of pole (six term test) = 0.1288 TOP MAIN SOLVE Loop x[1] = 0.2200000000000001 y[1] (analytic) = 0.8336546070121553 y[1] (numeric) = 0.8336546070121554 absolute error = 1.110223024625157e-16 relative error = 1.331754200464664e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.7717 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.154 Order of pole (six term test) = 0.1292 TOP MAIN SOLVE Loop x[1] = 0.2300000000000001 y[1] (analytic) = 0.8361702015588065 y[1] (numeric) = 0.8361702015588066 absolute error = 1.110223024625157e-16 relative error = 1.327747655388167e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.7824 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.165 Order of pole (six term test) = 0.1296 TOP MAIN SOLVE Loop x[1] = 0.2400000000000001 y[1] (analytic) = 0.838634282662277 y[1] (numeric) = 0.8386342826622771 absolute error = 1.110223024625157e-16 relative error = 1.323846457958659e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.7931 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.176 Order of pole (six term test) = 0.13 TOP MAIN SOLVE Loop x[1] = 0.2500000000000001 y[1] (analytic) = 0.8410482573684664 y[1] (numeric) = 0.8410482573684667 absolute error = 2.220446049250313e-16 relative error = 2.640093514012867e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.8039 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.188 Order of pole (six term test) = 0.1305 TOP MAIN SOLVE Loop x[1] = 0.2600000000000001 y[1] (analytic) = 0.8434134825616889 y[1] (numeric) = 0.8434134825616891 absolute error = 2.220446049250313e-16 relative error = 2.632689772169851e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.8146 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.199 Order of pole (six term test) = 0.1309 TOP MAIN SOLVE Loop x[1] = 0.2700000000000001 y[1] (analytic) = 0.8457312672404343 y[1] (numeric) = 0.8457312672404345 absolute error = 1.110223024625157e-16 relative error = 1.312737352430804e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.8254 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.211 Order of pole (six term test) = 0.1313 TOP MAIN SOLVE Loop x[1] = 0.2800000000000001 y[1] (analytic) = 0.848002874665279 y[1] (numeric) = 0.8480028746652791 absolute error = 1.110223024625157e-16 relative error = 1.309220826714037e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.8361 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.222 Order of pole (six term test) = 0.1318 TOP MAIN SOLVE Loop x[1] = 0.2900000000000001 y[1] (analytic) = 0.8502295243875967 y[1] (numeric) = 0.8502295243875968 absolute error = 1.110223024625157e-16 relative error = 1.305792133512216e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.8469 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.233 Order of pole (six term test) = 0.1322 TOP MAIN SOLVE Loop x[1] = 0.3000000000000002 y[1] (analytic) = 0.8524123941670346 y[1] (numeric) = 0.8524123941670346 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.8576 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.245 Order of pole (six term test) = 0.1326 TOP MAIN SOLVE Loop x[1] = 0.3100000000000002 y[1] (analytic) = 0.8545526217850941 y[1] (numeric) = 0.8545526217850941 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.8684 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.256 Order of pole (six term test) = 0.1331 TOP MAIN SOLVE Loop x[1] = 0.3200000000000002 y[1] (analytic) = 0.8566513067615884 y[1] (numeric) = 0.8566513067615885 absolute error = 1.110223024625157e-16 relative error = 1.29600342153466e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.8791 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.267 Order of pole (six term test) = 0.1335 TOP MAIN SOLVE Loop x[1] = 0.3300000000000002 y[1] (analytic) = 0.8587095119802312 y[1] (numeric) = 0.8587095119802313 absolute error = 1.110223024625157e-16 relative error = 1.292897084678754e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.8899 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.278 Order of pole (six term test) = 0.1339 TOP MAIN SOLVE Loop x[1] = 0.3400000000000002 y[1] (analytic) = 0.8607282652291354 y[1] (numeric) = 0.8607282652291355 absolute error = 1.110223024625157e-16 relative error = 1.28986472209043e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.9006 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.29 Order of pole (six term test) = 0.1343 TOP MAIN SOLVE Loop x[1] = 0.3500000000000002 y[1] (analytic) = 0.8627085606615759 y[1] (numeric) = 0.8627085606615759 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.9114 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.301 Order of pole (six term test) = 0.1348 TOP MAIN SOLVE Loop x[1] = 0.3600000000000002 y[1] (analytic) = 0.8646513601819672 y[1] (numeric) = 0.8646513601819673 absolute error = 1.110223024625157e-16 relative error = 1.284012349661381e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.9221 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.312 Order of pole (six term test) = 0.1352 TOP MAIN SOLVE Loop x[1] = 0.3700000000000002 y[1] (analytic) = 0.8665575947616552 y[1] (numeric) = 0.8665575947616553 absolute error = 1.110223024625157e-16 relative error = 1.28118780717688e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.9329 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.323 Order of pole (six term test) = 0.1356 TOP MAIN SOLVE Loop x[1] = 0.3800000000000002 y[1] (analytic) = 0.8684281656887811 y[1] (numeric) = 0.8684281656887812 absolute error = 1.110223024625157e-16 relative error = 1.278428163076216e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.9436 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.334 Order of pole (six term test) = 0.136 TOP MAIN SOLVE Loop x[1] = 0.3900000000000002 y[1] (analytic) = 0.8702639457561832 y[1] (numeric) = 0.8702639457561832 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.9544 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.345 Order of pole (six term test) = 0.1364 TOP MAIN SOLVE Loop x[1] = 0.4000000000000002 y[1] (analytic) = 0.8720657803910122 y[1] (numeric) = 0.8720657803910122 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.9651 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.357 Order of pole (six term test) = 0.1368 TOP MAIN SOLVE Loop x[1] = 0.4100000000000003 y[1] (analytic) = 0.8738344887294903 y[1] (numeric) = 0.8738344887294903 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.9759 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.368 Order of pole (six term test) = 0.1372 TOP MAIN SOLVE Loop x[1] = 0.4200000000000003 y[1] (analytic) = 0.8755708646399988 y[1] (numeric) = 0.8755708646399989 absolute error = 1.110223024625157e-16 relative error = 1.267999050061628e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.9866 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.379 Order of pole (six term test) = 0.1376 TOP MAIN SOLVE Loop x[1] = 0.4300000000000003 y[1] (analytic) = 0.8772756776974695 y[1] (numeric) = 0.8772756776974695 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.9974 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.39 Order of pole (six term test) = 0.1379 TOP MAIN SOLVE Loop x[1] = 0.4400000000000003 y[1] (analytic) = 0.8789496741118499 y[1] (numeric) = 0.8789496741118499 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.008 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.401 Order of pole (six term test) = 0.1383 TOP MAIN SOLVE Loop x[1] = 0.4500000000000003 y[1] (analytic) = 0.8805935776132313 y[1] (numeric) = 0.8805935776132314 absolute error = 1.110223024625157e-16 relative error = 1.260766661090483e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.019 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.412 Order of pole (six term test) = 0.1386 TOP MAIN SOLVE Loop x[1] = 0.4600000000000003 y[1] (analytic) = 0.8822080902960553 y[1] (numeric) = 0.8822080902960554 absolute error = 1.110223024625157e-16 relative error = 1.258459355380184e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.03 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.423 Order of pole (six term test) = 0.139 TOP MAIN SOLVE Loop x[1] = 0.4700000000000003 y[1] (analytic) = 0.8837938934246573 y[1] (numeric) = 0.8837938934246574 absolute error = 1.110223024625157e-16 relative error = 1.256201285033887e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.04 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.434 Order of pole (six term test) = 0.1393 TOP MAIN SOLVE Loop x[1] = 0.4800000000000003 y[1] (analytic) = 0.8853516482022625 y[1] (numeric) = 0.8853516482022626 absolute error = 1.110223024625157e-16 relative error = 1.25399102930401e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.051 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.445 Order of pole (six term test) = 0.1396 TOP MAIN SOLVE Loop x[1] = 0.4900000000000003 y[1] (analytic) = 0.8868819965054102 y[1] (numeric) = 0.8868819965054103 absolute error = 1.110223024625157e-16 relative error = 1.251827220531907e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.062 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.456 Order of pole (six term test) = 0.14 TOP MAIN SOLVE Loop x[1] = 0.5000000000000003 y[1] (analytic) = 0.8883855615856606 y[1] (numeric) = 0.8883855615856607 absolute error = 1.110223024625157e-16 relative error = 1.249708541687173e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.073 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.467 Order of pole (six term test) = 0.1403 TOP MAIN SOLVE Loop x[1] = 0.5100000000000003 y[1] (analytic) = 0.8898629487403211 y[1] (numeric) = 0.8898629487403212 absolute error = 1.110223024625157e-16 relative error = 1.247633724043432e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.083 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.478 Order of pole (six term test) = 0.1406 TOP MAIN SOLVE Loop x[1] = 0.5200000000000004 y[1] (analytic) = 0.8913147459538211 y[1] (numeric) = 0.8913147459538212 absolute error = 1.110223024625157e-16 relative error = 1.245601544981818e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.094 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.489 Order of pole (six term test) = 0.1408 TOP MAIN SOLVE Loop x[1] = 0.5300000000000004 y[1] (analytic) = 0.8927415245112643 y[1] (numeric) = 0.8927415245112644 absolute error = 1.110223024625157e-16 relative error = 1.243610825913977e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.105 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.5 Order of pole (six term test) = 0.1411 TOP MAIN SOLVE Loop x[1] = 0.5400000000000004 y[1] (analytic) = 0.8941438395855952 y[1] (numeric) = 0.8941438395855953 absolute error = 1.110223024625157e-16 relative error = 1.241660430317013e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.116 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.51 Order of pole (six term test) = 0.1414 TOP MAIN SOLVE Loop x[1] = 0.5500000000000004 y[1] (analytic) = 0.8955222307997287 y[1] (numeric) = 0.8955222307997288 absolute error = 1.110223024625157e-16 relative error = 1.239749261873369e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.127 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.521 Order of pole (six term test) = 0.1416 TOP MAIN SOLVE Loop x[1] = 0.5600000000000004 y[1] (analytic) = 0.8968772227649131 y[1] (numeric) = 0.8968772227649131 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.137 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.532 Order of pole (six term test) = 0.1418 TOP MAIN SOLVE Loop x[1] = 0.5700000000000004 y[1] (analytic) = 0.8982093255965184 y[1] (numeric) = 0.8982093255965186 absolute error = 1.110223024625157e-16 relative error = 1.236040411724556e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.148 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.543 Order of pole (six term test) = 0.142 TOP MAIN SOLVE Loop x[1] = 0.5800000000000004 y[1] (analytic) = 0.8995190354083774 y[1] (numeric) = 0.8995190354083775 absolute error = 1.110223024625157e-16 relative error = 1.234240723011626e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.159 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.554 Order of pole (six term test) = 0.1422 TOP MAIN SOLVE Loop x[1] = 0.5900000000000004 y[1] (analytic) = 0.900806834786734 y[1] (numeric) = 0.9008068347867341 absolute error = 1.110223024625157e-16 relative error = 1.232476244352655e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.17 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.565 Order of pole (six term test) = 0.1424 TOP MAIN SOLVE Loop x[1] = 0.6000000000000004 y[1] (analytic) = 0.9020731932448007 y[1] (numeric) = 0.9020731932448008 absolute error = 1.110223024625157e-16 relative error = 1.230746055795795e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.575 Order of pole (six term test) = 0.1426 TOP MAIN SOLVE Loop x[1] = 0.6100000000000004 y[1] (analytic) = 0.9033185676588645 y[1] (numeric) = 0.9033185676588645 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.191 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.586 Order of pole (six term test) = 0.1427 TOP MAIN SOLVE Loop x[1] = 0.6200000000000004 y[1] (analytic) = 0.9045434026868278 y[1] (numeric) = 0.9045434026868278 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.202 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.597 Order of pole (six term test) = 0.1429 TOP MAIN SOLVE Loop x[1] = 0.6300000000000004 y[1] (analytic) = 0.9057481311700254 y[1] (numeric) = 0.9057481311700253 absolute error = 1.110223024625157e-16 relative error = 1.225752487273692e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.213 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.607 Order of pole (six term test) = 0.143 TOP MAIN SOLVE Loop x[1] = 0.6400000000000005 y[1] (analytic) = 0.9069331745191064 y[1] (numeric) = 0.9069331745191063 absolute error = 1.110223024625157e-16 relative error = 1.224150858980148e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.223 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.618 Order of pole (six term test) = 0.1431 TOP MAIN SOLVE Loop x[1] = 0.6500000000000005 y[1] (analytic) = 0.9080989430847305 y[1] (numeric) = 0.9080989430847304 absolute error = 1.110223024625157e-16 relative error = 1.222579359969112e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.234 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.629 Order of pole (six term test) = 0.1432 TOP MAIN SOLVE Loop x[1] = 0.6600000000000005 y[1] (analytic) = 0.9092458365137851 y[1] (numeric) = 0.909245836513785 absolute error = 1.110223024625157e-16 relative error = 1.221037237719949e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.245 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.639 Order of pole (six term test) = 0.1433 TOP MAIN SOLVE Loop x[1] = 0.6700000000000005 y[1] (analytic) = 0.9103742440917924 y[1] (numeric) = 0.9103742440917922 absolute error = 1.110223024625157e-16 relative error = 1.219523763804124e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.256 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.65 Order of pole (six term test) = 0.1433 TOP MAIN SOLVE Loop x[1] = 0.6800000000000005 y[1] (analytic) = 0.9114845450721389 y[1] (numeric) = 0.9114845450721388 absolute error = 1.110223024625157e-16 relative error = 1.218038232932725e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.267 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.661 Order of pole (six term test) = 0.1434 TOP MAIN SOLVE Loop x[1] = 0.6900000000000005 y[1] (analytic) = 0.9125771089927275 y[1] (numeric) = 0.9125771089927274 absolute error = 1.110223024625157e-16 relative error = 1.216579962048998e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.277 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.671 Order of pole (six term test) = 0.1434 TOP MAIN SOLVE Loop x[1] = 0.7000000000000005 y[1] (analytic) = 0.9136522959806184 y[1] (numeric) = 0.9136522959806181 absolute error = 2.220446049250313e-16 relative error = 2.4302965789268e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.288 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.682 Order of pole (six term test) = 0.1434 TOP MAIN SOLVE Loop x[1] = 0.7100000000000005 y[1] (analytic) = 0.9147104570451972 y[1] (numeric) = 0.914710457045197 absolute error = 1.110223024625157e-16 relative error = 1.213742574028864e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.299 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.692 Order of pole (six term test) = 0.1434 TOP MAIN SOLVE Loop x[1] = 0.7200000000000005 y[1] (analytic) = 0.9157519343603815 y[1] (numeric) = 0.9157519343603814 absolute error = 1.110223024625157e-16 relative error = 1.212362194354092e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.31 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.703 Order of pole (six term test) = 0.1433 TOP MAIN SOLVE Loop x[1] = 0.7300000000000005 y[1] (analytic) = 0.916777061536346 y[1] (numeric) = 0.9167770615363459 absolute error = 1.110223024625157e-16 relative error = 1.21100654805284e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.321 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.714 Order of pole (six term test) = 0.1433 TOP MAIN SOLVE Loop x[1] = 0.7400000000000005 y[1] (analytic) = 0.9177861638812285 y[1] (numeric) = 0.9177861638812282 absolute error = 2.220446049250313e-16 relative error = 2.41935010205456e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.331 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.724 Order of pole (six term test) = 0.1432 TOP MAIN SOLVE Loop x[1] = 0.7500000000000006 y[1] (analytic) = 0.9187795586532502 y[1] (numeric) = 0.9187795586532501 absolute error = 1.110223024625157e-16 relative error = 1.208367136783631e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.342 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.735 Order of pole (six term test) = 0.1431 TOP MAIN SOLVE Loop x[1] = 0.7600000000000006 y[1] (analytic) = 0.9197575553036655 y[1] (numeric) = 0.9197575553036654 absolute error = 1.110223024625157e-16 relative error = 1.20708225577838e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.353 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.745 Order of pole (six term test) = 0.1429 TOP MAIN SOLVE Loop x[1] = 0.7700000000000006 y[1] (analytic) = 0.920720455710931 y[1] (numeric) = 0.920720455710931 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.364 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.755 Order of pole (six term test) = 0.1428 TOP MAIN SOLVE Loop x[1] = 0.7800000000000006 y[1] (analytic) = 0.9216685544064713 y[1] (numeric) = 0.9216685544064712 absolute error = 1.110223024625157e-16 relative error = 1.204579476339094e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.374 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.766 Order of pole (six term test) = 0.1426 TOP MAIN SOLVE Loop x[1] = 0.7900000000000006 y[1] (analytic) = 0.9226021387923933 y[1] (numeric) = 0.9226021387923932 absolute error = 1.110223024625157e-16 relative error = 1.20336055808232e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.385 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.776 Order of pole (six term test) = 0.1424 TOP MAIN SOLVE Loop x[1] = 0.8000000000000006 y[1] (analytic) = 0.9235214893514879 y[1] (numeric) = 0.9235214893514878 absolute error = 1.110223024625157e-16 relative error = 1.202162632300818e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.396 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.787 Order of pole (six term test) = 0.1422 TOP MAIN SOLVE Loop x[1] = 0.8100000000000006 y[1] (analytic) = 0.9244268798498404 y[1] (numeric) = 0.9244268798498403 absolute error = 1.110223024625157e-16 relative error = 1.200985225359842e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.407 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.797 Order of pole (six term test) = 0.1419 TOP MAIN SOLVE Loop x[1] = 0.8200000000000006 y[1] (analytic) = 0.9253185775323547 y[1] (numeric) = 0.9253185775323545 absolute error = 2.220446049250313e-16 relative error = 2.399655754423317e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.418 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.807 Order of pole (six term test) = 0.1416 TOP MAIN SOLVE Loop x[1] = 0.8300000000000006 y[1] (analytic) = 0.9261968433114826 y[1] (numeric) = 0.9261968433114823 absolute error = 2.220446049250313e-16 relative error = 2.397380281832348e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.428 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.818 Order of pole (six term test) = 0.1413 TOP MAIN SOLVE Loop x[1] = 0.8400000000000006 y[1] (analytic) = 0.9270619319494363 y[1] (numeric) = 0.9270619319494361 absolute error = 2.220446049250313e-16 relative error = 2.3951431643635e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.439 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.828 Order of pole (six term test) = 0.1409 TOP MAIN SOLVE Loop x[1] = 0.8500000000000006 y[1] (analytic) = 0.9279140922341471 y[1] (numeric) = 0.9279140922341469 absolute error = 2.220446049250313e-16 relative error = 2.39294355785041e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.45 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.838 Order of pole (six term test) = 0.1405 TOP MAIN SOLVE Loop x[1] = 0.8600000000000007 y[1] (analytic) = 0.928753567149222 y[1] (numeric) = 0.9287535671492217 absolute error = 2.220446049250313e-16 relative error = 2.390780641700142e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.461 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.848 Order of pole (six term test) = 0.1401 TOP MAIN SOLVE Loop x[1] = 0.8700000000000007 y[1] (analytic) = 0.9295805940381399 y[1] (numeric) = 0.9295805940381396 absolute error = 2.220446049250313e-16 relative error = 2.38865361808447e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.472 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.859 Order of pole (six term test) = 0.1396 TOP MAIN SOLVE Loop x[1] = 0.8800000000000007 y[1] (analytic) = 0.9303954047629146 y[1] (numeric) = 0.9303954047629143 absolute error = 3.33066907387547e-16 relative error = 3.579842566746337e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.482 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.869 Order of pole (six term test) = 0.1391 TOP MAIN SOLVE Loop x[1] = 0.8900000000000007 y[1] (analytic) = 0.9311982258574437 y[1] (numeric) = 0.9311982258574435 absolute error = 2.220446049250313e-16 relative error = 2.384504166345178e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.493 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.879 Order of pole (six term test) = 0.1385 TOP MAIN SOLVE Loop x[1] = 0.9000000000000007 y[1] (analytic) = 0.931989278675753 y[1] (numeric) = 0.9319892786757527 absolute error = 3.33066907387547e-16 relative error = 3.573720374345892e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.504 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.889 Order of pole (six term test) = 0.1379 TOP MAIN SOLVE Loop x[1] = 0.9100000000000007 y[1] (analytic) = 0.9327687795353322 y[1] (numeric) = 0.932768779535332 absolute error = 2.220446049250313e-16 relative error = 2.380489246602411e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.515 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.899 Order of pole (six term test) = 0.1372 TOP MAIN SOLVE Loop x[1] = 0.9200000000000007 y[1] (analytic) = 0.9335369398557575 y[1] (numeric) = 0.9335369398557571 absolute error = 3.33066907387547e-16 relative error = 3.567795693644536e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.526 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.909 Order of pole (six term test) = 0.1365 TOP MAIN SOLVE Loop x[1] = 0.9300000000000007 y[1] (analytic) = 0.9342939662927758 y[1] (numeric) = 0.9342939662927755 absolute error = 3.33066907387547e-16 relative error = 3.564904830854652e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.537 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.919 Order of pole (six term test) = 0.1358 TOP MAIN SOLVE Loop x[1] = 0.9400000000000007 y[1] (analytic) = 0.9350400608680312 y[1] (numeric) = 0.9350400608680308 absolute error = 3.33066907387547e-16 relative error = 3.562060293741308e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.547 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.929 Order of pole (six term test) = 0.1349 TOP MAIN SOLVE Loop x[1] = 0.9500000000000007 y[1] (analytic) = 0.9357754210945929 y[1] (numeric) = 0.9357754210945926 absolute error = 3.33066907387547e-16 relative error = 3.559261120557674e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.558 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.939 Order of pole (six term test) = 0.134 TOP MAIN SOLVE Loop x[1] = 0.9600000000000007 y[1] (analytic) = 0.9365002400984491 y[1] (numeric) = 0.9365002400984488 absolute error = 3.33066907387547e-16 relative error = 3.556506374761137e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.569 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.949 Order of pole (six term test) = 0.133 TOP MAIN SOLVE Loop x[1] = 0.9700000000000008 y[1] (analytic) = 0.9372147067361143 y[1] (numeric) = 0.937214706736114 absolute error = 3.33066907387547e-16 relative error = 3.553795144204097e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.58 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.959 Order of pole (six term test) = 0.132 TOP MAIN SOLVE Loop x[1] = 0.9800000000000008 y[1] (analytic) = 0.937919005708497 y[1] (numeric) = 0.9379190057084965 absolute error = 4.440892098500626e-16 relative error = 4.734835387140929e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.591 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.969 Order of pole (six term test) = 0.1309 TOP MAIN SOLVE Loop x[1] = 0.9900000000000008 y[1] (analytic) = 0.9386133176711662 y[1] (numeric) = 0.9386133176711658 absolute error = 3.33066907387547e-16 relative error = 3.548499697553126e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.601 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.978 Order of pole (six term test) = 0.1296 Finished! diff ( y , x , 1 ) = ( 1.0 - ( tanh ( sqrt ( 2.0 * x + 1.0 ) ) * tanh( sqrt ( 2.0 * x + 1.0 ) ) ) ) / sqrt ( 2.0 * x + 1.0 ) ; Iterations = 90 Total Elapsed Time = 0 Seconds Elapsed Time(since restart) = 0 Seconds Time to Timeout = 3 Minutes 0 Seconds Percent Done = 101.1 %