##############ECHO OF PROBLEM################# ##############temp/tanh_sqrtpostode.ode################# diff ( y , x , 1 ) = tanh(sqrt(2.0*x + 3.0)); ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=0.1; x_end=5.0; 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=0.1; 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(0.0); } /* 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 = 4.9 estimated_steps = 4900000.000000001 step_error = 2.040816326530612e-17 est_needed_step_err = 2.040816326530612e-17 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.344145481044364e-165 estimated_step_error = 1.344145481044364e-165 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 = 9.02040507999709e-158 estimated_step_error = 9.02040507999709e-158 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 = 6.053487957029652e-150 estimated_step_error = 6.053487957029652e-150 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 = 4.062422409624871e-142 estimated_step_error = 4.062422409624871e-142 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 = 2.7262393684489e-134 estimated_step_error = 2.7262393684489e-134 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 = 1.829540000275166e-126 estimated_step_error = 1.829540000275166e-126 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 = 1.227772411208053e-118 estimated_step_error = 1.227772411208053e-118 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 = 8.239292207073284e-111 estimated_step_error = 8.239292207073284e-111 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 = 5.529095469086841e-103 estimated_step_error = 5.529095469086841e-103 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 = 3.710244842855428e-95 estimated_step_error = 3.710244842855428e-95 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 = 2.489543116587482e-87 estimated_step_error = 2.489543116587482e-87 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 = 1.670221065279255e-79 estimated_step_error = 1.670221065279255e-79 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 = 1.120218624562508e-71 estimated_step_error = 1.120218624562508e-71 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 = 7.508981040900188e-64 estimated_step_error = 7.508981040900188e-64 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 = 5.027584005126509e-56 estimated_step_error = 5.027584005126509e-56 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 = 3.358484059516466e-48 estimated_step_error = 3.358484059516466e-48 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 = 2.233369985533775e-40 estimated_step_error = 2.233369985533775e-40 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 = 1.472102229063348e-32 estimated_step_error = 1.472102229063348e-32 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 0 y[1] (numeric) = 0 absolute error = 0 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.57 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 1.982 Order of pole (six term test) = -0.461 TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (analytic) = 0 y[1] (numeric) = 0.0948466321349032 absolute error = 0.0948466321349032 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.668 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 2.081 Order of pole (six term test) = -0.4331 TOP MAIN SOLVE Loop x[1] = 0.3 y[1] (analytic) = 0 y[1] (numeric) = 0.190210919064638 absolute error = 0.190210919064638 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.767 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 2.18 Order of pole (six term test) = -0.302 TOP MAIN SOLVE Loop x[1] = 0.4 y[1] (analytic) = 0 y[1] (numeric) = 0.2860294594483283 absolute error = 0.2860294594483283 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.866 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 2.277 Order of pole (six term test) = -0.7512 TOP MAIN SOLVE Loop x[1] = 0.5 y[1] (analytic) = 0 y[1] (numeric) = 0.3822481672271355 absolute error = 0.3822481672271355 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.966 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 2.513 Order of pole (six term test) = -0.5817 TOP MAIN SOLVE Loop x[1] = 0.6 y[1] (analytic) = 0 y[1] (numeric) = 0.4788206610284064 absolute error = 0.4788206610284064 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.065 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 2.641 Order of pole (six term test) = -0.5503 TOP MAIN SOLVE Loop x[1] = 0.7 y[1] (analytic) = 0 y[1] (numeric) = 0.575706975029923 absolute error = 0.575706975029923 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.164 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 2.754 Order of pole (six term test) = -0.5369 TOP MAIN SOLVE Loop x[1] = 0.7999999999999999 y[1] (analytic) = 0 y[1] (numeric) = 0.6728725185074256 absolute error = 0.6728725185074256 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.264 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 2.864 Order of pole (six term test) = -0.5294 TOP MAIN SOLVE Loop x[1] = 0.8999999999999999 y[1] (analytic) = 0 y[1] (numeric) = 0.7702872296931287 absolute error = 0.7702872296931287 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.363 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 2.971 Order of pole (six term test) = -0.5246 TOP MAIN SOLVE Loop x[1] = 0.9999999999999999 y[1] (analytic) = 0 y[1] (numeric) = 0.8679248828463588 absolute error = 0.8679248828463588 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.463 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 3.077 Order of pole (six term test) = -0.5213 TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (analytic) = 0 y[1] (numeric) = 0.9657625171392059 absolute error = 0.9657625171392059 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.562 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 3.182 Order of pole (six term test) = -0.519 TOP MAIN SOLVE Loop x[1] = 1.2 y[1] (analytic) = 0 y[1] (numeric) = 1.06377996313794 absolute error = 1.06377996313794 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.661 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 3.287 Order of pole (six term test) = -0.5173 TOP MAIN SOLVE Loop x[1] = 1.3 y[1] (analytic) = 0 y[1] (numeric) = 1.161959448030715 absolute error = 1.161959448030715 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.761 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 3.392 Order of pole (six term test) = -0.5163 TOP MAIN SOLVE Loop x[1] = 1.4 y[1] (analytic) = 0 y[1] (numeric) = 1.260285264810298 absolute error = 1.260285264810298 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.861 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 3.496 Order of pole (six term test) = -0.5159 TOP MAIN SOLVE Loop x[1] = 1.5 y[1] (analytic) = 0 y[1] (numeric) = 1.358743493716427 absolute error = 1.358743493716427 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.96 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 3.6 Order of pole (six term test) = -0.516 TOP MAIN SOLVE Loop x[1] = 1.6 y[1] (analytic) = 0 y[1] (numeric) = 1.457321766624732 absolute error = 1.457321766624732 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.06 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 3.704 Order of pole (six term test) = -0.5167 TOP MAIN SOLVE Loop x[1] = 1.7 y[1] (analytic) = 0 y[1] (numeric) = 1.556009066917161 absolute error = 1.556009066917161 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.159 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 3.808 Order of pole (six term test) = -0.5179 TOP MAIN SOLVE Loop x[1] = 1.8 y[1] (analytic) = 0 y[1] (numeric) = 1.654795558813202 absolute error = 1.654795558813202 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.26 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 3.912 Order of pole (six term test) = -0.5198 TOP MAIN SOLVE Loop x[1] = 1.900000000000001 y[1] (analytic) = 0 y[1] (numeric) = 1.753672441277983 absolute error = 1.753672441277983 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.36 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 4.016 Order of pole (six term test) = -0.5224 TOP MAIN SOLVE Loop x[1] = 2 y[1] (analytic) = 0 y[1] (numeric) = 1.852631822523907 absolute error = 1.852631822523907 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.462 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 4.12 Order of pole (six term test) = -0.5258 TOP MAIN SOLVE Loop x[1] = 2.100000000000001 y[1] (analytic) = 0 y[1] (numeric) = 1.951666611840373 absolute error = 1.951666611840373 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.564 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 4.223 Order of pole (six term test) = -0.5299 TOP MAIN SOLVE Loop x[1] = 2.200000000000001 y[1] (analytic) = 0 y[1] (numeric) = 2.050770426061705 absolute error = 2.050770426061705 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.667 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 4.327 Order of pole (six term test) = -0.5348 TOP MAIN SOLVE Loop x[1] = 2.300000000000001 y[1] (analytic) = 0 y[1] (numeric) = 2.149937508447387 absolute error = 2.149937508447387 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.77 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 4.431 Order of pole (six term test) = -0.5406 TOP MAIN SOLVE Loop x[1] = 2.400000000000001 y[1] (analytic) = 0 y[1] (numeric) = 2.249162658124708 absolute error = 2.249162658124708 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.874 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 4.534 Order of pole (six term test) = -0.5473 TOP MAIN SOLVE Loop x[1] = 2.500000000000001 y[1] (analytic) = 0 y[1] (numeric) = 2.348441168550069 absolute error = 2.348441168550069 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.979 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 4.638 Order of pole (six term test) = -0.555 TOP MAIN SOLVE Loop x[1] = 2.600000000000001 y[1] (analytic) = 0 y[1] (numeric) = 2.447768773695688 absolute error = 2.447768773695688 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.084 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 4.741 Order of pole (six term test) = -0.5637 TOP MAIN SOLVE Loop x[1] = 2.700000000000001 y[1] (analytic) = 0 y[1] (numeric) = 2.547141600874216 absolute error = 2.547141600874216 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.19 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 4.845 Order of pole (six term test) = -0.5733 TOP MAIN SOLVE Loop x[1] = 2.800000000000001 y[1] (analytic) = 0 y[1] (numeric) = 2.646556129283641 absolute error = 2.646556129283641 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.297 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 4.948 Order of pole (six term test) = -0.584 TOP MAIN SOLVE Loop x[1] = 2.900000000000001 y[1] (analytic) = 0 y[1] (numeric) = 2.746009153495497 absolute error = 2.746009153495497 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.404 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 5.051 Order of pole (six term test) = -0.5957 TOP MAIN SOLVE Loop x[1] = 3.000000000000001 y[1] (analytic) = 0 y[1] (numeric) = 2.845497751226438 absolute error = 2.845497751226438 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.512 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 5.154 Order of pole (six term test) = -0.6084 TOP MAIN SOLVE Loop x[1] = 3.100000000000001 y[1] (analytic) = 0 y[1] (numeric) = 2.94501925483084 absolute error = 2.94501925483084 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.621 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 5.257 Order of pole (six term test) = -0.6221 TOP MAIN SOLVE Loop x[1] = 3.200000000000002 y[1] (analytic) = 0 y[1] (numeric) = 3.044571226033927 absolute error = 3.044571226033927 relative error = -1 % Correct digits = -1 h = 0.1 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) = 28 Radius of convergence (six term test) for eq 1 = 5.36 Order of pole (six term test) = -0.6367 TOP MAIN SOLVE Loop x[1] = 3.300000000000002 y[1] (analytic) = 0 y[1] (numeric) = 3.144151433493607 absolute error = 3.144151433493607 relative error = -1 % Correct digits = -1 h = 0.1 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) = 28 Radius of convergence (six term test) for eq 1 = 5.463 Order of pole (six term test) = -0.6521 TOP MAIN SOLVE Loop x[1] = 3.400000000000002 y[1] (analytic) = 0 y[1] (numeric) = 3.243757832837167 absolute error = 3.243757832837167 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.948 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 5.565 Order of pole (six term test) = -0.6682 TOP MAIN SOLVE Loop x[1] = 3.500000000000002 y[1] (analytic) = 0 y[1] (numeric) = 3.343388548867967 absolute error = 3.343388548867967 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.058 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 5.668 Order of pole (six term test) = -0.685 TOP MAIN SOLVE Loop x[1] = 3.600000000000002 y[1] (analytic) = 0 y[1] (numeric) = 3.443041859678814 absolute error = 3.443041859678814 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.169 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 5.77 Order of pole (six term test) = -0.7022 TOP MAIN SOLVE Loop x[1] = 3.700000000000002 y[1] (analytic) = 0 y[1] (numeric) = 3.542716182444056 absolute error = 3.542716182444056 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.28 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 5.872 Order of pole (six term test) = -0.7199 TOP MAIN SOLVE Loop x[1] = 3.800000000000002 y[1] (analytic) = 0 y[1] (numeric) = 3.642410060692563 absolute error = 3.642410060692563 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.391 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 5.974 Order of pole (six term test) = -0.7377 TOP MAIN SOLVE Loop x[1] = 3.900000000000002 y[1] (analytic) = 0 y[1] (numeric) = 3.742122152889531 absolute error = 3.742122152889531 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.502 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 6.075 Order of pole (six term test) = -0.7556 TOP MAIN SOLVE Loop x[1] = 4.000000000000002 y[1] (analytic) = 0 y[1] (numeric) = 3.841851222177147 absolute error = 3.841851222177147 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.613 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 6.177 Order of pole (six term test) = -0.7734 TOP MAIN SOLVE Loop x[1] = 4.100000000000001 y[1] (analytic) = 0 y[1] (numeric) = 3.94159612714313 absolute error = 3.94159612714313 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.725 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 6.278 Order of pole (six term test) = -0.7908 TOP MAIN SOLVE Loop x[1] = 4.200000000000001 y[1] (analytic) = 0 y[1] (numeric) = 4.041355813502498 absolute error = 4.041355813502498 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.837 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 6.379 Order of pole (six term test) = -0.8078 TOP MAIN SOLVE Loop x[1] = 4.300000000000001 y[1] (analytic) = 0 y[1] (numeric) = 4.14112930659206 absolute error = 4.14112930659206 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.949 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 6.48 Order of pole (six term test) = -0.8241 TOP MAIN SOLVE Loop x[1] = 4.4 y[1] (analytic) = 0 y[1] (numeric) = 4.240915704589305 absolute error = 4.240915704589305 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.061 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 6.58 Order of pole (six term test) = -0.8395 TOP MAIN SOLVE Loop x[1] = 4.5 y[1] (analytic) = 0 y[1] (numeric) = 4.340714172377978 absolute error = 4.340714172377978 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.173 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 6.681 Order of pole (six term test) = -0.854 TOP MAIN SOLVE Loop x[1] = 4.6 y[1] (analytic) = 0 y[1] (numeric) = 4.440523935991794 absolute error = 4.440523935991794 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.285 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 6.781 Order of pole (six term test) = -0.8674 TOP MAIN SOLVE Loop x[1] = 4.699999999999999 y[1] (analytic) = 0 y[1] (numeric) = 4.540344277575802 absolute error = 4.540344277575802 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.398 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 6.882 Order of pole (six term test) = -0.8795 TOP MAIN SOLVE Loop x[1] = 4.799999999999999 y[1] (analytic) = 0 y[1] (numeric) = 4.640174530811831 absolute error = 4.640174530811831 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.51 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 6.982 Order of pole (six term test) = -0.8903 TOP MAIN SOLVE Loop x[1] = 4.899999999999999 y[1] (analytic) = 0 y[1] (numeric) = 4.740014076760603 absolute error = 4.740014076760603 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.622 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 7.083 Order of pole (six term test) = -0.8997 TOP MAIN SOLVE Loop x[1] = 4.999999999999998 y[1] (analytic) = 0 y[1] (numeric) = 4.839862340078398 absolute error = 4.839862340078398 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.735 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 7.183 Order of pole (six term test) = -0.9077 Finished! diff ( y , x , 1 ) = tanh(sqrt(2.0*x + 3.0)); Iterations = 50 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 104.1 %