##############ECHO OF PROBLEM################# ##############temp/expt_sin_sinpostode.ode################# diff ( y , x , 1 ) = expt(sin(0.1 * x) , sin(0.2 * x)); ! /* 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 = 6.158066706119337e-138 estimated_step_error = 6.158066706119337e-138 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 = 4.132590247716661e-130 estimated_step_error = 4.132590247716661e-130 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 = 2.773309722782001e-122 estimated_step_error = 2.773309722782001e-122 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 = 1.861103571429221e-114 estimated_step_error = 1.861103571429221e-114 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 = 1.24892106950604e-106 estimated_step_error = 1.24892106950604e-106 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 = 8.380771622328243e-99 estimated_step_error = 8.380771622328243e-99 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 = 5.623441135411773e-91 estimated_step_error = 5.623441135411773e-91 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 = 3.772754859963589e-83 estimated_step_error = 3.772754859963589e-83 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 = 2.530414538464354e-75 estimated_step_error = 2.530414538464354e-75 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 = 1.696205192055348e-67 estimated_step_error = 1.696205192055348e-67 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 = 1.135726209525316e-59 estimated_step_error = 1.135726209525316e-59 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 = 7.587369420563741e-52 estimated_step_error = 7.587369420563741e-52 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 = 5.046321143984286e-44 estimated_step_error = 5.046321143984286e-44 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 = 3.327212595559371e-36 estimated_step_error = 3.327212595559371e-36 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 = 2.157861588066366e-28 estimated_step_error = 2.157861588066366e-28 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 = 1.359863871404512e-20 estimated_step_error = 1.359863871404512e-20 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 = 8.274282990534723e-13 estimated_step_error = 8.274282990534723e-13 best_h = 0.032768 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 = 0.032768 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09995 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.231072 y[1] (analytic) = 0 y[1] (numeric) = 0.1151604036858582 absolute error = 0.1151604036858582 relative error = -1 % Correct digits = -1 h = 0.032768 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2309 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.329376 y[1] (analytic) = 0 y[1] (numeric) = 0.1959988142170304 absolute error = 0.1959988142170304 relative error = -1 % Correct digits = -1 h = 0.032768 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.329 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4276800000000001 y[1] (analytic) = 0 y[1] (numeric) = 0.2730480257552959 absolute error = 0.2730480257552959 relative error = -1 % Correct digits = -1 h = 0.032768 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4271 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5259840000000001 y[1] (analytic) = 0 y[1] (numeric) = 0.346882234647207 absolute error = 0.346882234647207 relative error = -1 % Correct digits = -1 h = 0.032768 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5252 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.603592852336809 y[1] (analytic) = 0 y[1] (numeric) = 0.4031273318879607 absolute error = 0.4031273318879607 relative error = -1 % Correct digits = -1 h = 0.01121021308420222 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6026 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 0.1998 Order of pole (six term test) = -1.074 TOP MAIN SOLVE Loop x[1] = 0.7044847700946291 y[1] (analytic) = 0 y[1] (numeric) = 0.4738928647786282 absolute error = 0.4738928647786282 relative error = -1 % Correct digits = -1 h = 0.01121021308420222 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7033 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 0.3404 Order of pole (six term test) = -1.074 TOP MAIN SOLVE Loop x[1] = 0.8053766878524491 y[1] (analytic) = 0 y[1] (numeric) = 0.5423567128545768 absolute error = 0.5423567128545768 relative error = -1 % Correct digits = -1 h = 0.01121021308420222 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8039 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 0.4655 Order of pole (six term test) = -1.074 TOP MAIN SOLVE Loop x[1] = 0.9062686056102691 y[1] (analytic) = 0 y[1] (numeric) = 0.608780277103712 absolute error = 0.608780277103712 relative error = -1 % Correct digits = -1 h = 0.01121021308420222 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9046 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 0.5897 Order of pole (six term test) = -1.073 TOP MAIN SOLVE Loop x[1] = 1.007160523368089 y[1] (analytic) = 0 y[1] (numeric) = 0.6733851122236585 absolute error = 0.6733851122236585 relative error = -1 % Correct digits = -1 h = 0.01121021308420222 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.005 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 0.7147 Order of pole (six term test) = -1.072 TOP MAIN SOLVE Loop x[1] = 1.108052441125909 y[1] (analytic) = 0 y[1] (numeric) = 0.7363618501987782 absolute error = 0.7363618501987782 relative error = -1 % Correct digits = -1 h = 0.01121021308420222 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.106 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 0.8411 Order of pole (six term test) = -1.07 TOP MAIN SOLVE Loop x[1] = 1.208944358883729 y[1] (analytic) = 0 y[1] (numeric) = 0.7978765486149166 absolute error = 0.7978765486149166 relative error = -1 % Correct digits = -1 h = 0.01121021308420222 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.206 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 0.969 Order of pole (six term test) = -1.068 TOP MAIN SOLVE Loop x[1] = 1.309836276641549 y[1] (analytic) = 0 y[1] (numeric) = 0.8580753600241522 absolute error = 0.8580753600241522 relative error = -1 % Correct digits = -1 h = 0.01121021308420222 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.307 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 1.098 Order of pole (six term test) = -1.066 TOP MAIN SOLVE Loop x[1] = 1.410728194399369 y[1] (analytic) = 0 y[1] (numeric) = 0.917088059896575 absolute error = 0.917088059896575 relative error = -1 % Correct digits = -1 h = 0.01121021308420222 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.408 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 1.229 Order of pole (six term test) = -1.064 TOP MAIN SOLVE Loop x[1] = 1.500409899072987 y[1] (analytic) = 0 y[1] (numeric) = 0.9686421886060921 absolute error = 0.9686421886060921 relative error = -1 % Correct digits = -1 h = 0.01121021308420222 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.497 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 1.347 Order of pole (six term test) = -1.062 TOP MAIN SOLVE Loop x[1] = 1.601301816830807 y[1] (analytic) = 0 y[1] (numeric) = 1.025721943518752 absolute error = 1.025721943518752 relative error = -1 % Correct digits = -1 h = 0.01121021308420222 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.598 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 1.48 Order of pole (six term test) = -1.06 TOP MAIN SOLVE Loop x[1] = 1.702193734588627 y[1] (analytic) = 0 y[1] (numeric) = 1.081921051806856 absolute error = 1.081921051806856 relative error = -1 % Correct digits = -1 h = 0.01121021308420222 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.699 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 1.615 Order of pole (six term test) = -1.057 TOP MAIN SOLVE Loop x[1] = 1.803085652346447 y[1] (analytic) = 0 y[1] (numeric) = 1.137326806186263 absolute error = 1.137326806186263 relative error = -1 % Correct digits = -1 h = 0.01121021308420222 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.8 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 1.75 Order of pole (six term test) = -1.055 TOP MAIN SOLVE Loop x[1] = 1.903977570104267 y[1] (analytic) = 0 y[1] (numeric) = 1.192019118649321 absolute error = 1.192019118649321 relative error = -1 % Correct digits = -1 h = 0.01121021308420222 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.9 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 1.887 Order of pole (six term test) = -1.053 TOP MAIN SOLVE Loop x[1] = 2.004869487862087 y[1] (analytic) = 0 y[1] (numeric) = 1.24607148377939 absolute error = 1.24607148377939 relative error = -1 % Correct digits = -1 h = 0.01121021308420222 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.001 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 2.024 Order of pole (six term test) = -1.051 TOP MAIN SOLVE Loop x[1] = 2.105761405619905 y[1] (analytic) = 0 y[1] (numeric) = 1.299551783450708 absolute error = 1.299551783450708 relative error = -1 % Correct digits = -1 h = 0.01121021308420222 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.102 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 2.162 Order of pole (six term test) = -1.048 TOP MAIN SOLVE Loop x[1] = 2.206653323377723 y[1] (analytic) = 0 y[1] (numeric) = 1.352522964590104 absolute error = 1.352522964590104 relative error = -1 % Correct digits = -1 h = 0.01121021308420222 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.203 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 2.301 Order of pole (six term test) = -1.046 TOP MAIN SOLVE Loop x[1] = 2.307545241135541 y[1] (analytic) = 0 y[1] (numeric) = 1.405043614234545 absolute error = 1.405043614234545 relative error = -1 % Correct digits = -1 h = 0.01121021308420222 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.304 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 2.441 Order of pole (six term test) = -1.045 TOP MAIN SOLVE Loop x[1] = 2.408437158893359 y[1] (analytic) = 0 y[1] (numeric) = 1.457168450667952 absolute error = 1.457168450667952 relative error = -1 % Correct digits = -1 h = 0.01121021308420222 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.405 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 2.581 Order of pole (six term test) = -1.043 TOP MAIN SOLVE Loop x[1] = 2.509329076651177 y[1] (analytic) = 0 y[1] (numeric) = 1.508948745368001 absolute error = 1.508948745368001 relative error = -1 % Correct digits = -1 h = 0.01121021308420222 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.505 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 2.722 Order of pole (six term test) = -1.041 TOP MAIN SOLVE Loop x[1] = 2.610220994408995 y[1] (analytic) = 0 y[1] (numeric) = 1.560432687438656 absolute error = 1.560432687438656 relative error = -1 % Correct digits = -1 h = 0.01121021308420222 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.606 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 2.863 Order of pole (six term test) = -1.04 TOP MAIN SOLVE Loop x[1] = 2.711112912166813 y[1] (analytic) = 0 y[1] (numeric) = 1.611665699872482 absolute error = 1.611665699872482 relative error = -1 % Correct digits = -1 h = 0.01121021308420222 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.707 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 3.005 Order of pole (six term test) = -1.038 TOP MAIN SOLVE Loop x[1] = 2.800794616840429 y[1] (analytic) = 0 y[1] (numeric) = 1.657030257225013 absolute error = 1.657030257225013 relative error = -1 % Correct digits = -1 h = 0.01121021308420222 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.797 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 3.132 Order of pole (six term test) = -1.037 TOP MAIN SOLVE Loop x[1] = 2.901686534598247 y[1] (analytic) = 0 y[1] (numeric) = 1.707904605054615 absolute error = 1.707904605054615 relative error = -1 % Correct digits = -1 h = 0.01121021308420222 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.898 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 3.274 Order of pole (six term test) = -1.036 TOP MAIN SOLVE Loop x[1] = 3.002578452356065 y[1] (analytic) = 0 y[1] (numeric) = 1.758646085204223 absolute error = 1.758646085204223 relative error = -1 % Correct digits = -1 h = 0.01121021308420222 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.999 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 3.417 Order of pole (six term test) = -1.035 TOP MAIN SOLVE Loop x[1] = 3.103470370113883 y[1] (analytic) = 0 y[1] (numeric) = 1.809291689221213 absolute error = 1.809291689221213 relative error = -1 % Correct digits = -1 h = 0.01121021308420222 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.099 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 3.561 Order of pole (six term test) = -1.035 TOP MAIN SOLVE Loop x[1] = 3.204362287871701 y[1] (analytic) = 0 y[1] (numeric) = 1.859876704708406 absolute error = 1.859876704708406 relative error = -1 % Correct digits = -1 h = 0.01121021308420222 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.2 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 3.704 Order of pole (six term test) = -1.034 TOP MAIN SOLVE Loop x[1] = 3.305254205629519 y[1] (analytic) = 0 y[1] (numeric) = 1.910434862923427 absolute error = 1.910434862923427 relative error = -1 % Correct digits = -1 h = 0.01121021308420222 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.301 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 3.848 Order of pole (six term test) = -1.034 TOP MAIN SOLVE Loop x[1] = 3.406146123387337 y[1] (analytic) = 0 y[1] (numeric) = 1.960998469606006 absolute error = 1.960998469606006 relative error = -1 % Correct digits = -1 h = 0.01121021308420222 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.402 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 3.993 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.507038041145155 y[1] (analytic) = 0 y[1] (numeric) = 2.011598521122539 absolute error = 2.011598521122539 relative error = -1 % Correct digits = -1 h = 0.01121021308420222 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.503 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 4.137 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.607929958902973 y[1] (analytic) = 0 y[1] (numeric) = 2.062264807701033 absolute error = 2.062264807701033 relative error = -1 % Correct digits = -1 h = 0.01121021308420222 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.604 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 4.282 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.708821876660791 y[1] (analytic) = 0 y[1] (numeric) = 2.113026005268297 absolute error = 2.113026005268297 relative error = -1 % Correct digits = -1 h = 0.01121021308420222 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.705 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 4.427 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.809713794418609 y[1] (analytic) = 0 y[1] (numeric) = 2.16390975718425 absolute error = 2.16390975718425 relative error = -1 % Correct digits = -1 h = 0.01121021308420222 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.806 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 4.572 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.910605712176427 y[1] (analytic) = 0 y[1] (numeric) = 2.214942746987147 absolute error = 2.214942746987147 relative error = -1 % Correct digits = -1 h = 0.01121021308420222 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.907 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 4.717 Order of pole (six term test) = -1.034 TOP MAIN SOLVE Loop x[1] = 4.000287416850044 y[1] (analytic) = 0 y[1] (numeric) = 2.260451557506065 absolute error = 2.260451557506065 relative error = -1 % Correct digits = -1 h = 0.01121021308420222 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.996 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 4.847 Order of pole (six term test) = -1.034 TOP MAIN SOLVE Loop x[1] = 4.101179334607862 y[1] (analytic) = 0 y[1] (numeric) = 2.311836123847204 absolute error = 2.311836123847204 relative error = -1 % Correct digits = -1 h = 0.01121021308420222 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.097 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 4.992 Order of pole (six term test) = -1.035 TOP MAIN SOLVE Loop x[1] = 4.20207125236568 y[1] (analytic) = 0 y[1] (numeric) = 2.363442184164009 absolute error = 2.363442184164009 relative error = -1 % Correct digits = -1 h = 0.01121021308420222 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.198 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 5.138 Order of pole (six term test) = -1.036 TOP MAIN SOLVE Loop x[1] = 4.302963170123498 y[1] (analytic) = 0 y[1] (numeric) = 2.415293241802311 absolute error = 2.415293241802311 relative error = -1 % Correct digits = -1 h = 0.01121021308420222 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) = 28 Radius of convergence (six term test) for eq 1 = 5.015 Order of pole (six term test) = -1.037 TOP MAIN SOLVE Loop x[1] = 4.403855087881316 y[1] (analytic) = 0 y[1] (numeric) = 2.467412094574227 absolute error = 2.467412094574227 relative error = -1 % Correct digits = -1 h = 0.01121021308420222 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.4 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 4.438 Order of pole (six term test) = -1.038 TOP MAIN SOLVE Loop x[1] = 4.504747005639134 y[1] (analytic) = 0 y[1] (numeric) = 2.519820870436609 absolute error = 2.519820870436609 relative error = -1 % Correct digits = -1 h = 0.01121021308420222 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.501 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.605638923396952 y[1] (analytic) = 0 y[1] (numeric) = 2.572541058774442 absolute error = 2.572541058774442 relative error = -1 % Correct digits = -1 h = 0.01121021308420222 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.602 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.70653084115477 y[1] (analytic) = 0 y[1] (numeric) = 2.625593537679924 absolute error = 2.625593537679924 relative error = -1 % Correct digits = -1 h = 0.01121021308420222 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.703 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.807422758912588 y[1] (analytic) = 0 y[1] (numeric) = 2.678998597575603 absolute error = 2.678998597575603 relative error = -1 % Correct digits = -1 h = 0.01121021308420222 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.804 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.908314676670406 y[1] (analytic) = 0 y[1] (numeric) = 2.7327759614936 absolute error = 2.7327759614936 relative error = -1 % Correct digits = -1 h = 0.01121021308420222 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.905 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = expt(sin(0.1 * x) , sin(0.2 * x)); Iterations = 411 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100.4 %