##############ECHO OF PROBLEM################# ##############temp/expt_lin_sinpostode.ode################# diff ( y , x , 1 ) = expt((0.2 * x + 0.3) , sin(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 = 1.000829488412713e-167 estimated_step_error = 1.000829488412713e-167 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 = 7.094233389451058e-156 estimated_step_error = 7.094233389451058e-156 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 = 4.76085662689039e-148 estimated_step_error = 4.76085662689039e-148 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 = 3.194953027089047e-140 estimated_step_error = 3.194953027089047e-140 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 = 2.144091619291599e-132 estimated_step_error = 2.144091619291599e-132 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 = 1.438868734072729e-124 estimated_step_error = 1.438868734072729e-124 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 = 9.655993422536699e-117 estimated_step_error = 9.655993422536699e-117 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 = 6.479905095602758e-109 estimated_step_error = 6.479905095602758e-109 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 = 4.348426427215101e-101 estimated_step_error = 4.348426427215101e-101 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 = 2.917959121792323e-93 estimated_step_error = 2.917959121792323e-93 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 = 1.957913395632059e-85 estimated_step_error = 1.957913395632059e-85 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 = 1.313536571476618e-77 estimated_step_error = 1.313536571476618e-77 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 = 8.809672906379384e-70 estimated_step_error = 8.809672906379384e-70 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 = 5.90494160433328e-62 estimated_step_error = 5.90494160433328e-62 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 = 3.953204673246663e-54 estimated_step_error = 3.953204673246663e-54 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 = 2.640247379950358e-46 estimated_step_error = 2.640247379950358e-46 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 = 1.755041371217243e-38 estimated_step_error = 1.755041371217243e-38 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 = 1.15591672498111e-30 estimated_step_error = 1.15591672498111e-30 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 = 1.597 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (analytic) = 0 y[1] (numeric) = 0.08494521191206113 absolute error = 0.08494521191206113 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 = 1.685 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3 y[1] (analytic) = 0 y[1] (numeric) = 0.162137212252082 absolute error = 0.162137212252082 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 = 1.781 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4 y[1] (analytic) = 0 y[1] (numeric) = 0.2333021631460201 absolute error = 0.2333021631460201 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 = 1.876 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5 y[1] (analytic) = 0 y[1] (numeric) = 0.2997404540332474 absolute error = 0.2997404540332474 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 = 1.97 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6 y[1] (analytic) = 0 y[1] (numeric) = 0.362526861674144 absolute error = 0.362526861674144 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 = 2.045 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7 y[1] (analytic) = 0 y[1] (numeric) = 0.4225626836591664 absolute error = 0.4225626836591664 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 = 2.105 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7999999999999999 y[1] (analytic) = 0 y[1] (numeric) = 0.4806153789250198 absolute error = 0.4806153789250198 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 = 2.155 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8999999999999999 y[1] (analytic) = 0 y[1] (numeric) = 0.5373488055956528 absolute error = 0.5373488055956528 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9999999999999999 y[1] (analytic) = 0 y[1] (numeric) = 0.5933462691641715 absolute error = 0.5933462691641715 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (analytic) = 0 y[1] (numeric) = 0.6491279717125857 absolute error = 0.6491279717125857 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.2 y[1] (analytic) = 0 y[1] (numeric) = 0.7051640070005472 absolute error = 0.7051640070005472 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.3 y[1] (analytic) = 0 y[1] (numeric) = 0.7618837261875883 absolute error = 0.7618837261875883 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.4 y[1] (analytic) = 0 y[1] (numeric) = 0.8196820716805805 absolute error = 0.8196820716805805 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.5 y[1] (analytic) = 0 y[1] (numeric) = 0.8789233204782909 absolute error = 0.8789233204782909 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.6 y[1] (analytic) = 0 y[1] (numeric) = 0.9399425790449967 absolute error = 0.9399425790449967 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.7 y[1] (analytic) = 0 y[1] (numeric) = 1.003045319214735 absolute error = 1.003045319214735 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.8 y[1] (analytic) = 0 y[1] (numeric) = 1.068505231191238 absolute error = 1.068505231191238 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.900000000000001 y[1] (analytic) = 0 y[1] (numeric) = 1.136560688227431 absolute error = 1.136560688227431 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2 y[1] (analytic) = 0 y[1] (numeric) = 1.20741016020068 absolute error = 1.20741016020068 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.100000000000001 y[1] (analytic) = 0 y[1] (numeric) = 1.281206970655816 absolute error = 1.281206970655816 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.661 Order of pole (six term test) = 6.5 TOP MAIN SOLVE Loop x[1] = 2.200000000000001 y[1] (analytic) = 0 y[1] (numeric) = 1.358053852720172 absolute error = 1.358053852720172 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.187 Order of pole (six term test) = 8.302 TOP MAIN SOLVE Loop x[1] = 2.300000000000001 y[1] (analytic) = 0 y[1] (numeric) = 1.437997810826536 absolute error = 1.437997810826536 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.273 Order of pole (six term test) = 8.177 TOP MAIN SOLVE Loop x[1] = 2.400000000000001 y[1] (analytic) = 0 y[1] (numeric) = 1.521025824110543 absolute error = 1.521025824110543 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.439 Order of pole (six term test) = 7.985 TOP MAIN SOLVE Loop x[1] = 2.500000000000001 y[1] (analytic) = 0 y[1] (numeric) = 1.607061921465218 absolute error = 1.607061921465218 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.582 Order of pole (six term test) = 7.749 TOP MAIN SOLVE Loop x[1] = 2.600000000000001 y[1] (analytic) = 0 y[1] (numeric) = 1.695966108397978 absolute error = 1.695966108397978 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.61 Order of pole (six term test) = 7.528 TOP MAIN SOLVE Loop x[1] = 2.700000000000001 y[1] (analytic) = 0 y[1] (numeric) = 1.78753552797067 absolute error = 1.78753552797067 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 = 0.05481 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 3.659 Order of pole (six term test) = 7.652 TOP MAIN SOLVE Loop x[1] = 2.800000000000001 y[1] (analytic) = 0 y[1] (numeric) = 1.881508094728811 absolute error = 1.881508094728811 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.638 Order of pole (six term test) = 7.886 TOP MAIN SOLVE Loop x[1] = 2.900000000000001 y[1] (analytic) = 0 y[1] (numeric) = 1.977568661357591 absolute error = 1.977568661357591 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 = 0.05798 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 3.591 Order of pole (six term test) = 7.796 TOP MAIN SOLVE Loop x[1] = 3.000000000000001 y[1] (analytic) = 0 y[1] (numeric) = 2.075357579116034 absolute error = 2.075357579116034 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.561 Order of pole (six term test) = 7.627 TOP MAIN SOLVE Loop x[1] = 3.100000000000001 y[1] (analytic) = 0 y[1] (numeric) = 2.174481315788618 absolute error = 2.174481315788618 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 = 0.05211 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 3.566 Order of pole (six term test) = 7.757 TOP MAIN SOLVE Loop x[1] = 3.200000000000002 y[1] (analytic) = 0 y[1] (numeric) = 2.274524621447059 absolute error = 2.274524621447059 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.599 Order of pole (six term test) = 7.889 TOP MAIN SOLVE Loop x[1] = 3.300000000000002 y[1] (analytic) = 0 y[1] (numeric) = 2.375063603272646 absolute error = 2.375063603272646 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.629 Order of pole (six term test) = 7.7 TOP MAIN SOLVE Loop x[1] = 3.400000000000002 y[1] (analytic) = 0 y[1] (numeric) = 2.475679001255374 absolute error = 2.475679001255374 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.633 Order of pole (six term test) = 7.532 TOP MAIN SOLVE Loop x[1] = 3.500000000000002 y[1] (analytic) = 0 y[1] (numeric) = 2.575968954124623 absolute error = 2.575968954124623 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.617 Order of pole (six term test) = 7.658 TOP MAIN SOLVE Loop x[1] = 3.600000000000002 y[1] (analytic) = 0 y[1] (numeric) = 2.675560607803737 absolute error = 2.675560607803737 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.609 Order of pole (six term test) = 7.712 TOP MAIN SOLVE Loop x[1] = 3.700000000000002 y[1] (analytic) = 0 y[1] (numeric) = 2.774120037016718 absolute error = 2.774120037016718 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.627 Order of pole (six term test) = 7.463 TOP MAIN SOLVE Loop x[1] = 3.800000000000002 y[1] (analytic) = 0 y[1] (numeric) = 2.871360107939668 absolute error = 2.871360107939668 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.657 Order of pole (six term test) = 7.286 TOP MAIN SOLVE Loop x[1] = 3.900000000000002 y[1] (analytic) = 0 y[1] (numeric) = 2.967046085974104 absolute error = 2.967046085974104 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.66 Order of pole (six term test) = 7.38 TOP MAIN SOLVE Loop x[1] = 4.000000000000002 y[1] (analytic) = 0 y[1] (numeric) = 3.060998967530709 absolute error = 3.060998967530709 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.606 Order of pole (six term test) = 7.362 TOP MAIN SOLVE Loop x[1] = 4.100000000000001 y[1] (analytic) = 0 y[1] (numeric) = 3.153096670496545 absolute error = 3.153096670496545 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.498 Order of pole (six term test) = 7.006 TOP MAIN SOLVE Loop x[1] = 4.200000000000001 y[1] (analytic) = 0 y[1] (numeric) = 3.243273341899766 absolute error = 3.243273341899766 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.386 Order of pole (six term test) = 6.683 TOP MAIN SOLVE Loop x[1] = 4.300000000000001 y[1] (analytic) = 0 y[1] (numeric) = 3.331517126017397 absolute error = 3.331517126017397 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.362 Order of pole (six term test) = 6.812 TOP MAIN SOLVE Loop x[1] = 4.4 y[1] (analytic) = 0 y[1] (numeric) = 3.417866780317607 absolute error = 3.417866780317607 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.494 Order of pole (six term test) = 7.41 TOP MAIN SOLVE Loop x[1] = 4.5 y[1] (analytic) = 0 y[1] (numeric) = 3.502407533481334 absolute error = 3.502407533481334 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.229 Order of pole (six term test) = 8.022 TOP MAIN SOLVE Loop x[1] = 4.6 y[1] (analytic) = 0 y[1] (numeric) = 3.585266555931982 absolute error = 3.585266555931982 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.699999999999999 y[1] (analytic) = 0 y[1] (numeric) = 3.666608367165354 absolute error = 3.666608367165354 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.799999999999999 y[1] (analytic) = 0 y[1] (numeric) = 3.746630444324623 absolute error = 3.746630444324623 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.899999999999999 y[1] (analytic) = 0 y[1] (numeric) = 3.825559230645346 absolute error = 3.825559230645346 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.999999999999998 y[1] (analytic) = 0 y[1] (numeric) = 3.903646676755391 absolute error = 3.903646676755391 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = expt((0.2 * x + 0.3) , sin(x)); 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 %