##############ECHO OF PROBLEM################# ##############temp/div_lin_exppostode.ode################# diff ( y , x , 1 ) = (0.2 * x + 0.3) / exp(x); ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=1.0; /* # did poorly with x_start := -5.0; */ x_end=5.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_iter=1000000; glob_display_interval=0.1; glob_max_minutes=10; /* 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(-(0.1 * (5.0 + 2.0*x))/exp(x)); } /* 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 estimated_steps = 4000000 step_error = 2.5e-17 est_needed_step_err = 2.5e-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 = 4.104860300807793e-183 estimated_step_error = 4.104860300807793e-183 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 = 2.754725063378627e-175 estimated_step_error = 2.754725063378627e-175 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 = 1.84866462484485e-167 estimated_step_error = 1.84866462484485e-167 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 = 1.240617732921702e-159 estimated_step_error = 1.240617732921702e-159 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 = 8.325643383220975e-152 estimated_step_error = 8.325643383220975e-152 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 = 5.587242966122243e-144 estimated_step_error = 5.587242966122243e-144 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 = 3.749532962796977e-136 estimated_step_error = 3.749532962796977e-136 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 = 2.516265861870037e-128 estimated_step_error = 2.516265861870037e-128 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 = 1.688633254564145e-120 estimated_step_error = 1.688633254564145e-120 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 = 1.13321698325619e-112 estimated_step_error = 1.13321698325619e-112 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 = 7.604815132584731e-105 estimated_step_error = 7.604815132584731e-105 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 = 5.103403970178553e-97 estimated_step_error = 5.103403970178553e-97 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 = 3.424700777446082e-89 estimated_step_error = 3.424700777446082e-89 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 = 2.298095738573963e-81 estimated_step_error = 2.298095738573963e-81 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 = 1.541981658244821e-73 estimated_step_error = 1.541981658244821e-73 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 = 1.034478649508161e-65 estimated_step_error = 1.034478649508161e-65 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 = 6.937874085921917e-58 estimated_step_error = 6.937874085921917e-58 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 = 4.650040947907314e-50 estimated_step_error = 4.650040947907314e-50 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = 1 y[1] (analytic) = -0.2575156088200097 y[1] (numeric) = -0.2575156088200097 absolute error = 0 relative error = 0 % Correct digits = 16 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 = 168.7 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (analytic) = -0.2396671802626173 y[1] (numeric) = -0.2396671802626173 absolute error = 2.775557561562891e-17 relative error = 1.158088294993729e-14 % Correct digits = 16 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 = 166.2 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.2 y[1] (analytic) = -0.2228837168150296 y[1] (numeric) = -0.2228837168150296 absolute error = 5.551115123125783e-17 relative error = 2.490588008155228e-14 % Correct digits = 16 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 = 163.6 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.3 y[1] (analytic) = -0.2071241627058495 y[1] (numeric) = -0.2071241627058496 absolute error = 8.326672684688674e-17 relative error = 4.020135833458466e-14 % Correct digits = 16 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 = 161 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.4 y[1] (analytic) = -0.192345631874453 y[1] (numeric) = -0.1923456318744531 absolute error = 1.110223024625157e-16 relative error = 5.77202099057709e-14 % Correct digits = 16 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 = 158.5 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.5 y[1] (analytic) = -0.1785041281187438 y[1] (numeric) = -0.1785041281187439 absolute error = 1.387778780781446e-16 relative error = 7.774491242344116e-14 % Correct digits = 16 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 = 156 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.600000000000001 y[1] (analytic) = -0.1655551447556174 y[1] (numeric) = -0.1655551447556175 absolute error = 1.110223024625157e-16 relative error = 6.706061755217583e-14 % Correct digits = 16 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 = 153.5 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.700000000000001 y[1] (analytic) = -0.1534541602042971 y[1] (numeric) = -0.1534541602042972 absolute error = 1.110223024625157e-16 relative error = 7.234883845098048e-14 % Correct digits = 16 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 = 151 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.800000000000001 y[1] (analytic) = -0.1421570438705644 y[1] (numeric) = -0.1421570438705645 absolute error = 1.387778780781446e-16 relative error = 9.762293467814613e-14 % Correct digits = 16 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 = 148.6 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.900000000000001 y[1] (analytic) = -0.1316203849159188 y[1] (numeric) = -0.1316203849159189 absolute error = 1.665334536937735e-16 relative error = 1.265255786937242e-13 % Correct digits = 15 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 = 146.2 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.000000000000001 y[1] (analytic) = -0.1218017549129514 y[1] (numeric) = -0.1218017549129515 absolute error = 1.52655665885959e-16 relative error = 1.253312532278851e-13 % Correct digits = 15 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 = 143.7 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.100000000000001 y[1] (analytic) = -0.1126599139927433 y[1] (numeric) = -0.1126599139927434 absolute error = 1.665334536937735e-16 relative error = 1.478196172815296e-13 % Correct digits = 15 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 = 141.4 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.200000000000001 y[1] (analytic) = -0.1041549688605938 y[1] (numeric) = -0.1041549688605939 absolute error = 1.804112415015879e-16 relative error = 1.73214243617181e-13 % Correct digits = 15 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 = 139 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.300000000000001 y[1] (analytic) = -0.09624848997389149 y[1] (numeric) = -0.09624848997389168 absolute error = 1.942890293094024e-16 relative error = 2.018618986771694e-13 % Correct digits = 15 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 = 136.6 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.400000000000001 y[1] (analytic) = -0.08890359422362418 y[1] (numeric) = -0.08890359422362436 absolute error = 1.804112415015879e-16 relative error = 2.029290751145443e-13 % Correct digits = 15 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 = 134.3 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.500000000000001 y[1] (analytic) = -0.08208499862389873 y[1] (numeric) = -0.08208499862389891 absolute error = 1.804112415015879e-16 relative error = 2.197858860036113e-13 % Correct digits = 15 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 = 132 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.600000000000001 y[1] (analytic) = -0.07575904977862047 y[1] (numeric) = -0.07575904977862068 absolute error = 2.081668171172169e-16 relative error = 2.747748522790507e-13 % Correct digits = 15 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 = 129.7 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.700000000000002 y[1] (analytic) = -0.06989373324933967 y[1] (numeric) = -0.06989373324933988 absolute error = 2.081668171172169e-16 relative error = 2.978333069927747e-13 % Correct digits = 15 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 = 127.4 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.800000000000002 y[1] (analytic) = -0.06445866638273096 y[1] (numeric) = -0.06445866638273118 absolute error = 2.220446049250313e-16 relative error = 3.444759523981077e-13 % Correct digits = 15 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 = 125.2 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.900000000000002 y[1] (analytic) = -0.05942507766091974 y[1] (numeric) = -0.05942507766091995 absolute error = 2.151057110211241e-16 relative error = 3.619780057310485e-13 % Correct digits = 15 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 = 123 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.000000000000002 y[1] (analytic) = -0.05476577520465026 y[1] (numeric) = -0.05476577520465049 absolute error = 2.289834988289385e-16 relative error = 4.18114229139032e-13 % Correct digits = 15 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 = 120.8 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.100000000000002 y[1] (analytic) = -0.05045510668078466 y[1] (numeric) = -0.0504551066807849 absolute error = 2.359223927328458e-16 relative error = 4.675887303647194e-13 % Correct digits = 15 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 = 118.6 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.200000000000002 y[1] (analytic) = -0.04646891253533741 y[1] (numeric) = -0.04646891253533765 absolute error = 2.359223927328458e-16 relative error = 5.076994056046349e-13 % Correct digits = 15 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 = 116.4 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.300000000000002 y[1] (analytic) = -0.04278447418543834 y[1] (numeric) = -0.04278447418543858 absolute error = 2.359223927328458e-16 relative error = 5.51420573057181e-13 % Correct digits = 15 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 = 114.2 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.400000000000002 y[1] (analytic) = -0.0393804585531847 y[1] (numeric) = -0.03938045855318495 absolute error = 2.498001805406602e-16 relative error = 6.343252204727283e-13 % Correct digits = 15 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 = 112.1 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.500000000000002 y[1] (analytic) = -0.03623686010678213 y[1] (numeric) = -0.03623686010678238 absolute error = 2.567390744445674e-16 relative error = 7.085025404740183e-13 % Correct digits = 15 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 = 110 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.600000000000002 y[1] (analytic) = -0.03333494138569686 y[1] (numeric) = -0.03333494138569711 absolute error = 2.498001805406602e-16 relative error = 7.493643911065728e-13 % Correct digits = 15 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 = 107.9 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.700000000000002 y[1] (analytic) = -0.03065717282322079 y[1] (numeric) = -0.03065717282322104 absolute error = 2.498001805406602e-16 relative error = 8.148180589941843e-13 % Correct digits = 15 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 = 105.8 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.800000000000002 y[1] (analytic) = -0.0281871725387686 y[1] (numeric) = -0.02818717253876885 absolute error = 2.532696274926138e-16 relative error = 8.985279638965815e-13 % Correct digits = 15 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 = 103.8 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.900000000000003 y[1] (analytic) = -0.02590964665062956 y[1] (numeric) = -0.02590964665062982 absolute error = 2.602085213965211e-16 relative error = 1.004292049618509e-12 % Correct digits = 14 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 = 101.8 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.000000000000003 y[1] (analytic) = -0.02381033055535439 y[1] (numeric) = -0.02381033055535464 absolute error = 2.567390744445674e-16 relative error = 1.078267577376547e-12 % Correct digits = 14 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 = 99.75 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.100000000000002 y[1] (analytic) = -0.02187593153032481 y[1] (numeric) = -0.02187593153032506 absolute error = 2.532696274926138e-16 relative error = 1.157754709286446e-12 % Correct digits = 14 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 = 97.76 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.200000000000002 y[1] (analytic) = -0.0200940729394401 y[1] (numeric) = -0.02009407293944034 absolute error = 2.463307335887066e-16 relative error = 1.22588752579481e-12 % Correct digits = 14 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 = 95.79 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.300000000000002 y[1] (analytic) = -0.01845324025659324 y[1] (numeric) = -0.01845324025659349 absolute error = 2.42861286636753e-16 relative error = 1.316090200201994e-12 % Correct digits = 14 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 = 93.84 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.400000000000001 y[1] (analytic) = -0.01694272906623443 y[1] (numeric) = -0.01694272906623467 absolute error = 2.324529457808922e-16 relative error = 1.371992344752494e-12 % Correct digits = 14 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 = 91.91 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.500000000000001 y[1] (analytic) = -0.01555259515353922 y[1] (numeric) = -0.01555259515353945 absolute error = 2.307182223049153e-16 relative error = 1.483470893617469e-12 % Correct digits = 14 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 = 90 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.600000000000001 y[1] (analytic) = -0.01427360675737968 y[1] (numeric) = -0.01427360675737991 absolute error = 2.272487753529617e-16 relative error = 1.592090767356124e-12 % Correct digits = 14 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 = 88.11 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.7 y[1] (analytic) = -0.01309719902644198 y[1] (numeric) = -0.0130971990264422 absolute error = 2.220446049250313e-16 relative error = 1.695359477066392e-12 % Correct digits = 14 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 = 86.24 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.8 y[1] (analytic) = -0.01201543069156925 y[1] (numeric) = -0.01201543069156946 absolute error = 2.185751579730777e-16 relative error = 1.819120459214527e-12 % Correct digits = 14 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 = 84.39 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.899999999999999 y[1] (analytic) = -0.01102094294496803 y[1] (numeric) = -0.01102094294496824 absolute error = 2.151057110211241e-16 relative error = 1.951790442026901e-12 % Correct digits = 14 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 = 82.56 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.999999999999999 y[1] (analytic) = -0.01010692049862821 y[1] (numeric) = -0.01010692049862842 absolute error = 2.116362640691705e-16 relative error = 2.093973768744846e-12 % Correct digits = 14 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 = 80.75 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = (0.2 * x + 0.3) / exp(x); Iterations = 41 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 105 %