##############ECHO OF PROBLEM################# ##############temp/expt_sin_cpostode.ode################# diff ( y , x , 1 ) = expt(sin(0.2 * x + 0.3) , 2.0); ! /* 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(-2.5000000000000000000000000000000*sin(0.20000000000000000000000000000000*x+0.30000000000000000000000000000000)*cos(0.20000000000000000000000000000000*x+0.30000000000000000000000000000000)+0.50000000000000000000000000000000*x+0.75000000000000000000000000000000); } /* 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 = 8.881515326224724e-184 estimated_step_error = 8.881515326224724e-184 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 = 5.960282454644306e-176 estimated_step_error = 5.960282454644306e-176 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 = 3.999875716776835e-168 estimated_step_error = 3.999875716776835e-168 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 = 2.684268296475168e-160 estimated_step_error = 2.684268296475168e-160 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 = 1.801378123921355e-152 estimated_step_error = 1.801378123921355e-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 = 1.208879246003906e-144 estimated_step_error = 1.208879246003906e-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 = 8.112582179347103e-137 estimated_step_error = 8.112582179347103e-137 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 = 5.444168983586109e-129 estimated_step_error = 5.444168983586109e-129 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 = 3.653395467794425e-121 estimated_step_error = 3.653395467794425e-121 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 = 2.45158512361816e-113 estimated_step_error = 2.45158512361816e-113 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 = 1.645006732022313e-105 estimated_step_error = 1.645006732022313e-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 = 1.103644545774066e-97 estimated_step_error = 1.103644545774066e-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 = 7.402399432180782e-90 estimated_step_error = 7.402399432180782e-90 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 = 4.962261098020074e-82 estimated_step_error = 4.962261098020074e-82 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 = 3.322886448245222e-74 estimated_step_error = 3.322886448245222e-74 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 = 2.220310908577614e-66 estimated_step_error = 2.220310908577614e-66 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 = 1.477258888076705e-58 estimated_step_error = 1.477258888076705e-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 = 9.747001200300532e-51 estimated_step_error = 9.747001200300532e-51 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 0.05350569829701002 y[1] (numeric) = 0.05350569829701002 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 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (analytic) = 0.06400871997691449 y[1] (numeric) = 0.06400871997691444 absolute error = 4.163336342344337e-17 relative error = 6.504326822729613e-14 % Correct digits = 16 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] = 0.3 y[1] (analytic) = 0.0757691600356587 y[1] (numeric) = 0.07576916003565864 absolute error = 5.551115123125783e-17 relative error = 7.32635167199069e-14 % Correct digits = 16 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] = 0.4 y[1] (analytic) = 0.08884819361181084 y[1] (numeric) = 0.08884819361181091 absolute error = 6.938893903907228e-17 relative error = 7.809831153376226e-14 % Correct digits = 16 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] = 0.5 y[1] (analytic) = 0.1033048863755964 y[1] (numeric) = 0.1033048863755966 absolute error = 2.081668171172169e-16 relative error = 2.015072320590557e-13 % Correct digits = 15 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] = 0.6 y[1] (analytic) = 0.1191961000364259 y[1] (numeric) = 0.1191961000364259 absolute error = 5.551115123125783e-17 relative error = 4.657128145492497e-14 % Correct digits = 16 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] = 0.7 y[1] (analytic) = 0.1365764013762885 y[1] (numeric) = 0.1365764013762885 absolute error = 2.775557561562891e-17 relative error = 2.032238024719815e-14 % Correct digits = 16 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] = 0.7999999999999999 y[1] (analytic) = 0.1554979749545424 y[1] (numeric) = 0.1554979749545426 absolute error = 1.387778780781446e-16 relative error = 8.924738609535864e-14 % Correct digits = 16 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] = 0.8999999999999999 y[1] (analytic) = 0.1760105396237521 y[1] (numeric) = 0.1760105396237523 absolute error = 1.387778780781446e-16 relative error = 7.884634543749611e-14 % Correct digits = 16 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) = 0.1981612689901293 y[1] (numeric) = 0.1981612689901295 absolute error = 1.665334536937735e-16 relative error = 8.403935569370457e-14 % Correct digits = 16 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) = 0.2219947159458268 y[1] (numeric) = 0.2219947159458271 absolute error = 3.608224830031759e-16 relative error = 1.62536518703097e-13 % Correct digits = 15 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) = 0.2475527413938156 y[1] (numeric) = 0.2475527413938158 absolute error = 2.220446049250313e-16 relative error = 8.969587800758586e-14 % Correct digits = 16 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) = 0.2748744472793688 y[1] (numeric) = 0.2748744472793689 absolute error = 5.551115123125783e-17 relative error = 2.01950933528714e-14 % Correct digits = 16 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) = 0.3039961140352913 y[1] (numeric) = 0.3039961140352915 absolute error = 2.220446049250313e-16 relative error = 7.304192214090404e-14 % Correct digits = 16 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) = 0.3349511425409671 y[1] (numeric) = 0.3349511425409672 absolute error = 5.551115123125783e-17 relative error = 1.657290995043206e-14 % Correct digits = 16 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) = 0.3677700006880763 y[1] (numeric) = 0.3677700006880764 absolute error = 1.110223024625157e-16 relative error = 3.018797135568409e-14 % Correct digits = 16 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) = 0.4024801746384691 y[1] (numeric) = 0.402480174638469 absolute error = 1.110223024625157e-16 relative error = 2.758453942787177e-14 % Correct digits = 16 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) = 0.4391061248521687 y[1] (numeric) = 0.4391061248521686 absolute error = 1.110223024625157e-16 relative error = 2.528370618831447e-14 % Correct digits = 16 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) = 0.4776692469558551 y[1] (numeric) = 0.4776692469558549 absolute error = 1.665334536937735e-16 relative error = 3.486375871067204e-14 % Correct digits = 16 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) = 0.5181878375144249 y[1] (numeric) = 0.518187837514425 absolute error = 1.110223024625157e-16 relative error = 2.142510773603889e-14 % Correct digits = 16 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) = 0.560677064760392 y[1] (numeric) = 0.5606770647603921 absolute error = 1.110223024625157e-16 relative error = 1.980147030090513e-14 % Correct digits = 16 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] = 2.200000000000001 y[1] (analytic) = 0.6051489443279503 y[1] (numeric) = 0.6051489443279502 absolute error = 1.110223024625157e-16 relative error = 1.834627714435027e-14 % Correct digits = 16 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] = 2.300000000000001 y[1] (analytic) = 0.6516123200305215 y[1] (numeric) = 0.6516123200305215 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 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.400000000000001 y[1] (analytic) = 0.7000728497125424 y[1] (numeric) = 0.7000728497125425 absolute error = 1.110223024625157e-16 relative error = 1.585867849440278e-14 % Correct digits = 16 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] = 2.500000000000001 y[1] (analytic) = 0.7505329961981189 y[1] (numeric) = 0.7505329961981189 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 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.600000000000001 y[1] (analytic) = 0.8029920233510333 y[1] (numeric) = 0.8029920233510333 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 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.700000000000001 y[1] (analytic) = 0.8574459972524058 y[1] (numeric) = 0.8574459972524054 absolute error = 3.33066907387547e-16 relative error = 3.884406813429934e-14 % Correct digits = 16 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] = 2.800000000000001 y[1] (analytic) = 0.913887792494124 y[1] (numeric) = 0.9138877924941236 absolute error = 4.440892098500626e-16 relative error = 4.85934064879106e-14 % Correct digits = 16 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] = 2.900000000000001 y[1] (analytic) = 0.9723071035779776 y[1] (numeric) = 0.9723071035779773 absolute error = 2.220446049250313e-16 relative error = 2.283687984052907e-14 % Correct digits = 16 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] = 3.000000000000001 y[1] (analytic) = 1.032690461402257 y[1] (numeric) = 1.032690461402257 absolute error = 2.220446049250313e-16 relative error = 2.150156443040291e-14 % Correct digits = 16 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] = 3.100000000000001 y[1] (analytic) = 1.095021254809441 y[1] (numeric) = 1.09502125480944 absolute error = 2.220446049250313e-16 relative error = 2.027765250672438e-14 % Correct digits = 16 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] = 3.200000000000002 y[1] (analytic) = 1.159279757160507 y[1] (numeric) = 1.159279757160506 absolute error = 4.440892098500626e-16 relative error = 3.830733756084872e-14 % Correct digits = 16 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] = 3.300000000000002 y[1] (analytic) = 1.225443157893345 y[1] (numeric) = 1.225443157893344 absolute error = 6.661338147750939e-16 relative error = 5.435860574065648e-14 % Correct digits = 16 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] = 3.400000000000002 y[1] (analytic) = 1.293485599014791 y[1] (numeric) = 1.29348559901479 absolute error = 4.440892098500626e-16 relative error = 3.433275253998282e-14 % Correct digits = 16 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] = 3.500000000000002 y[1] (analytic) = 1.363378216467899 y[1] (numeric) = 1.363378216467899 absolute error = 6.661338147750939e-16 relative error = 4.885906249117323e-14 % Correct digits = 16 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] = 3.600000000000002 y[1] (analytic) = 1.435089186308277 y[1] (numeric) = 1.435089186308276 absolute error = 6.661338147750939e-16 relative error = 4.641759000976816e-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 = 0.3564 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) = 1.508583775615606 y[1] (numeric) = 1.508583775615605 absolute error = 8.881784197001252e-16 relative error = 5.887498155928976e-14 % Correct digits = 16 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] = 3.800000000000002 y[1] (analytic) = 1.583824398058906 y[1] (numeric) = 1.583824398058906 absolute error = 8.881784197001252e-16 relative error = 5.607808673667696e-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 = 0.5248 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.900000000000002 y[1] (analytic) = 1.660770674026648 y[1] (numeric) = 1.660770674026647 absolute error = 8.881784197001252e-16 relative error = 5.347989542389247e-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 = 0.6926 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.000000000000002 y[1] (analytic) = 1.739379495225513 y[1] (numeric) = 1.739379495225513 absolute error = 4.440892098500626e-16 relative error = 2.553147321036377e-14 % Correct digits = 16 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] = 4.100000000000001 y[1] (analytic) = 1.819605093644476 y[1] (numeric) = 1.819605093644476 absolute error = 4.440892098500626e-16 relative error = 2.44058016435093e-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 = 0.95 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.200000000000001 y[1] (analytic) = 1.901399114773849 y[1] (numeric) = 1.901399114773848 absolute error = 2.220446049250313e-16 relative error = 1.167795878307439e-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 = 0.8475 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.300000000000001 y[1] (analytic) = 1.984710694962187 y[1] (numeric) = 1.984710694962187 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 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.4 y[1] (analytic) = 2.06948654278728 y[1] (numeric) = 2.069486542787281 absolute error = 4.440892098500626e-16 relative error = 2.145890783382156e-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 = 0.9426 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.5 y[1] (analytic) = 2.155671024311062 y[1] (numeric) = 2.155671024311062 absolute error = 8.881784197001252e-16 relative error = 4.120194638622938e-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 = 1.138 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.6 y[1] (analytic) = 2.243206252082036 y[1] (numeric) = 2.243206252082038 absolute error = 1.332267629550188e-15 relative error = 5.939122309032623e-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 = 1.209 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.699999999999999 y[1] (analytic) = 2.33203217774286 y[1] (numeric) = 2.332032177742862 absolute error = 1.332267629550188e-15 relative error = 5.712904145429374e-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 = 1.123 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.799999999999999 y[1] (analytic) = 2.422086688094897 y[1] (numeric) = 2.422086688094899 absolute error = 2.220446049250313e-15 relative error = 9.167492064443056e-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 = 1.162 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) = 2.513305704466091 y[1] (numeric) = 2.513305704466093 absolute error = 2.220446049250313e-15 relative error = 8.834763098275819e-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 = 1.106 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.999999999999998 y[1] (analytic) = 2.605623285223168 y[1] (numeric) = 2.605623285223171 absolute error = 2.664535259100376e-15 relative error = 1.022609551507812e-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 = 1.097 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = expt(sin(0.2 * x + 0.3) , 2.0); 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 %