##############ECHO OF PROBLEM################# ##############temp/sqrtpostode.ode################# diff ( y , x , 1 ) = sqrt ( x ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=40; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=0.1; x_end=0.5; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_min_h=0.001; glob_type_given_pole=1; array_given_rad_poles[1][1]=0.0; array_given_rad_poles[1][2]=0.0; array_given_ord_poles[1][1]=1.5; array_given_ord_poles[1][2]=0.0; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=100000000; glob_max_minutes=10.0; glob_subiter_method=3; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(2.0*expt(x,1.5)/3.0); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.001 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.4 estimated_steps = 400 step_error = 1.25e-13 est_needed_step_err = 1.25e-13 opt_iter = 1 Radius of convergence (given) for eq 1 = 0.1 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0210818510677892 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.001 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.4 estimated_steps = 400 step_error = 1.25e-13 est_needed_step_err = 1.25e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.204116264324181e-78 estimated_step_error = 1.204116264324181e-78 Double H and LOOP opt_iter = 2 Radius of convergence (given) for eq 1 = 0.1 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0210818510677892 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.002 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.4 estimated_steps = 200 step_error = 1.767766952966369e-13 est_needed_step_err = 1.767766952966369e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.236403653689294e-68 estimated_step_error = 8.236403653689294e-68 Double H and LOOP opt_iter = 3 Radius of convergence (given) for eq 1 = 0.1 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0210818510677892 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.004 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.4 estimated_steps = 100 step_error = 2.5e-13 est_needed_step_err = 2.5e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.608205902107171e-57 estimated_step_error = 5.608205902107171e-57 Double H and LOOP opt_iter = 4 Radius of convergence (given) for eq 1 = 0.1 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0210818510677892 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.008 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.4 estimated_steps = 50 step_error = 3.535533905932737e-13 est_needed_step_err = 3.535533905932737e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.784643348666978e-46 estimated_step_error = 3.784643348666978e-46 Double H and LOOP opt_iter = 5 SETTING H FOR DISPLAY INTERVAL SETTING H FOR POLE Radius of convergence (given) for eq 1 = 0.1 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0625 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 0.0210818510677892 y[1] (numeric) = 0.0210818510677892 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 16 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.1 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1125000000000001 y[1] (analytic) = 0.02515576474687267 y[1] (numeric) = 0.02515576474687267 absolute error = 3.469446951953614e-18 relative error = 1.379185640692928e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.1125 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1125 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1250000000000002 y[1] (analytic) = 0.02946278254943955 y[1] (numeric) = 0.02946278254943955 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.125 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.125 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1312500000000002 y[1] (analytic) = 0.03169988663228948 y[1] (numeric) = 0.03169988663228948 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.1313 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1312 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1437500000000003 y[1] (analytic) = 0.03633461150274712 y[1] (numeric) = 0.03633461150274713 absolute error = 6.938893903907228e-18 relative error = 1.909720131005833e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.1438 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1438 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1500000000000003 y[1] (analytic) = 0.03872983346207429 y[1] (numeric) = 0.03872983346207431 absolute error = 1.387778780781446e-17 relative error = 3.58322940412437e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.15 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.15 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1625000000000004 y[1] (analytic) = 0.04367056280328397 y[1] (numeric) = 0.04367056280328399 absolute error = 2.081668171172169e-17 relative error = 4.76675370672262e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.1625 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1625 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1750000000000005 y[1] (analytic) = 0.04880516821448794 y[1] (numeric) = 0.04880516821448797 absolute error = 2.775557561562891e-17 relative error = 5.68701566474462e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.175 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.175 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1812500000000005 y[1] (analytic) = 0.05144293798040288 y[1] (numeric) = 0.05144293798040292 absolute error = 3.469446951953614e-17 relative error = 6.744262843765446e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.1813 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1813 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1937500000000006 y[1] (analytic) = 0.05685534611577413 y[1] (numeric) = 0.05685534611577418 absolute error = 4.85722573273506e-17 relative error = 8.543129300179311e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.1938 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1938 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2000000000000006 y[1] (analytic) = 0.05962847939999466 y[1] (numeric) = 0.05962847939999472 absolute error = 5.551115123125783e-17 relative error = 9.309503074677232e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.2 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2125000000000007 y[1] (analytic) = 0.0653051065724916 y[1] (numeric) = 0.06530510657249165 absolute error = 5.551115123125783e-17 relative error = 8.500277259273432e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.2125 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2125 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2250000000000007 y[1] (analytic) = 0.07115124735378887 y[1] (numeric) = 0.07115124735378894 absolute error = 6.938893903907228e-17 relative error = 9.75231519049079e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.225 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.225 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2312500000000008 y[1] (analytic) = 0.07413637607102534 y[1] (numeric) = 0.07413637607102541 absolute error = 6.938893903907228e-17 relative error = 9.359634597271811e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.2313 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2313 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2437500000000008 y[1] (analytic) = 0.08022794673615963 y[1] (numeric) = 0.0802279467361597 absolute error = 6.938893903907228e-17 relative error = 8.648973563696841e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.2438 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2437 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2500000000000009 y[1] (analytic) = 0.08333333333333377 y[1] (numeric) = 0.08333333333333384 absolute error = 6.938893903907228e-17 relative error = 8.32667268468863e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.25 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.262500000000001 y[1] (analytic) = 0.08966081920214697 y[1] (numeric) = 0.08966081920214705 absolute error = 8.326672684688674e-17 relative error = 9.28685769189279e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.2625 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2625 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.275000000000001 y[1] (analytic) = 0.09614081108226442 y[1] (numeric) = 0.09614081108226452 absolute error = 9.71445146547012e-17 relative error = 1.010439932440116e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.275 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.275 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2812500000000011 y[1] (analytic) = 0.09943689110435881 y[1] (numeric) = 0.09943689110435891 absolute error = 9.71445146547012e-17 relative error = 9.769464187365656e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.2813 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2812 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2937500000000011 y[1] (analytic) = 0.1061391374237406 y[1] (numeric) = 0.1061391374237407 absolute error = 1.249000902703301e-16 relative error = 1.176758105463868e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.2938 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2937 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3000000000000012 y[1] (analytic) = 0.1095445115010339 y[1] (numeric) = 0.109544511501034 absolute error = 1.249000902703301e-16 relative error = 1.140176614591515e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.3 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3125000000000012 y[1] (analytic) = 0.1164618738281147 y[1] (numeric) = 0.1164618738281149 absolute error = 1.249000902703301e-16 relative error = 1.072454754202816e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.3125 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3125 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3250000000000013 y[1] (analytic) = 0.1235190043857407 y[1] (numeric) = 0.1235190043857408 absolute error = 1.249000902703301e-16 relative error = 1.011181161080901e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.325 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.325 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3312500000000013 y[1] (analytic) = 0.1270991281168197 y[1] (numeric) = 0.1270991281168198 absolute error = 1.387778780781446e-16 relative error = 1.091886940015754e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.3313 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3313 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3437500000000014 y[1] (analytic) = 0.1343608681199428 y[1] (numeric) = 0.1343608681199429 absolute error = 1.387778780781446e-16 relative error = 1.03287422908178e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.3438 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3437 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3500000000000014 y[1] (analytic) = 0.1380418616056585 y[1] (numeric) = 0.1380418616056587 absolute error = 1.387778780781446e-16 relative error = 1.005331835313759e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.35 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.35 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3625000000000015 y[1] (analytic) = 0.1455026011604078 y[1] (numeric) = 0.1455026011604079 absolute error = 1.110223024625157e-16 relative error = 7.63026238548961e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.3625 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3625 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3750000000000016 y[1] (analytic) = 0.1530931089239496 y[1] (numeric) = 0.1530931089239497 absolute error = 1.387778780781446e-16 relative error = 9.064933036736733e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.375 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.375 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3812500000000016 y[1] (analytic) = 0.1569363398226961 y[1] (numeric) = 0.1569363398226963 absolute error = 1.387778780781446e-16 relative error = 8.842940916994326e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.3813 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3813 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3937500000000017 y[1] (analytic) = 0.1647174427238972 y[1] (numeric) = 0.1647174427238973 absolute error = 1.665334536937735e-16 relative error = 1.011025007065708e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.3938 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3938 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4000000000000017 y[1] (analytic) = 0.1686548085423146 y[1] (numeric) = 0.1686548085423148 absolute error = 1.665334536937735e-16 relative error = 9.874219130371909e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.4 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4125000000000018 y[1] (analytic) = 0.1766219479566467 y[1] (numeric) = 0.1766219479566468 absolute error = 1.665334536937735e-16 relative error = 9.428808572230815e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.4125 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4125 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4250000000000018 y[1] (analytic) = 0.1847107348140762 y[1] (numeric) = 0.1847107348140764 absolute error = 2.220446049250313e-16 relative error = 1.202120738399607e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.425 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.425 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4312500000000019 y[1] (analytic) = 0.1888001795881044 y[1] (numeric) = 0.1888001795881046 absolute error = 2.220446049250313e-16 relative error = 1.176082593827265e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.4313 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4313 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4437500000000019 y[1] (analytic) = 0.1970680821265992 y[1] (numeric) = 0.1970680821265995 absolute error = 2.220446049250313e-16 relative error = 1.126740578834003e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.4438 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4438 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.450000000000002 y[1] (analytic) = 0.2012461179749824 y[1] (numeric) = 0.2012461179749826 absolute error = 2.498001805406602e-16 relative error = 1.241267076623628e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.45 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.45 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.462500000000002 y[1] (analytic) = 0.2096893370096728 y[1] (numeric) = 0.209689337009673 absolute error = 2.775557561562891e-16 relative error = 1.323652218631822e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.4625 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4625 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4750000000000021 y[1] (analytic) = 0.2182474385747633 y[1] (numeric) = 0.2182474385747636 absolute error = 2.775557561562891e-16 relative error = 1.271748057932918e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.475 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.475 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4812500000000021 y[1] (analytic) = 0.2225690923467502 y[1] (numeric) = 0.2225690923467505 absolute error = 2.775557561562891e-16 relative error = 1.247054356154146e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.4813 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4813 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4937500000000022 y[1] (analytic) = 0.2312966826003891 y[1] (numeric) = 0.2312966826003894 absolute error = 3.05311331771918e-16 relative error = 1.319998749395831e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.4938 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4938 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = sqrt ( x ) ; Iterations = 64 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 10 Minutes 0.0 Seconds Percent Done = 101.6 %