##############ECHO OF PROBLEM################# ##############temp/arcsin_sqrtpostode.ode################# diff ( y , x , 1 ) = arcsin(sqrt(0.1 * x + 0.2)); ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=0.0; x_end=0.5; 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=0.01; 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(10.0 * (0.1 * x + 0.2) * arcsin(sqrt ( 0.1 * x + 0.2)) + 5.0 * sqrt( 0.1 * x + 0.2) * sqrt( 0.8 - 0.1 * x) - 5.0 * arcsin(sqrt( 0.1 * x + 0.2))); } // 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 = 0.5 estimated_steps = 500000 step_error = 2e-16 est_needed_step_err = 2e-16 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.172096533994529e-168 estimated_step_error = 1.172096533994529e-168 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 = 7.865804904946756e-161 estimated_step_error = 7.865804904946756e-161 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 = 5.278649921019755e-153 estimated_step_error = 5.278649921019755e-153 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 = 3.54243878182671e-145 estimated_step_error = 3.54243878182671e-145 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 = 2.377286109685047e-137 estimated_step_error = 2.377286109685047e-137 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 = 1.59536391118642e-129 estimated_step_error = 1.59536391118642e-129 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 = 1.070622824928351e-121 estimated_step_error = 1.070622824928351e-121 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 = 7.184723836425156e-114 estimated_step_error = 7.184723836425156e-114 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 = 4.821446539804461e-106 estimated_step_error = 4.821446539804461e-106 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 = 3.235430101625356e-98 estimated_step_error = 3.235430101625356e-98 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 = 2.171008236243645e-90 estimated_step_error = 2.171008236243645e-90 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 = 1.456600652460744e-82 estimated_step_error = 1.456600652460744e-82 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 = 9.770543937362868e-75 estimated_step_error = 9.770543937362868e-75 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 = 6.550819349617229e-67 estimated_step_error = 6.550819349617229e-67 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 = 4.388040640368088e-59 estimated_step_error = 4.388040640368088e-59 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 = 2.933900639709124e-51 estimated_step_error = 2.933900639709124e-51 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 = 1.9544915641618e-43 estimated_step_error = 1.9544915641618e-43 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 = 1.292731496281798e-35 estimated_step_error = 1.292731496281798e-35 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0 y[1] (analytic) = 0.6090571729975818 y[1] (numeric) = 0.6090571729975818 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.244 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.01 y[1] (analytic) = 0.6136998951900672 y[1] (numeric) = 0.613699895190067 absolute error = 2.220446049250313e-16 relative error = 3.618130077344441e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.255 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.02 y[1] (analytic) = 0.6183550940668948 y[1] (numeric) = 0.6183550940668947 absolute error = 1.110223024625157e-16 relative error = 1.795445748369707e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.266 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.03 y[1] (analytic) = 0.6230227465023471 y[1] (numeric) = 0.6230227465023471 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.277 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.04 y[1] (analytic) = 0.6277028295756553 y[1] (numeric) = 0.6277028295756552 absolute error = 1.110223024625157e-16 relative error = 1.76870801327389e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.288 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.05 y[1] (analytic) = 0.6323953205685542 y[1] (numeric) = 0.6323953205685544 absolute error = 2.220446049250313e-16 relative error = 3.511167741174973e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.3 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.06 y[1] (analytic) = 0.6371001969628829 y[1] (numeric) = 0.637100196962883 absolute error = 1.110223024625157e-16 relative error = 1.742619182850194e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.311 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.07000000000000001 y[1] (analytic) = 0.6418174364382213 y[1] (numeric) = 0.6418174364382214 absolute error = 1.110223024625157e-16 relative error = 1.729811254094874e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.322 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.08 y[1] (analytic) = 0.6465470168695726 y[1] (numeric) = 0.6465470168695726 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.333 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.09 y[1] (analytic) = 0.6512889163250815 y[1] (numeric) = 0.6512889163250816 absolute error = 1.110223024625157e-16 relative error = 1.704655179593145e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.345 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.09999999999999999 y[1] (analytic) = 0.6560431130637939 y[1] (numeric) = 0.6560431130637943 absolute error = 3.33066907387547e-16 relative error = 5.076905781878993e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.356 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (analytic) = 0.6608095855334544 y[1] (numeric) = 0.6608095855334544 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.367 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (analytic) = 0.6655883123683368 y[1] (numeric) = 0.6655883123683369 absolute error = 1.110223024625157e-16 relative error = 1.668032632175727e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.378 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (analytic) = 0.6703792723871187 y[1] (numeric) = 0.670379272387119 absolute error = 3.33066907387547e-16 relative error = 4.968335405143813e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.389 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (analytic) = 0.6751824445907852 y[1] (numeric) = 0.6751824445907851 absolute error = 1.110223024625157e-16 relative error = 1.644330408054434e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.401 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (analytic) = 0.679997808160568 y[1] (numeric) = 0.6799978081605685 absolute error = 5.551115123125783e-16 relative error = 8.163430905964034e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.412 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.16 y[1] (analytic) = 0.6848253424559257 y[1] (numeric) = 0.6848253424559257 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.423 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.17 y[1] (analytic) = 0.6896650270125453 y[1] (numeric) = 0.6896650270125454 absolute error = 1.110223024625157e-16 relative error = 1.609800382998051e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.434 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.18 y[1] (analytic) = 0.6945168415403891 y[1] (numeric) = 0.694516841540389 absolute error = 1.110223024625157e-16 relative error = 1.598554503246834e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.446 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.19 y[1] (analytic) = 0.6993807659217643 y[1] (numeric) = 0.6993807659217642 absolute error = 1.110223024625157e-16 relative error = 1.587437171169432e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.457 Order of pole (ratio test) Not computed 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) = 0.7042567802094298 y[1] (numeric) = 0.7042567802094298 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.468 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.21 y[1] (analytic) = 0.7091448646247309 y[1] (numeric) = 0.7091448646247308 absolute error = 1.110223024625157e-16 relative error = 1.565580010528131e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.479 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2200000000000001 y[1] (analytic) = 0.7140449995557641 y[1] (numeric) = 0.7140449995557637 absolute error = 3.33066907387547e-16 relative error = 4.664508645740271e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.49 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2300000000000001 y[1] (analytic) = 0.7189571655555725 y[1] (numeric) = 0.7189571655555723 absolute error = 2.220446049250313e-16 relative error = 3.088426064346223e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.502 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2400000000000001 y[1] (analytic) = 0.7238813433403714 y[1] (numeric) = 0.723881343340371 absolute error = 3.33066907387547e-16 relative error = 4.601125729399242e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.513 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2500000000000001 y[1] (analytic) = 0.7288175137877978 y[1] (numeric) = 0.7288175137877977 absolute error = 1.110223024625157e-16 relative error = 1.523321000966517e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.524 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2600000000000001 y[1] (analytic) = 0.7337656579351937 y[1] (numeric) = 0.7337656579351933 absolute error = 3.33066907387547e-16 relative error = 4.539145485832529e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.535 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2700000000000001 y[1] (analytic) = 0.73872575697791 y[1] (numeric) = 0.73872575697791 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.546 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2800000000000001 y[1] (analytic) = 0.7436977922676443 y[1] (numeric) = 0.7436977922676444 absolute error = 1.110223024625157e-16 relative error = 1.492841630254035e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.558 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2900000000000001 y[1] (analytic) = 0.7486817453107986 y[1] (numeric) = 0.7486817453107986 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.569 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3000000000000001 y[1] (analytic) = 0.7536775977668657 y[1] (numeric) = 0.7536775977668654 absolute error = 3.33066907387547e-16 relative error = 4.419222600942614e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.58 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3100000000000001 y[1] (analytic) = 0.75868533144684 y[1] (numeric) = 0.7586853314468398 absolute error = 2.220446049250313e-16 relative error = 2.926702227148432e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.591 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3200000000000001 y[1] (analytic) = 0.7637049283116548 y[1] (numeric) = 0.7637049283116545 absolute error = 3.33066907387547e-16 relative error = 4.361198874595034e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.603 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3300000000000001 y[1] (analytic) = 0.7687363704706399 y[1] (numeric) = 0.76873637047064 absolute error = 1.110223024625157e-16 relative error = 1.444218157579106e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.614 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3400000000000001 y[1] (analytic) = 0.7737796401800086 y[1] (numeric) = 0.773779640180008 absolute error = 5.551115123125783e-16 relative error = 7.174025827087408e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.625 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3500000000000001 y[1] (analytic) = 0.7788347198413585 y[1] (numeric) = 0.7788347198413584 absolute error = 1.110223024625157e-16 relative error = 1.425492465014013e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.636 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3600000000000002 y[1] (analytic) = 0.7839015920002093 y[1] (numeric) = 0.783901592000209 absolute error = 2.220446049250313e-16 relative error = 2.832557137158768e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.647 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3700000000000002 y[1] (analytic) = 0.7889802393445473 y[1] (numeric) = 0.7889802393445476 absolute error = 3.33066907387547e-16 relative error = 4.221486049691756e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.659 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3800000000000002 y[1] (analytic) = 0.7940706447034064 y[1] (numeric) = 0.794070644703406 absolute error = 3.33066907387547e-16 relative error = 4.194424131016087e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.67 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3900000000000002 y[1] (analytic) = 0.7991727910454559 y[1] (numeric) = 0.7991727910454556 absolute error = 3.33066907387547e-16 relative error = 4.167645734683209e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.681 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4000000000000002 y[1] (analytic) = 0.8042866614776243 y[1] (numeric) = 0.8042866614776241 absolute error = 2.220446049250313e-16 relative error = 2.76076448311469e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.692 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4100000000000002 y[1] (analytic) = 0.8094122392437332 y[1] (numeric) = 0.8094122392437331 absolute error = 1.110223024625157e-16 relative error = 1.371641014055438e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.704 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4200000000000002 y[1] (analytic) = 0.8145495077231562 y[1] (numeric) = 0.8145495077231558 absolute error = 3.33066907387547e-16 relative error = 4.088970703800948e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.715 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4300000000000002 y[1] (analytic) = 0.8196984504294951 y[1] (numeric) = 0.8196984504294951 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.726 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4400000000000002 y[1] (analytic) = 0.8248590510092806 y[1] (numeric) = 0.8248590510092806 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.737 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4500000000000002 y[1] (analytic) = 0.8300312932406855 y[1] (numeric) = 0.8300312932406855 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.748 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4600000000000002 y[1] (analytic) = 0.8352151610322623 y[1] (numeric) = 0.8352151610322623 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.76 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4700000000000003 y[1] (analytic) = 0.8404106384216971 y[1] (numeric) = 0.8404106384216969 absolute error = 1.110223024625157e-16 relative error = 1.321048275531317e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.771 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4800000000000003 y[1] (analytic) = 0.8456177095745808 y[1] (numeric) = 0.8456177095745807 absolute error = 1.110223024625157e-16 relative error = 1.312913639407688e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.782 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4900000000000003 y[1] (analytic) = 0.850836358783201 y[1] (numeric) = 0.8508363587832012 absolute error = 2.220446049250313e-16 relative error = 2.609721630168485e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.793 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = arcsin(sqrt(0.1 * x + 0.2)); Iterations = 50 Total Elapsed Time = 0 Seconds Elapsed Time(since restart) = 0 Seconds Time to Timeout = 3 Minutes 0 Seconds Percent Done = 102 %