##############ECHO OF PROBLEM################# ##############temp/mtest2_sm_hpostode.ode################# diff ( y1 , x , 1 ) = m1 * y2 ; diff ( y2 , x , 1 ) = y1 ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=64; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=0.2; x_end=0.6; array_y1_init[0 + 1] = exact_soln_y1(x_start); array_y2_init[0 + 1] = exact_soln_y2(x_start); glob_look_poles=true; glob_max_h=0.000001; glob_type_given_pole=3; /* 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_y1 (double x) { return(cos(x)); } double exact_soln_y2 (double x) { return(sin(x)); } /* 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 = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.4 estimated_steps = 400000 step_error = 5.270462766947299e-15 est_needed_step_err = 5.270462766947299e-15 opt_iter = 1 SETTING H FOR MAX H NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.2 y1[1] (analytic) = 0.9800665778412416 y1[1] (numeric) = 0.9800665778412416 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 16 h = 1e-06 y2[1] (analytic) = 0.1986693307950612 y2[1] (numeric) = 0.1986693307950612 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 16 h = 1e-06 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.21000000000001 y1[1] (analytic) = 0.9780309147241462 y1[1] (numeric) = 0.9780798845335987 absolute error = 4.896980945257035e-05 relative error = 0.005006979709468825 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 5 h = 1e-06 y2[1] (analytic) = 0.2084598998461094 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.009790569051048137 relative error = 4.696619857476568 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 1e-06 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.22000000000002 y1[1] (analytic) = 0.9758974493306011 y1[1] (numeric) = 0.9760931912259558 absolute error = 0.0001957418953547618 relative error = 0.02005762956845798 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 4 h = 1e-06 y2[1] (analytic) = 0.2182296230808889 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.01956029228582765 relative error = 8.963170081899213 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-06 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.23000000000003 y1[1] (analytic) = 0.973666395005368 y1[1] (numeric) = 0.9741064979183129 absolute error = 0.0004401029129449396 relative error = 0.0452005856628659 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 4 h = 1e-06 y2[1] (analytic) = 0.2279775235352176 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.02930819274015639 relative error = 12.85573783137832 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 2 h = 1e-06 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.24000000000004 y1[1] (analytic) = 0.9713379748520201 y1[1] (numeric) = 0.97211980461067 absolute error = 0.0007818297586499323 relative error = 0.08048998174595627 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 4 h = 1e-06 y2[1] (analytic) = 0.2377026264271735 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.03903329563211225 relative error = 16.42106198774843 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 2 h = 1e-06 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.25000000000005 y1[1] (analytic) = 0.9689124217106324 y1[1] (numeric) = 0.9701331113030272 absolute error = 0.001220689592394741 relative error = 0.1259855447244233 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-06 y2[1] (analytic) = 0.2474039592545714 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.04873462845951018 relative error = 19.69840280905274 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 2 h = 1e-06 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2600009999997824 y1[1] (analytic) = 0.966389721053534 y1[1] (numeric) = 0.9681462193260535 absolute error = 0.001756498272519447 relative error = 0.18175879091559 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-06 y2[1] (analytic) = 0.2570815182817944 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.05841218748673321 relative error = 22.72127062152556 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 2 h = 1e-06 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2700009999995149 y1[1] (analytic) = 0.9637706296341013 y1[1] (numeric) = 0.9661595260184106 absolute error = 0.00238889638430928 relative error = 0.2478698054137874 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-06 y2[1] (analytic) = 0.2667324004591266 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.06806306966406539 relative error = 25.51736105059168 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 2 h = 1e-06 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2800009999992473 y1[1] (analytic) = 0.9610551619548499 y1[1] (numeric) = 0.9641728327107677 absolute error = 0.003117670755917845 relative error = 0.3244008127042673 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-06 y2[1] (analytic) = 0.2763566096186905 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.0776872788236293 relative error = 28.11124327036004 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 2 h = 1e-06 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2900009999989798 y1[1] (analytic) = 0.9582435895602847 y1[1] (numeric) = 0.9621861394031248 absolute error = 0.003942549842840148 relative error = 0.4114350344518654 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-06 y2[1] (analytic) = 0.2859531833475905 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.08728385255252924 relative error = 30.52382614899284 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 2 h = 1e-06 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3000009999987122 y1[1] (analytic) = 0.9553361936053023 y1[1] (numeric) = 0.9601994460954819 absolute error = 0.004863252490179604 relative error = 0.5090618907493061 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-06 y2[1] (analytic) = 0.2955211619964507 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.09685183120138946 relative error = 32.77323036600428 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 2 h = 1e-06 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3100009999984447 y1[1] (analytic) = 0.9523332648270753 y1[1] (numeric) = 0.958212752787839 absolute error = 0.005879487960763763 relative error = 0.6173771491465606 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-06 y2[1] (analytic) = 0.3050595887753796 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.1063902579803184 relative error = 34.87523811574246 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 2 h = 1e-06 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3200009999981771 y1[1] (analytic) = 0.9492351035159791 y1[1] (numeric) = 0.9562260594801961 absolute error = 0.00699095596421706 relative error = 0.7364830839401608 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-06 y2[1] (analytic) = 0.3145675098496482 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.115898179054587 relative error = 36.84365849161666 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 2 h = 1e-06 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3300009999979095 y1[1] (analytic) = 0.946042019485563 y1[1] (numeric) = 0.9542393661725532 absolute error = 0.008197346686990237 relative error = 0.8664886461859036 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-06 y2[1] (analytic) = 0.3240439744350722 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.125374643640011 relative error = 38.6906264369165 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 2 h = 1e-06 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.340000999997642 y1[1] (analytic) = 0.9427543320415691 y1[1] (numeric) = 0.9522526728649103 absolute error = 0.009498340823341223 relative error = 1.007509644932866 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-06 y2[1] (analytic) = 0.3334880348930901 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.1348187040980289 relative error = 40.42684893964763 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 2 h = 1e-06 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3500009999973744 y1[1] (analytic) = 0.9393723699500021 y1[1] (numeric) = 0.9502659795572674 absolute error = 0.01089360960726538 relative error = 1.159668940214325 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-06 y2[1] (analytic) = 0.3428987468255263 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.1442294160304651 relative error = 42.06180902254854 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 2 h = 1e-06 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3600009999971069 y1[1] (analytic) = 0.9358964714042528 y1[1] (numeric) = 0.9482792862496245 absolute error = 0.01238281484537174 relative error = 1.323096648370959 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-06 y2[1] (analytic) = 0.3522751691690298 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.1536058383739686 relative error = 43.60393573475653 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 2 h = 1e-06 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3700009999968393 y1[1] (analytic) = 0.9323269839912792 y1[1] (numeric) = 0.9462925929419816 absolute error = 0.01396560895070242 relative error = 1.497930360324426 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-06 y2[1] (analytic) = 0.36161636428918 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.1629470334941188 relative error = 45.06074657722406 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 2 h = 1e-06 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3800009999965718 y1[1] (analytic) = 0.9286642646568481 y1[1] (numeric) = 0.9443058996343388 absolute error = 0.0156416349774906 relative error = 1.684315373464959 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-06 y2[1] (analytic) = 0.3709213980742491 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.1722520672791879 relative error = 46.43896743986374 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 2 h = 1e-06 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3900009999963042 y1[1] (analytic) = 0.9249086796698406 y1[1] (numeric) = 0.9423192063266959 absolute error = 0.01741052665685527 relative error = 1.882404937865889 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-06 y2[1] (analytic) = 0.3801893400286129 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.1815200092335517 relative error = 47.74463408676597 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 2 h = 1e-06 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4000009999960367 y1[1] (analytic) = 0.9210606045856257 y1[1] (numeric) = 0.940332513019053 absolute error = 0.0192719084334273 relative error = 2.092360517590208 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-06 y2[1] (analytic) = 0.3894192633657993 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.1907499325707381 relative error = 48.98317841856682 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 2 h = 1e-06 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4100009999957691 y1[1] (analytic) = 0.917120424208505 y1[1] (numeric) = 0.9383458197114101 absolute error = 0.02122539550290503 relative error = 2.314352067911148 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-06 y2[1] (analytic) = 0.3986102451011662 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.1999409143061049 relative error = 50.15950211098075 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 2 h = 1e-06 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4200009999955016 y1[1] (analytic) = 0.913088532553233 y1[1] (numeric) = 0.9363591264037672 absolute error = 0.0232705938505342 relative error = 2.548558329329093 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-06 y2[1] (analytic) = 0.4077613661441992 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.209092035349138 relative error = 51.27803973346398 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 2 h = 1e-06 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.430000999995234 y1[1] (analytic) = 0.908965332805615 y1[1] (numeric) = 0.9343724330961243 absolute error = 0.0254071002905093 relative error = 2.79516713933277 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-06 y2[1] (analytic) = 0.4168717113904199 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.2182023805953587 relative error = 52.34281306053936 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 2 h = 1e-06 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4400009999949664 y1[1] (analytic) = 0.90475123728219 y1[1] (numeric) = 0.9323857397884814 absolute error = 0.0276345025062914 relative error = 3.054375762922804 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-06 y2[1] (analytic) = 0.4259403698128957 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.2272710390178345 relative error = 53.35747797694513 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 2 h = 1e-06 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4500009999946989 y1[1] (analytic) = 0.9004466673889984 y1[1] (numeric) = 0.9303990464808385 absolute error = 0.02995237909184012 relative error = 3.326391242991908 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-06 y2[1] (analytic) = 0.4349664345533417 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.2362971037582805 relative error = 54.32536512867464 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 2 h = 1e-06 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4600009999944313 y1[1] (analytic) = 0.8960520535794424 y1[1] (numeric) = 0.9284123531731956 absolute error = 0.03236029959375319 relative error = 3.611430771737435 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-06 y2[1] (analytic) = 0.4439490030128055 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.2452796722177443 relative error = 55.2495152716154 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 2 h = 1e-06 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4700009999941638 y1[1] (analytic) = 0.891567835311241 y1[1] (numeric) = 0.9264256598655527 absolute error = 0.03485782455431174 relative error = 3.909722084370965 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-06 y2[1] (analytic) = 0.4528871769419267 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.2542178461468654 relative error = 56.13271010750291 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 2 h = 1e-06 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4800009999938962 y1[1] (analytic) = 0.8869944610024838 y1[1] (numeric) = 0.9244389665579098 absolute error = 0.037444505555426 relative error = 4.221503876484878 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-06 y2[1] (analytic) = 0.4617800625307608 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.2631107317356995 relative error = 56.97749926528559 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 2 h = 1e-06 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4900009999936287 y1[1] (analytic) = 0.8823323879867907 y1[1] (numeric) = 0.9224522732502669 absolute error = 0.04011988526347621 relative error = 4.547026246539284 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-06 y2[1] (analytic) = 0.4706267704981597 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.2719574397030985 relative error = 57.78622397855328 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 2 h = 1e-06 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5000009999933611 y1[1] (analytic) = 0.8775820824675782 y1[1] (numeric) = 0.920465579942624 absolute error = 0.04288349747504583 relative error = 4.886551165045025 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-06 y2[1] (analytic) = 0.479426416180699 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.2807570853856378 relative error = 58.56103792157722 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 2 h = 1e-06 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5100009999936487 y1[1] (analytic) = 0.8727440194711686 y1[1] (numeric) = 0.9184788866349811 absolute error = 0.04573486716381248 relative error = 5.240352972172196 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-06 y2[1] (analytic) = 0.488178119621628 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.2895087888265668 relative error = 59.30392559399348 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 2 h = 1e-06 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5200009999939362 y1[1] (analytic) = 0.8678186828000911 y1[1] (numeric) = 0.9164921933273382 absolute error = 0.04867351052724711 relative error = 5.608718905451294 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-06 y2[1] (analytic) = 0.4968810056574057 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.2982116748623445 relative error = 60.01671858391752 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 2 h = 1e-06 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5300009999942238 y1[1] (analytic) = 0.8628065649839085 y1[1] (numeric) = 0.9145055000196953 absolute error = 0.05169893503578682 relative error = 5.991949659858118 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-06 y2[1] (analytic) = 0.5055342040066809 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.3068648732116197 relative error = 60.70110999008967 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 2 h = 1e-06 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5400009999945113 y1[1] (analytic) = 0.8577081672302256 y1[1] (numeric) = 0.9125188067120524 absolute error = 0.05481063948182685 relative error = 6.390359982093374 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-06 y2[1] (analytic) = 0.5141368493568297 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.3154675185617685 relative error = 61.35866724130145 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 2 h = 1e-06 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5500009999947989 y1[1] (analytic) = 0.8525239993745691 y1[1] (numeric) = 0.9105321134044095 absolute error = 0.05800811402984041 relative error = 6.804279301508986 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-06 y2[1] (analytic) = 0.5226880814504858 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.3240187506554246 relative error = 61.99084351727635 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 2 h = 1e-06 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5600009999950865 y1[1] (analytic) = 0.8472545798294046 y1[1] (numeric) = 0.9085454200967666 absolute error = 0.06129084026736209 relative error = 7.2340524001302 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-06 y2[1] (analytic) = 0.5311870451715658 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.3325177143765046 relative error = 62.59898794578209 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 2 h = 1e-06 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.570000999995374 y1[1] (analytic) = 0.8419004355322954 y1[1] (numeric) = 0.9065587267891237 absolute error = 0.06465829125682832 relative error = 7.680040124453411 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-06 y2[1] (analytic) = 0.53963289063078 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.3409635598357188 relative error = 63.18435472625928 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 2 h = 1e-06 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5800009999956616 y1[1] (analytic) = 0.8364621018932095 y1[1] (numeric) = 0.9045720334814809 absolute error = 0.06810993158827139 relative error = 8.142620141918508 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-06 y2[1] (analytic) = 0.5480247732506205 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.3493554424555593 relative error = 63.74811130952166 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 2 h = 1e-06 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5900009999959491 y1[1] (analytic) = 0.8309401227409788 y1[1] (numeric) = 0.902585340173838 absolute error = 0.07164521743285912 relative error = 8.62218774519237 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-06 y2[1] (analytic) = 0.5563618538498186 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.3576925230547574 relative error = 64.29134574551745 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 2 h = 1e-06 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 Finished! diff ( y1 , x , 1 ) = m1 * y2 ; diff ( y2 , x , 1 ) = y1 ; Iterations = 400001 Total Elapsed Time = 2 Minutes 32.0 Seconds Elapsed Time(since restart) = 2 Minutes 32.0 Seconds Time to Timeout = 7 Minutes 28.0 Seconds Percent Done = 100 %