##############ECHO OF PROBLEM################# ##############temp/mtest3postode.ode################# diff ( y2 , x , 1 ) = m1 * y1 + 1.0 ; diff ( y1 , x , 1 ) = y2 - 1.0 ; ! /* 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_y1_init[0 + 1] = exact_soln_y1(x_start); array_y2_init[0 + 1] = exact_soln_y2(x_start); 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(1.0 + cos(x)); } double exact_soln_y2 (double x) { return(1.0 - 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 = 400000.0000000001 step_error = 3.952847075210474e-15 est_needed_step_err = 3.952847075210474e-15 opt_iter = 1 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 min_size = 0.9001665833531718 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 = 400000.0000000001 step_error = 3.952847075210474e-15 est_needed_step_err = 3.952847075210474e-15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.674790358513323e-258 estimated_step_error = 2.674790358513323e-258 Double H and LOOP opt_iter = 2 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 min_size = 0.9001665833531718 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 2e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.4 estimated_steps = 200000 step_error = 5.590169943749474e-15 est_needed_step_err = 5.590169943749474e-15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.838101935663098e-247 estimated_step_error = 1.838101935663098e-247 Double H and LOOP opt_iter = 3 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 min_size = 0.9001665833531718 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 4e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.4 estimated_steps = 100000 step_error = 7.905694150420947e-15 est_needed_step_err = 7.905694150420947e-15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.263134028636665e-236 estimated_step_error = 1.263134028636665e-236 Double H and LOOP opt_iter = 4 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 min_size = 0.9001665833531718 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 8e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.4 estimated_steps = 50000.00000000001 step_error = 1.118033988749895e-14 est_needed_step_err = 1.118033988749895e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.68019090245767e-226 estimated_step_error = 8.68019090245767e-226 Double H and LOOP opt_iter = 5 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 min_size = 0.9001665833531718 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 1.6e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.4 estimated_steps = 25000 step_error = 1.581138830084189e-14 est_needed_step_err = 1.581138830084189e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.964981703152477e-215 estimated_step_error = 5.964981703152477e-215 Double H and LOOP opt_iter = 6 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 min_size = 0.9001665833531718 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 3.2e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.4 estimated_steps = 12500 step_error = 2.23606797749979e-14 est_needed_step_err = 2.23606797749979e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.099104124878063e-204 estimated_step_error = 4.099104124878063e-204 Double H and LOOP opt_iter = 7 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 min_size = 0.9001665833531718 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 6.4e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.4 estimated_steps = 6250.000000000001 step_error = 3.162277660168379e-14 est_needed_step_err = 3.162277660168379e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.816882783259633e-193 estimated_step_error = 2.816882783259633e-193 Double H and LOOP opt_iter = 8 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 min_size = 0.9001665833531718 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.000128 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.4 estimated_steps = 3125 step_error = 4.472135954999579e-14 est_needed_step_err = 4.472135954999579e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.935746940941988e-182 estimated_step_error = 1.935746940941988e-182 Double H and LOOP opt_iter = 9 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09933 Order of pole (three term test) = 32.99 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.09933 Order of pole (three term test) = 32.01 NO COMPLEX POLE (six term test) for Equation 2 SETTING H FOR POLE ACCURACY START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y2[1] (analytic) = 0.9001665833531718 y2[1] (numeric) = 0.9001665833531718 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.000128 y1[1] (analytic) = 1.995004165278026 y1[1] (numeric) = 1.995004165278026 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.000128 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] = 0.1101120000000003 y2[1] (analytic) = 0.890110376768616 y2[1] (numeric) = 0.8901103767686163 absolute error = 2.220446049250313e-16 relative error = 2.494573827249649e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.000128 y1[1] (analytic) = 1.993943796552936 y1[1] (numeric) = 1.993943796552935 absolute error = 1.110223024625157e-15 relative error = 5.567975519392639e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.000128 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] = 0.1200960000000005 y2[1] (analytic) = 0.8801924836338184 y2[1] (numeric) = 0.8801924836338191 absolute error = 6.661338147750939e-16 relative error = 7.568047071079306e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.000128 y1[1] (analytic) = 1.992797138907122 y1[1] (numeric) = 1.992797138907121 absolute error = 8.881784197001252e-16 relative error = 4.456943470860335e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.000128 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] = 0.1300800000000002 y2[1] (analytic) = 0.8702865328437216 y2[1] (numeric) = 0.8702865328437223 absolute error = 6.661338147750939e-16 relative error = 7.654189621876091e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.000128 y1[1] (analytic) = 1.991551519810391 y1[1] (numeric) = 1.991551519810391 absolute error = 8.881784197001252e-16 relative error = 4.459731073312558e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.000128 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] = 0.1400639999999994 y2[1] (analytic) = 0.8603935118178341 y2[1] (numeric) = 0.8603935118178343 absolute error = 2.220446049250313e-16 relative error = 2.580733139838501e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.000128 y1[1] (analytic) = 1.990207063425344 y1[1] (numeric) = 1.990207063425343 absolute error = 8.881784197001252e-16 relative error = 4.462743781903185e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.000128 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] = 0.1500479999999985 y2[1] (analytic) = 0.8505144066868322 y2[1] (numeric) = 0.8505144066868316 absolute error = 5.551115123125783e-16 relative error = 6.526773773004127e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.000128 y1[1] (analytic) = 1.988763903766622 y1[1] (numeric) = 1.988763903766621 absolute error = 1.332267629550188e-15 relative error = 6.698973302094521e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.000128 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] = 0.1600319999999977 y2[1] (analytic) = 0.8406502021942646 y2[1] (numeric) = 0.8406502021942633 absolute error = 1.221245327087672e-15 relative error = 1.452738991675703e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.987222184687556 y1[1] (numeric) = 1.987222184687555 absolute error = 8.881784197001252e-16 relative error = 4.469446982546495e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.000128 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] = 0.1700159999999968 y2[1] (analytic) = 0.8308018815983926 y2[1] (numeric) = 0.8308018815983909 absolute error = 1.77635683940025e-15 relative error = 2.138123274327075e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.985582059865822 y1[1] (numeric) = 1.985582059865821 absolute error = 8.881784197001252e-16 relative error = 4.473138822377077e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.000128 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] = 0.180127999999996 y2[1] (analytic) = 0.820844496048457 y2[1] (numeric) = 0.8208444960484542 absolute error = 2.775557561562891e-15 relative error = 3.381343938985298e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.983820768943139 y1[1] (numeric) = 1.983820768943138 absolute error = 6.661338147750939e-16 relative error = 3.357832649014811e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.000128 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] = 0.1901119999999951 y2[1] (analytic) = 0.811031121733924 y2[1] (numeric) = 0.8110311217339204 absolute error = 3.552713678800501e-15 relative error = 4.380489951119341e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.981983076761948 y1[1] (numeric) = 1.981983076761947 absolute error = 6.661338147750939e-16 relative error = 3.360946027164802e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.000128 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] = 0.2000959999999943 y2[1] (analytic) = 0.8012365837290845 y2[1] (numeric) = 0.80123658372908 absolute error = 4.440892098500626e-15 relative error = 5.542547842526108e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.980047501069369 y1[1] (numeric) = 1.980047501069369 absolute error = 2.220446049250313e-16 relative error = 1.121410495481099e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.000128 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] = 0.2100799999999935 y2[1] (analytic) = 0.7914618583478841 y2[1] (numeric) = 0.7914618583478792 absolute error = 4.884981308350689e-15 relative error = 6.172099459786619e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.978014234802481 y1[1] (numeric) = 1.978014234802481 absolute error = 2.220446049250313e-16 relative error = 1.122563230426924e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.000128 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] = 0.2200639999999926 y2[1] (analytic) = 0.7817079199293576 y2[1] (numeric) = 0.7817079199293513 absolute error = 6.328271240363392e-15 relative error = 8.095442145367125e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.975883480636102 y1[1] (numeric) = 1.975883480636101 absolute error = 2.220446049250313e-16 relative error = 1.123773780696561e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.000128 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] = 0.2300479999999918 y2[1] (analytic) = 0.7719757407405075 y2[1] (numeric) = 0.7719757407405003 absolute error = 7.105427357601002e-15 relative error = 9.204210679969315e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.973655450962588 y1[1] (numeric) = 1.973655450962588 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.000128 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] = 0.2400319999999909 y2[1] (analytic) = 0.762266290879388 y2[1] (numeric) = 0.7622662908793804 absolute error = 7.66053886991358e-15 relative error = 1.004968862138191e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.971330367870662 y1[1] (numeric) = 1.971330367870662 absolute error = 4.440892098500626e-16 relative error = 2.252738643344427e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.000128 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] = 0.2500159999999901 y2[1] (analytic) = 0.7525805381784076 y2[1] (numeric) = 0.7525805381783994 absolute error = 8.215650382226158e-15 relative error = 1.091663943650712e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.968908463123278 y1[1] (numeric) = 1.968908463123277 absolute error = 1.332267629550188e-15 relative error = 6.766529041359354e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.000128 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] = 0.2601279999999915 y2[1] (analytic) = 0.7427957522969936 y2[1] (numeric) = 0.7427957522969866 absolute error = 6.994405055138486e-15 relative error = 9.416323442223858e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.966357063907296 y1[1] (numeric) = 1.966357063907295 absolute error = 1.554312234475219e-15 relative error = 7.904526919371838e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.000128 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] = 0.2701119999999928 y2[1] (analytic) = 0.733160622643948 y2[1] (numeric) = 0.7331606226439421 absolute error = 5.88418203051333e-15 relative error = 8.025774774010091e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.963741016400275 y1[1] (numeric) = 1.963741016400274 absolute error = 8.881784197001252e-16 relative error = 4.52288979189446e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.000128 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] = 0.2800959999999941 y2[1] (analytic) = 0.7235520913874026 y2[1] (numeric) = 0.723552091387398 absolute error = 4.662936703425657e-15 relative error = 6.44450725653288e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.961028903740008 y1[1] (numeric) = 1.961028903740007 absolute error = 4.440892098500626e-16 relative error = 2.264572485408607e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.000128 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] = 0.2900799999999955 y2[1] (analytic) = 0.7139711163002567 y2[1] (numeric) = 0.7139711163002536 absolute error = 3.108624468950438e-15 relative error = 4.353991916450473e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.958220996268334 y1[1] (numeric) = 1.958220996268333 absolute error = 8.881784197001252e-16 relative error = 4.535639345062045e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.000128 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] = 0.3000639999999968 y2[1] (analytic) = 0.7044186524086267 y2[1] (numeric) = 0.7044186524086247 absolute error = 1.998401444325282e-15 relative error = 2.836951346322425e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.955317573875865 y1[1] (numeric) = 1.955317573875864 absolute error = 6.661338147750939e-16 relative error = 3.406780687060833e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.000128 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] = 0.3100479999999981 y2[1] (analytic) = 0.6948956518966489 y2[1] (numeric) = 0.6948956518966483 absolute error = 6.661338147750939e-16 relative error = 9.586098473302396e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.000128 y1[1] (analytic) = 1.952318925974082 y1[1] (numeric) = 1.952318925974081 absolute error = 8.881784197001252e-16 relative error = 4.549351071096036e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.000128 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] = 0.3200319999999994 y2[1] (analytic) = 0.6854030640115674 y2[1] (numeric) = 0.6854030640115681 absolute error = 7.771561172376096e-16 relative error = 1.133867293631611e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.949225351466495 y1[1] (numeric) = 1.949225351466494 absolute error = 8.881784197001252e-16 relative error = 4.556571250378549e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.000128 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] = 0.3300160000000008 y2[1] (analytic) = 0.6759418349691126 y2[1] (numeric) = 0.6759418349691146 absolute error = 1.998401444325282e-15 relative error = 2.956469537673458e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.946037158718839 y1[1] (numeric) = 1.946037158718839 absolute error = 6.661338147750939e-16 relative error = 3.423027210917384e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.000128 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] = 0.3400000000000021 y2[1] (analytic) = 0.6665129078591836 y2[1] (numeric) = 0.6665129078591874 absolute error = 3.774758283725532e-15 relative error = 5.663443632096976e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.942754665528346 y1[1] (numeric) = 1.942754665528345 absolute error = 1.110223024625157e-15 relative error = 5.714684639932257e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.000128 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] = 0.3501120000000034 y2[1] (analytic) = 0.6569969849515815 y2[1] (numeric) = 0.6569969849515866 absolute error = 5.10702591327572e-15 relative error = 7.773286682056982e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.939334302401277 y1[1] (numeric) = 1.939334302401277 absolute error = 2.220446049250313e-16 relative error = 1.144952701811629e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.000128 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] = 0.3600960000000047 y2[1] (analytic) = 0.6476359222532502 y2[1] (numeric) = 0.6476359222532564 absolute error = 6.217248937900877e-15 relative error = 9.599913661783722e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.935863001038978 y1[1] (numeric) = 1.935863001038979 absolute error = 8.881784197001252e-16 relative error = 4.588023115393185e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.000128 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] = 0.3700800000000061 y2[1] (analytic) = 0.6383099830046328 y2[1] (numeric) = 0.63830998300464 absolute error = 7.216449660063518e-15 relative error = 1.130555662954615e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.932298413388058 y1[1] (numeric) = 1.932298413388059 absolute error = 6.661338147750939e-16 relative error = 3.447365117932827e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.000128 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] = 0.3800640000000074 y2[1] (analytic) = 0.6290200968100192 y2[1] (numeric) = 0.6290200968100274 absolute error = 8.104628079763643e-15 relative error = 1.288452963723265e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.928640894764576 y1[1] (numeric) = 1.928640894764577 absolute error = 1.332267629550188e-15 relative error = 6.907805559690851e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.000128 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] = 0.3900480000000087 y2[1] (analytic) = 0.6197671896799515 y2[1] (numeric) = 0.6197671896799609 absolute error = 9.436895709313831e-15 relative error = 1.522651709618099e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.924890809747896 y1[1] (numeric) = 1.924890809747897 absolute error = 1.554312234475219e-15 relative error = 8.074807290907003e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.000128 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] = 0.40003200000001 y2[1] (analytic) = 0.6105521839389194 y2[1] (numeric) = 0.6105521839389301 absolute error = 1.06581410364015e-14 relative error = 1.745656033468183e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.921048532144346 y1[1] (numeric) = 1.921048532144348 absolute error = 2.220446049250313e-15 relative error = 1.155851094907929e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 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] = 0.4100160000000114 y2[1] (analytic) = 0.6013759981334242 y2[1] (numeric) = 0.6013759981334365 absolute error = 1.221245327087672e-14 relative error = 2.030751694244905e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.917114444949962 y1[1] (numeric) = 1.917114444949963 absolute error = 1.554312234475219e-15 relative error = 8.107561019998408e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.000128 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] = 0.4200000000000127 y2[1] (analytic) = 0.5922395469404182 y2[1] (numeric) = 0.592239546940432 absolute error = 1.376676550535194e-14 relative error = 2.324526549514083e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.913088940312303 y1[1] (numeric) = 1.913088940312305 absolute error = 1.998401444325282e-15 relative error = 1.044594112806408e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 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] = 0.430112000000014 y2[1] (analytic) = 0.5830273960216394 y2[1] (numeric) = 0.583027396021655 absolute error = 1.554312234475219e-14 relative error = 2.665933445119841e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.908919054444072 y1[1] (numeric) = 1.908919054444073 absolute error = 1.77635683940025e-15 relative error = 9.305563980121584e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.000128 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] = 0.4400960000000154 y2[1] (analytic) = 0.5739736807371798 y2[1] (numeric) = 0.5739736807371967 absolute error = 1.687538997430238e-14 relative error = 2.940098220641157e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.904710768862278 y1[1] (numeric) = 1.90471076886228 absolute error = 2.442490654175344e-15 relative error = 1.282342019641278e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 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] = 0.4500800000000167 y2[1] (analytic) = 0.5649624315125331 y2[1] (numeric) = 0.5649624315125509 absolute error = 1.77635683940025e-14 relative error = 3.144203473219517e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.900412302228547 y1[1] (numeric) = 1.90041230222855 absolute error = 2.442490654175344e-15 relative error = 1.285242497804882e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 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] = 0.460064000000018 y2[1] (analytic) = 0.5559945465838674 y2[1] (numeric) = 0.5559945465838859 absolute error = 1.854072451124011e-14 relative error = 3.334695389578501e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.896024083011575 y1[1] (numeric) = 1.896024083011579 absolute error = 3.33066907387547e-15 relative error = 1.75665968787968e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 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] = 0.4700480000000193 y2[1] (analytic) = 0.5470709198648225 y2[1] (numeric) = 0.5470709198648424 absolute error = 1.98729921407903e-14 relative error = 3.632617165193278e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.891546548626544 y1[1] (numeric) = 1.891546548626547 absolute error = 3.552713678800501e-15 relative error = 1.878205789532451e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 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] = 0.4800320000000207 y2[1] (analytic) = 0.5381924408574057 y2[1] (numeric) = 0.5381924408574265 absolute error = 2.076117056049043e-14 relative error = 3.8575737941275e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.886980145391518 y1[1] (numeric) = 1.886980145391524 absolute error = 5.10702591327572e-15 relative error = 2.706454503905812e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 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] = 0.490016000000022 y2[1] (analytic) = 0.5293599945633255 y2[1] (numeric) = 0.529359994563348 absolute error = 2.253752739989068e-14 relative error = 4.257504841952047e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.882325328482962 y1[1] (numeric) = 1.882325328482968 absolute error = 5.773159728050814e-15 relative error = 3.067036096626094e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 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 ( y2 , x , 1 ) = m1 * y1 + 1.0 ; diff ( y1 , x , 1 ) = y2 - 1.0 ; Iterations = 3125 Total Elapsed Time = 2.0 Seconds Elapsed Time(since restart) = 2.0 Seconds Time to Timeout = 9 Minutes 58.0 Seconds Percent Done = 100 %