##############ECHO OF PROBLEM################# ##############temp/mtest8postode.ode################# diff ( y2 , x , 4 ) = y1 - 1.0 ; diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=40; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=0.1; x_end=1.4; array_y1_init[0 + 1] = exact_soln_y1(x_start); array_y2_init[0 + 1] = exact_soln_y2(x_start); array_y2_init[1 + 1] = exact_soln_y2p(x_start); array_y2_init[2 + 1] = exact_soln_y2pp(x_start); array_y2_init[3 + 1] = exact_soln_y2ppp(x_start); glob_look_poles=true; 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 + sin(x)); } double exact_soln_y2 (double x) { return(1.0 + sin(x)); } double exact_soln_y2p (double x) { return( cos(x)); } double exact_soln_y2pp (double x) { return( -sin(x)); } double exact_soln_y2ppp (double x) { return( -cos(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 = 1.3 estimated_steps = 1300000 step_error = 2.192645048267573e-15 est_needed_step_err = 2.192645048267573e-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 = 1.099833416646828 glob_desired_digits_correct = 10 estimated_h = 1e-06 estimated_answer = 1.099833416646828 desired_abs_gbl_error = 1.099833416646828e-10 range = 1.3 estimated_steps = 1300000 step_error = 2.411544294929875e-15 est_needed_step_err = 2.411544294929875e-15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.683742500284562e-259 estimated_step_error = 2.683742500284562e-259 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 = 1.099833416646828 glob_desired_digits_correct = 10 estimated_h = 2e-06 estimated_answer = 1.099833416646828 desired_abs_gbl_error = 1.099833416646828e-10 range = 1.3 estimated_steps = 649999.9999999999 step_error = 3.410438648153292e-15 est_needed_step_err = 3.410438648153292e-15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.844254051529349e-248 estimated_step_error = 1.844254051529349e-248 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 = 1.099833416646828 glob_desired_digits_correct = 10 estimated_h = 4e-06 estimated_answer = 1.099833416646828 desired_abs_gbl_error = 1.099833416646828e-10 range = 1.3 estimated_steps = 324999.9999999999 step_error = 4.82308858985975e-15 est_needed_step_err = 4.82308858985975e-15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.267362075281025e-237 estimated_step_error = 1.267362075281025e-237 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 = 1.099833416646828 glob_desired_digits_correct = 10 estimated_h = 8e-06 estimated_answer = 1.099833416646828 desired_abs_gbl_error = 1.099833416646828e-10 range = 1.3 estimated_steps = 162500 step_error = 6.820877296306584e-15 est_needed_step_err = 6.820877296306584e-15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.709250556831444e-227 estimated_step_error = 8.709250556831444e-227 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 = 1.099833416646828 glob_desired_digits_correct = 10 estimated_h = 1.6e-05 estimated_answer = 1.099833416646828 desired_abs_gbl_error = 1.099833416646828e-10 range = 1.3 estimated_steps = 81249.99999999999 step_error = 9.646177179719501e-15 est_needed_step_err = 9.646177179719501e-15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.984957858910743e-216 estimated_step_error = 5.984957858910743e-216 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 = 1.099833416646828 glob_desired_digits_correct = 10 estimated_h = 3.2e-05 estimated_answer = 1.099833416646828 desired_abs_gbl_error = 1.099833416646828e-10 range = 1.3 estimated_steps = 40624.99999999999 step_error = 1.364175459261317e-14 est_needed_step_err = 1.364175459261317e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.112840586441793e-205 estimated_step_error = 4.112840586441793e-205 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 = 1.099833416646828 glob_desired_digits_correct = 10 estimated_h = 6.4e-05 estimated_answer = 1.099833416646828 desired_abs_gbl_error = 1.099833416646828e-10 range = 1.3 estimated_steps = 20312.5 step_error = 1.9292354359439e-14 est_needed_step_err = 1.9292354359439e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.82633471110443e-194 estimated_step_error = 2.82633471110443e-194 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 = 1.099833416646828 glob_desired_digits_correct = 10 estimated_h = 0.000128 estimated_answer = 1.099833416646828 desired_abs_gbl_error = 1.099833416646828e-10 range = 1.3 estimated_steps = 10156.25 step_error = 2.728350918522634e-14 est_needed_step_err = 2.728350918522634e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.942259165876972e-183 estimated_step_error = 1.942259165876972e-183 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) = 32.99 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) = 1.099833416646828 y2[1] (numeric) = 1.099833416646828 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.000128 y1[1] (analytic) = 1.099833416646828 y1[1] (numeric) = 1.099833416646828 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) = 1.109889623231384 y2[1] (numeric) = 1.109889623231384 absolute error = 4.440892098500626e-16 relative error = 4.001201565945997e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.000128 y1[1] (analytic) = 1.109889623231384 y1[1] (numeric) = 1.109889623231384 absolute error = 4.440892098500626e-16 relative error = 4.001201565945997e-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) = 1.119807516366182 y2[1] (numeric) = 1.119807516366181 absolute error = 2.220446049250313e-16 relative error = 1.982881894252457e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.000128 y1[1] (analytic) = 1.119807516366182 y1[1] (numeric) = 1.119807516366181 absolute error = 2.220446049250313e-16 relative error = 1.982881894252457e-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) = 1.129713467156278 y2[1] (numeric) = 1.129713467156278 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.000128 y1[1] (analytic) = 1.129713467156278 y1[1] (numeric) = 1.129713467156278 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] = 0.1400639999999994 y2[1] (analytic) = 1.139606488182166 y2[1] (numeric) = 1.139606488182167 absolute error = 1.554312234475219e-15 relative error = 1.363902584439097e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.139606488182166 y1[1] (numeric) = 1.139606488182167 absolute error = 1.554312234475219e-15 relative error = 1.363902584439097e-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] = 0.1500479999999985 y2[1] (analytic) = 1.149485593313168 y2[1] (numeric) = 1.14948559331317 absolute error = 1.998401444325282e-15 relative error = 1.73851804315814e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.149485593313168 y1[1] (numeric) = 1.14948559331317 absolute error = 2.220446049250313e-15 relative error = 1.931686714620155e-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] = 0.1600319999999977 y2[1] (analytic) = 1.159349797805735 y2[1] (numeric) = 1.159349797805738 absolute error = 2.664535259100376e-15 relative error = 2.298301396302873e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.159349797805735 y1[1] (numeric) = 1.159349797805738 absolute error = 2.886579864025407e-15 relative error = 2.489826512661446e-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] = 0.1700159999999968 y2[1] (analytic) = 1.169198118401607 y2[1] (numeric) = 1.169198118401611 absolute error = 3.996802888650564e-15 relative error = 3.418413719408419e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.169198118401607 y1[1] (numeric) = 1.169198118401612 absolute error = 4.218847493575595e-15 relative error = 3.608325592708886e-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] = 0.180127999999996 y2[1] (analytic) = 1.179155503951543 y2[1] (numeric) = 1.179155503951547 absolute error = 4.218847493575595e-15 relative error = 3.577855066136355e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.179155503951543 y1[1] (numeric) = 1.179155503951547 absolute error = 4.440892098500626e-15 relative error = 3.766163227511953e-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] = 0.1901119999999951 y2[1] (analytic) = 1.188968878266076 y2[1] (numeric) = 1.188968878266082 absolute error = 5.551115123125783e-15 relative error = 4.668848129331367e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.188968878266076 y1[1] (numeric) = 1.188968878266082 absolute error = 5.773159728050814e-15 relative error = 4.855602054504621e-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] = 0.2000959999999943 y2[1] (analytic) = 1.198763416270916 y2[1] (numeric) = 1.198763416270922 absolute error = 6.661338147750939e-15 relative error = 5.556841372814721e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.198763416270916 y1[1] (numeric) = 1.198763416270922 absolute error = 6.883382752675971e-15 relative error = 5.742069418575212e-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] = 0.2100799999999935 y2[1] (analytic) = 1.208538141652116 y2[1] (numeric) = 1.208538141652123 absolute error = 7.105427357601002e-15 relative error = 5.879357144564443e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.208538141652116 y1[1] (numeric) = 1.208538141652123 absolute error = 7.327471962526033e-15 relative error = 6.063087055332081e-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] = 0.2200639999999926 y2[1] (analytic) = 1.218292080070642 y2[1] (numeric) = 1.21829208007065 absolute error = 7.105427357601002e-15 relative error = 5.832285601978956e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.218292080070642 y1[1] (numeric) = 1.21829208007065 absolute error = 7.327471962526033e-15 relative error = 6.014544527040798e-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] = 0.2300479999999918 y2[1] (analytic) = 1.228024259259493 y2[1] (numeric) = 1.228024259259501 absolute error = 8.215650382226158e-15 relative error = 6.690136876595788e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.228024259259493 y1[1] (numeric) = 1.228024259259501 absolute error = 8.43769498715119e-15 relative error = 6.870951386774054e-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] = 0.2400319999999909 y2[1] (analytic) = 1.237733709120612 y2[1] (numeric) = 1.237733709120621 absolute error = 9.325873406851315e-15 relative error = 7.534636358475834e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.237733709120612 y1[1] (numeric) = 1.237733709120622 absolute error = 9.547918011776346e-15 relative error = 7.714032462249068e-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] = 0.2500159999999901 y2[1] (analytic) = 1.247419461821592 y2[1] (numeric) = 1.247419461821602 absolute error = 9.325873406851315e-15 relative error = 7.476132682131518e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.247419461821592 y1[1] (numeric) = 1.247419461821602 absolute error = 9.547918011776346e-15 relative error = 7.654135841229886e-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] = 0.2601279999999915 y2[1] (analytic) = 1.257204247703006 y2[1] (numeric) = 1.257204247703014 absolute error = 7.549516567451064e-15 relative error = 6.005004024799089e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.257204247703006 y1[1] (numeric) = 1.257204247703014 absolute error = 7.771561172376096e-15 relative error = 6.181621790234357e-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] = 0.2701119999999928 y2[1] (analytic) = 1.266839377356052 y2[1] (numeric) = 1.266839377356058 absolute error = 5.995204332975845e-15 relative error = 4.732410785563118e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.266839377356052 y1[1] (numeric) = 1.266839377356058 absolute error = 6.217248937900877e-15 relative error = 4.907685259102493e-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] = 0.2800959999999941 y2[1] (analytic) = 1.276447908612597 y2[1] (numeric) = 1.276447908612603 absolute error = 5.329070518200751e-15 relative error = 4.174922049105043e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.276447908612597 y1[1] (numeric) = 1.276447908612603 absolute error = 5.551115123125783e-15 relative error = 4.34887713448442e-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] = 0.2900799999999955 y2[1] (analytic) = 1.286028883699743 y2[1] (numeric) = 1.286028883699748 absolute error = 4.218847493575595e-15 relative error = 3.28052312591806e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.286028883699743 y1[1] (numeric) = 1.286028883699748 absolute error = 4.440892098500626e-15 relative error = 3.453182237808484e-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] = 0.3000639999999968 y2[1] (analytic) = 1.295581347591373 y2[1] (numeric) = 1.295581347591376 absolute error = 3.108624468950438e-15 relative error = 2.399405081533251e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.295581347591373 y1[1] (numeric) = 1.295581347591377 absolute error = 3.33066907387547e-15 relative error = 2.570791158785626e-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] = 0.3100479999999981 y2[1] (analytic) = 1.305104348103351 y2[1] (numeric) = 1.305104348103352 absolute error = 1.110223024625157e-15 relative error = 8.506775923615559e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.000128 y1[1] (analytic) = 1.305104348103351 y1[1] (numeric) = 1.305104348103352 absolute error = 1.332267629550188e-15 relative error = 1.020813110833867e-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] = 0.3200319999999994 y2[1] (analytic) = 1.314596935988433 y2[1] (numeric) = 1.314596935988432 absolute error = 4.440892098500626e-16 relative error = 3.378139699649887e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.000128 y1[1] (analytic) = 1.314596935988433 y1[1] (numeric) = 1.314596935988432 absolute error = 2.220446049250313e-16 relative error = 1.689069849824944e-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) = 1.324058165030887 y2[1] (numeric) = 1.324058165030886 absolute error = 1.332267629550188e-15 relative error = 1.0062002295187e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.324058165030887 y1[1] (numeric) = 1.324058165030886 absolute error = 1.110223024625157e-15 relative error = 8.385001912655835e-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) = 1.333487092140816 y2[1] (numeric) = 1.333487092140814 absolute error = 1.998401444325282e-15 relative error = 1.498628262773053e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.333487092140816 y1[1] (numeric) = 1.333487092140815 absolute error = 1.77635683940025e-15 relative error = 1.332114011353825e-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] = 0.3501120000000034 y2[1] (analytic) = 1.343003015048418 y2[1] (numeric) = 1.343003015048416 absolute error = 2.664535259100376e-15 relative error = 1.984012864635537e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.343003015048418 y1[1] (numeric) = 1.343003015048416 absolute error = 2.442490654175344e-15 relative error = 1.818678459249242e-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] = 0.3600960000000047 y2[1] (analytic) = 1.35236407774675 y2[1] (numeric) = 1.352364077746746 absolute error = 3.552713678800501e-15 relative error = 2.627039372947467e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.35236407774675 y1[1] (numeric) = 1.352364077746746 absolute error = 3.33066907387547e-15 relative error = 2.46284941213825e-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] = 0.3700800000000061 y2[1] (analytic) = 1.361690016995367 y2[1] (numeric) = 1.361690016995362 absolute error = 4.884981308350689e-15 relative error = 3.587440054183278e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.361690016995367 y1[1] (numeric) = 1.361690016995363 absolute error = 4.662936703425657e-15 relative error = 3.424374597174947e-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] = 0.3800640000000074 y2[1] (analytic) = 1.370979903189981 y2[1] (numeric) = 1.370979903189975 absolute error = 5.995204332975845e-15 relative error = 4.372933781907576e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.370979903189981 y1[1] (numeric) = 1.370979903189975 absolute error = 5.773159728050814e-15 relative error = 4.210973271466555e-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] = 0.3900480000000087 y2[1] (analytic) = 1.380232810320049 y2[1] (numeric) = 1.380232810320041 absolute error = 7.327471962526033e-15 relative error = 5.30886666925918e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.380232810320049 y1[1] (numeric) = 1.380232810320041 absolute error = 7.105427357601002e-15 relative error = 5.147991921705871e-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] = 0.40003200000001 y2[1] (analytic) = 1.389447816061081 y2[1] (numeric) = 1.389447816061072 absolute error = 8.659739592076221e-15 relative error = 6.232504374741869e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.389447816061081 y1[1] (numeric) = 1.389447816061072 absolute error = 8.43769498715119e-15 relative error = 6.072696570261309e-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) = 1.398624001866576 y2[1] (numeric) = 1.398624001866566 absolute error = 9.325873406851315e-15 relative error = 6.667891723869454e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.398624001866576 y1[1] (numeric) = 1.398624001866567 absolute error = 9.103828801926284e-15 relative error = 6.509132397110657e-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] = 0.4200000000000127 y2[1] (analytic) = 1.407760453059582 y2[1] (numeric) = 1.407760453059571 absolute error = 1.06581410364015e-14 relative error = 7.570990514215283e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.407760453059582 y1[1] (numeric) = 1.407760453059571 absolute error = 1.043609643147647e-14 relative error = 7.413261545169132e-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) = 1.416972603978361 y2[1] (numeric) = 1.416972603978349 absolute error = 1.199040866595169e-14 relative error = 8.461990466355412e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.416972603978361 y1[1] (numeric) = 1.416972603978349 absolute error = 1.176836406102666e-14 relative error = 8.305286939200683e-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] = 0.4400960000000154 y2[1] (analytic) = 1.42602631926282 y2[1] (numeric) = 1.426026319262807 absolute error = 1.354472090042691e-14 relative error = 9.498226447481566e-13 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.42602631926282 y1[1] (numeric) = 1.426026319262807 absolute error = 1.310063169057685e-14 relative error = 9.1868091869084e-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) = 1.435037568487467 y2[1] (numeric) = 1.435037568487452 absolute error = 1.443289932012704e-14 relative error = 1.00575062542365e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.435037568487467 y1[1] (numeric) = 1.435037568487453 absolute error = 1.398881011027697e-14 relative error = 9.748044523336914e-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) = 1.444005453416133 y2[1] (numeric) = 1.444005453416117 absolute error = 1.532107773982716e-14 relative error = 1.061012456953093e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.444005453416133 y1[1] (numeric) = 1.444005453416118 absolute error = 1.48769885299771e-14 relative error = 1.030258472693583e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 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) = 1.452929080135178 y2[1] (numeric) = 1.45292908013516 absolute error = 1.709743457922741e-14 relative error = 1.176756306483775e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.452929080135178 y1[1] (numeric) = 1.452929080135161 absolute error = 1.643130076445232e-14 relative error = 1.130908658179213e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 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) = 1.461807559142594 y2[1] (numeric) = 1.461807559142577 absolute error = 1.731947918415244e-14 relative error = 1.184798852340795e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.461807559142594 y1[1] (numeric) = 1.461807559142578 absolute error = 1.665334536937735e-14 relative error = 1.139229665712303e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 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) = 1.470640005436675 y2[1] (numeric) = 1.470640005436657 absolute error = 1.77635683940025e-14 relative error = 1.207880128946173e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.470640005436675 y1[1] (numeric) = 1.470640005436658 absolute error = 1.709743457922741e-14 relative error = 1.162584624110691e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 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] = 0.5000000000000233 y2[1] (analytic) = 1.479425538604223 y2[1] (numeric) = 1.479425538604205 absolute error = 1.865174681370263e-14 relative error = 1.26074251978236e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.479425538604223 y1[1] (numeric) = 1.479425538604205 absolute error = 1.798561299892754e-14 relative error = 1.215716001218704e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 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] = 0.5101120000000247 y2[1] (analytic) = 1.488274991205733 y2[1] (numeric) = 1.488274991205713 absolute error = 2.020605904817785e-14 relative error = 1.357683167934429e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.488274991205733 y1[1] (numeric) = 1.488274991205714 absolute error = 1.953992523340276e-14 relative error = 1.312924382178349e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 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] = 0.520096000000026 y2[1] (analytic) = 1.496963446195257 y2[1] (numeric) = 1.496963446195235 absolute error = 2.19824158875781e-14 relative error = 1.468467112102804e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.496963446195257 y1[1] (numeric) = 1.496963446195235 absolute error = 2.131628207280301e-14 relative error = 1.423968108705749e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 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] = 0.5300800000000273 y2[1] (analytic) = 1.505602364152731 y2[1] (numeric) = 1.505602364152709 absolute error = 2.264854970235319e-14 relative error = 1.504284945454275e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.505602364152731 y1[1] (numeric) = 1.505602364152709 absolute error = 2.19824158875781e-14 relative error = 1.460041270587973e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 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] = 0.5400640000000286 y2[1] (analytic) = 1.514190883955757 y2[1] (numeric) = 1.514190883955734 absolute error = 2.309263891220326e-14 relative error = 1.52508109491947e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.514190883955757 y1[1] (numeric) = 1.514190883955735 absolute error = 2.242650509742816e-14 relative error = 1.481088371027562e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 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] = 0.55004800000003 y2[1] (analytic) = 1.522728149505592 y2[1] (numeric) = 1.522728149505568 absolute error = 2.464695114667848e-14 relative error = 1.618604814961947e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.522728149505592 y1[1] (numeric) = 1.522728149505568 absolute error = 2.398081733190338e-14 relative error = 1.574858738881895e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 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] = 0.5600320000000313 y2[1] (analytic) = 1.53121330981249 y2[1] (numeric) = 1.531213309812464 absolute error = 2.620126338115369e-14 relative error = 1.711143915302189e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.53121330981249 y1[1] (numeric) = 1.531213309812465 absolute error = 2.55351295663786e-14 relative error = 1.667640256438574e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 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] = 0.5700160000000326 y2[1] (analytic) = 1.539645519080526 y2[1] (numeric) = 1.539645519080499 absolute error = 2.731148640577885e-14 relative error = 1.773881459551107e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.539645519080526 y1[1] (numeric) = 1.539645519080499 absolute error = 2.664535259100376e-14 relative error = 1.730616058098641e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 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] = 0.5800000000000339 y2[1] (analytic) = 1.548023936791902 y2[1] (numeric) = 1.548023936791874 absolute error = 2.775557561562891e-14 relative error = 1.792968116058275e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.548023936791902 y1[1] (numeric) = 1.548023936791875 absolute error = 2.708944180085382e-14 relative error = 1.749936881272877e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 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] = 0.5901120000000353 y2[1] (analytic) = 1.556454084779181 y2[1] (numeric) = 1.556454084779154 absolute error = 2.775557561562891e-14 relative error = 1.783256948409543e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.556454084779181 y1[1] (numeric) = 1.556454084779154 absolute error = 2.708944180085382e-14 relative error = 1.740458781647714e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 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] = 0.6000960000000366 y2[1] (analytic) = 1.564721703012103 y2[1] (numeric) = 1.564721703012073 absolute error = 2.953193245502916e-14 relative error = 1.887360058864138e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.564721703012103 y1[1] (numeric) = 1.564721703012074 absolute error = 2.886579864025407e-14 relative error = 1.844788027461187e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 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] = 0.6100800000000379 y2[1] (analytic) = 1.572933030108694 y2[1] (numeric) = 1.572933030108664 absolute error = 3.019806626980426e-14 relative error = 1.919857088112485e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.572933030108694 y1[1] (numeric) = 1.572933030108665 absolute error = 2.953193245502916e-14 relative error = 1.877507299404122e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 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] = 0.6200640000000393 y2[1] (analytic) = 1.581087247568568 y2[1] (numeric) = 1.581087247568537 absolute error = 3.130828929442941e-14 relative error = 1.980174676797629e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.581087247568568 y1[1] (numeric) = 1.581087247568537 absolute error = 3.064215547965432e-14 relative error = 1.938043300695551e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 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] = 0.6300480000000406 y2[1] (analytic) = 1.589183542583992 y2[1] (numeric) = 1.58918354258396 absolute error = 3.153033389935445e-14 relative error = 1.984058672548706e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.589183542583992 y1[1] (numeric) = 1.589183542583961 absolute error = 3.086420008457935e-14 relative error = 1.942141940030071e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 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] = 0.6400320000000419 y2[1] (analytic) = 1.59722110812091 y2[1] (numeric) = 1.597221108120876 absolute error = 3.33066907387547e-14 relative error = 2.085289918184163e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.59722110812091 y1[1] (numeric) = 1.597221108120877 absolute error = 3.26405569239796e-14 relative error = 2.04358411982048e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 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] = 0.6500160000000432 y2[1] (analytic) = 1.605199142999386 y2[1] (numeric) = 1.605199142999352 absolute error = 3.419486915845482e-14 relative error = 2.130257127758004e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.605199142999386 y1[1] (numeric) = 1.605199142999353 absolute error = 3.352873534367973e-14 relative error = 2.088758612282199e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 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] = 0.6600000000000446 y2[1] (analytic) = 1.613116851973469 y2[1] (numeric) = 1.613116851973434 absolute error = 3.486100297322992e-14 relative error = 2.16109595102062e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.613116851973469 y1[1] (numeric) = 1.613116851973435 absolute error = 3.419486915845482e-14 relative error = 2.119801123931053e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 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] = 0.6701120000000459 y2[1] (analytic) = 1.621073771168167 y2[1] (numeric) = 1.621073771168132 absolute error = 3.419486915845482e-14 relative error = 2.109396238877739e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.621073771168167 y1[1] (numeric) = 1.621073771168133 absolute error = 3.352873534367973e-14 relative error = 2.068304104354146e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 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] = 0.6800960000000472 y2[1] (analytic) = 1.628867668101913 y2[1] (numeric) = 1.628867668101878 absolute error = 3.463895836830488e-14 relative error = 2.126566758407635e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.628867668101913 y1[1] (numeric) = 1.628867668101879 absolute error = 3.375077994860476e-14 relative error = 2.072039405627952e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 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] = 0.6900800000000485 y2[1] (analytic) = 1.63659887986622 y2[1] (numeric) = 1.636598879866185 absolute error = 3.508304757815495e-14 relative error = 2.143655846875731e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.63659887986622 y1[1] (numeric) = 1.636598879866186 absolute error = 3.419486915845482e-14 relative error = 2.089386078600396e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 0.7000640000000499 y2[1] (analytic) = 1.644266635818324 y2[1] (numeric) = 1.644266635818288 absolute error = 3.663735981263017e-14 relative error = 2.228188483213756e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.644266635818324 y1[1] (numeric) = 1.644266635818288 absolute error = 3.574918139293004e-14 relative error = 2.174171792711604e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 0.7100480000000512 y2[1] (analytic) = 1.651870171640696 y2[1] (numeric) = 1.65187017164066 absolute error = 3.663735981263017e-14 relative error = 2.217932162080306e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.651870171640696 y1[1] (numeric) = 1.651870171640661 absolute error = 3.552713678800501e-14 relative error = 2.150722096562721e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 0.7200320000000525 y2[1] (analytic) = 1.659408729417236 y2[1] (numeric) = 1.659408729417198 absolute error = 3.752553823233029e-14 relative error = 2.261380066712606e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.659408729417236 y1[1] (numeric) = 1.6594087294172 absolute error = 3.641531520770513e-14 relative error = 2.194475331011049e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 0.7300160000000538 y2[1] (analytic) = 1.666881557708816 y2[1] (numeric) = 1.666881557708778 absolute error = 3.796962744218035e-14 relative error = 2.277883948417479e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.666881557708816 y1[1] (numeric) = 1.666881557708779 absolute error = 3.663735981263017e-14 relative error = 2.197958195841427e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 0.7400000000000552 y2[1] (analytic) = 1.674287911628186 y2[1] (numeric) = 1.674287911628147 absolute error = 3.930189507173054e-14 relative error = 2.347379730736444e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.674287911628186 y1[1] (numeric) = 1.674287911628148 absolute error = 3.796962744218035e-14 relative error = 2.267807536474192e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 0.7501120000000565 y2[1] (analytic) = 1.68172070490128 y2[1] (numeric) = 1.681720704901241 absolute error = 3.930189507173054e-14 relative error = 2.337004887743095e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.68172070490128 y1[1] (numeric) = 1.681720704901242 absolute error = 3.796962744218035e-14 relative error = 2.257784383073838e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 0.7600960000000578 y2[1] (analytic) = 1.688991026192967 y2[1] (numeric) = 1.688991026192928 absolute error = 3.930189507173054e-14 relative error = 2.326945167986955e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.688991026192967 y1[1] (numeric) = 1.68899102619293 absolute error = 3.796962744218035e-14 relative error = 2.248065670767058e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 0.7700800000000592 y2[1] (analytic) = 1.696192669253274 y2[1] (numeric) = 1.696192669253233 absolute error = 4.085620730620576e-14 relative error = 2.408700853788748e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.696192669253274 y1[1] (numeric) = 1.696192669253235 absolute error = 3.952393967665557e-14 relative error = 2.330156260730419e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 0.7800640000000605 y2[1] (analytic) = 1.703324916226539 y2[1] (numeric) = 1.703324916226496 absolute error = 4.263256414560601e-14 relative error = 2.50290263116987e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.703324916226539 y1[1] (numeric) = 1.703324916226497 absolute error = 4.130029651605582e-14 relative error = 2.424686923945811e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 0.7900480000000618 y2[1] (analytic) = 1.710387056174463 y2[1] (numeric) = 1.710387056174418 absolute error = 4.440892098500626e-14 relative error = 2.596425225780969e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.710387056174463 y1[1] (numeric) = 1.71038705617442 absolute error = 4.307665335545607e-14 relative error = 2.51853246900754e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 0.8000320000000631 y2[1] (analytic) = 1.717378385146976 y2[1] (numeric) = 1.717378385146931 absolute error = 4.463096558993129e-14 relative error = 2.598784634529549e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.717378385146976 y1[1] (numeric) = 1.717378385146932 absolute error = 4.329869796038111e-14 relative error = 2.521208973797323e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 0.8100160000000645 y2[1] (analytic) = 1.724298206252405 y2[1] (numeric) = 1.724298206252359 absolute error = 4.618527782440651e-14 relative error = 2.678497121723842e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.724298206252405 y1[1] (numeric) = 1.72429820625236 absolute error = 4.463096558993129e-14 relative error = 2.588355391665828e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 0.8200000000000658 y2[1] (analytic) = 1.731145829726941 y2[1] (numeric) = 1.731145829726893 absolute error = 4.729550084903167e-14 relative error = 2.732034473172704e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.731145829726941 y1[1] (numeric) = 1.731145829726895 absolute error = 4.574118861455645e-14 relative error = 2.642249302692851e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 0.8301120000000671 y2[1] (analytic) = 1.738006952566672 y2[1] (numeric) = 1.738006952566625 absolute error = 4.75175454539567e-14 relative error = 2.734025050002432e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.738006952566672 y1[1] (numeric) = 1.738006952566627 absolute error = 4.551914400963142e-14 relative error = 2.619042688086441e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 0.8400960000000685 y2[1] (analytic) = 1.744707192970772 y2[1] (numeric) = 1.744707192970723 absolute error = 4.862776847858186e-14 relative error = 2.787159282342484e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.744707192970772 y1[1] (numeric) = 1.744707192970725 absolute error = 4.662936703425657e-14 relative error = 2.67261848991745e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 0.8500800000000698 y2[1] (analytic) = 1.751333201387856 y2[1] (numeric) = 1.751333201387808 absolute error = 4.840572387365683e-14 relative error = 2.763935716818329e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.751333201387856 y1[1] (numeric) = 1.75133320138781 absolute error = 4.640732242933154e-14 relative error = 2.649828278968031e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 0.8600640000000711 y2[1] (analytic) = 1.757884317341196 y2[1] (numeric) = 1.757884317341146 absolute error = 4.929390229335695e-14 relative error = 2.804160763429194e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.757884317341196 y1[1] (numeric) = 1.757884317341149 absolute error = 4.685141163918161e-14 relative error = 2.665215860736757e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 0.8700480000000724 y2[1] (analytic) = 1.764359887819301 y2[1] (numeric) = 1.764359887819251 absolute error = 4.996003610813204e-14 relative error = 2.831623891080479e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.764359887819301 y1[1] (numeric) = 1.764359887819253 absolute error = 4.729550084903167e-14 relative error = 2.680603950222853e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 0.8800320000000738 y2[1] (analytic) = 1.770759267341009 y2[1] (numeric) = 1.770759267340959 absolute error = 4.996003610813204e-14 relative error = 2.821390633361054e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.770759267341009 y1[1] (numeric) = 1.770759267340962 absolute error = 4.729550084903167e-14 relative error = 2.670916466248464e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 0.8900160000000751 y2[1] (analytic) = 1.777081818019831 y2[1] (numeric) = 1.77708181801978 absolute error = 5.084821452783217e-14 relative error = 2.861332213982775e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.777081818019831 y1[1] (numeric) = 1.777081818019783 absolute error = 4.75175454539567e-14 relative error = 2.673908706516654e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 0.9000000000000764 y2[1] (analytic) = 1.783326909627531 y2[1] (numeric) = 1.783326909627479 absolute error = 5.151434834260726e-14 relative error = 2.888665452447339e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.783326909627531 y1[1] (numeric) = 1.783326909627483 absolute error = 4.818367926873179e-14 relative error = 2.701898289573589e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 0.9101120000000777 y2[1] (analytic) = 1.78957247426203 y2[1] (numeric) = 1.789572474261977 absolute error = 5.240252676230739e-14 relative error = 2.928214839911233e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.78957247426203 y1[1] (numeric) = 1.789572474261981 absolute error = 4.884981308350689e-14 relative error = 2.729691799917251e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 0.9200960000000791 y2[1] (analytic) = 1.79565977510523 y2[1] (numeric) = 1.795659775105177 absolute error = 5.306866057708248e-14 relative error = 2.955385051935717e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.79565977510523 y1[1] (numeric) = 1.795659775105181 absolute error = 4.951594689828198e-14 relative error = 2.757535006617845e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 0.9300800000000804 y2[1] (analytic) = 1.801667765037173 y2[1] (numeric) = 1.80166776503712 absolute error = 5.351274978693255e-14 relative error = 2.970178565959326e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.801667765037173 y1[1] (numeric) = 1.801667765037124 absolute error = 4.951594689828198e-14 relative error = 2.748339502941617e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 0.9400640000000817 y2[1] (analytic) = 1.80759584518486 y2[1] (numeric) = 1.807595845184806 absolute error = 5.329070518200751e-14 relative error = 2.948153776960998e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.80759584518486 y1[1] (numeric) = 1.807595845184811 absolute error = 4.907185768843192e-14 relative error = 2.714758269618252e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 0.950048000000083 y2[1] (analytic) = 1.813443424640651 y2[1] (numeric) = 1.813443424640597 absolute error = 5.395683899678261e-14 relative error = 2.97538033244542e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.813443424640651 y1[1] (numeric) = 1.813443424640602 absolute error = 4.929390229335695e-14 relative error = 2.718248698777297e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 0.9600320000000844 y2[1] (analytic) = 1.819209920521172 y2[1] (numeric) = 1.819209920521118 absolute error = 5.417888360170764e-14 relative error = 2.978154581863006e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.819209920521172 y1[1] (numeric) = 1.819209920521122 absolute error = 4.951594689828198e-14 relative error = 2.721837998997748e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 0.9700160000000857 y2[1] (analytic) = 1.824894758025411 y2[1] (numeric) = 1.824894758025357 absolute error = 5.440092820663267e-14 relative error = 2.981044685858819e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.824894758025411 y1[1] (numeric) = 1.824894758025362 absolute error = 4.951594689828198e-14 relative error = 2.713359040598027e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 0.980000000000087 y2[1] (analytic) = 1.830497370492019 y2[1] (numeric) = 1.830497370491964 absolute error = 5.506706202140776e-14 relative error = 3.008311451799917e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.830497370492019 y1[1] (numeric) = 1.83049737049197 absolute error = 4.951594689828198e-14 relative error = 2.705054248997506e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 0.9901120000000884 y2[1] (analytic) = 1.836087426621271 y2[1] (numeric) = 1.836087426621216 absolute error = 5.46229728115577e-14 relative error = 2.974965789732232e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.836087426621271 y1[1] (numeric) = 1.836087426621222 absolute error = 4.907185768843192e-14 relative error = 2.672631868011477e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 1.00009600000009 y2[1] (analytic) = 1.84152284995173 y2[1] (numeric) = 1.841522849951676 absolute error = 5.46229728115577e-14 relative error = 2.966184905769129e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.84152284995173 y1[1] (numeric) = 1.841522849951681 absolute error = 4.907185768843192e-14 relative error = 2.664743350304786e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 1.010080000000082 y2[1] (analytic) = 1.846874390765862 y2[1] (numeric) = 1.846874390765811 absolute error = 5.10702591327572e-14 relative error = 2.765226448972493e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.846874390765862 y1[1] (numeric) = 1.846874390765817 absolute error = 4.463096558993129e-14 relative error = 2.416567461928135e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 1.020064000000075 y2[1] (analytic) = 1.852141515625142 y2[1] (numeric) = 1.852141515625096 absolute error = 4.618527782440651e-14 relative error = 2.493614955162747e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.852141515625142 y1[1] (numeric) = 1.852141515625103 absolute error = 3.952393967665557e-14 relative error = 2.133958952014274e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 1.030048000000068 y2[1] (analytic) = 1.857323699505579 y2[1] (numeric) = 1.857323699505537 absolute error = 4.174438572590589e-14 relative error = 2.24755575654466e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.857323699505579 y1[1] (numeric) = 1.857323699505544 absolute error = 3.486100297322992e-14 relative error = 1.87694815839102e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 1.04003200000006 y2[1] (analytic) = 1.862420425850047 y2[1] (numeric) = 1.862420425850009 absolute error = 3.730349362740526e-14 relative error = 2.002957716186944e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.862420425850047 y1[1] (numeric) = 1.862420425850016 absolute error = 3.019806626980426e-14 relative error = 1.621441960722765e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 1.050016000000053 y2[1] (analytic) = 1.867431186619779 y2[1] (numeric) = 1.867431186619746 absolute error = 3.33066907387547e-14 relative error = 1.783556522853345e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.867431186619779 y1[1] (numeric) = 1.867431186619753 absolute error = 2.55351295663786e-14 relative error = 1.367393334187565e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 1.060000000000046 y2[1] (analytic) = 1.872355482345009 y2[1] (numeric) = 1.872355482344978 absolute error = 3.042011087472929e-14 relative error = 1.624697401832583e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.872355482345009 y1[1] (numeric) = 1.872355482344986 absolute error = 2.242650509742816e-14 relative error = 1.197769617409423e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 1.070112000000038 y2[1] (analytic) = 1.877254272686437 y2[1] (numeric) = 1.87725427268641 absolute error = 2.708944180085382e-14 relative error = 1.443035298680534e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.877254272686437 y1[1] (numeric) = 1.877254272686418 absolute error = 1.887379141862766e-14 relative error = 1.005393445802012e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 1.080096000000031 y2[1] (analytic) = 1.882003050343791 y2[1] (numeric) = 1.882003050343769 absolute error = 2.264854970235319e-14 relative error = 1.203427895518868e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.882003050343791 y1[1] (numeric) = 1.882003050343777 absolute error = 1.443289932012704e-14 relative error = 7.668903255757493e-13 % Desired digits = 10 Estimated correct digits = 10 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] = 1.090080000000023 y2[1] (analytic) = 1.886663910441603 y2[1] (numeric) = 1.886663910441582 absolute error = 2.065014825802791e-14 relative error = 1.094532425396022e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 0.000128 y1[1] (analytic) = 1.886663910441603 y1[1] (numeric) = 1.886663910441591 absolute error = 1.13242748511766e-14 relative error = 6.002274590881413e-13 % Desired digits = 10 Estimated correct digits = 10 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] = 1.100064000000016 y2[1] (analytic) = 1.891236388388001 y2[1] (numeric) = 1.891236388387984 absolute error = 1.731947918415244e-14 relative error = 9.157754837254759e-13 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.891236388388001 y1[1] (numeric) = 1.891236388387993 absolute error = 7.993605777301127e-15 relative error = 4.226656078732966e-13 % Desired digits = 10 Estimated correct digits = 10 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] = 1.110048000000009 y2[1] (analytic) = 1.895720028401002 y2[1] (numeric) = 1.895720028400987 absolute error = 1.465494392505207e-14 relative error = 7.730542329825564e-13 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.895720028401002 y1[1] (numeric) = 1.895720028400997 absolute error = 5.10702591327572e-15 relative error = 2.693976872514969e-13 % Desired digits = 10 Estimated correct digits = 10 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] = 1.120032000000001 y2[1] (analytic) = 1.900114383553933 y2[1] (numeric) = 1.900114383553921 absolute error = 1.199040866595169e-14 relative error = 6.31036150756624e-13 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.900114383553933 y1[1] (numeric) = 1.900114383553931 absolute error = 1.998401444325282e-15 relative error = 1.051726917927707e-13 % Desired digits = 10 Estimated correct digits = 10 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] = 1.130015999999994 y2[1] (analytic) = 1.904419015819985 y2[1] (numeric) = 1.904419015819976 absolute error = 9.325873406851315e-15 relative error = 4.896965074062693e-13 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.904419015819985 y1[1] (numeric) = 1.904419015819986 absolute error = 8.881784197001252e-16 relative error = 4.663776261012089e-14 % Desired digits = 10 Estimated correct digits = 10 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] = 1.140127999999987 y2[1] (analytic) = 1.908686940768713 y2[1] (numeric) = 1.908686940768707 absolute error = 5.551115123125783e-15 relative error = 2.908342381642797e-13 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.908686940768713 y1[1] (numeric) = 1.908686940768717 absolute error = 4.662936703425657e-15 relative error = 2.44300760057995e-13 % Desired digits = 10 Estimated correct digits = 10 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] = 1.150111999999979 y2[1] (analytic) = 1.91280968512894 y2[1] (numeric) = 1.912809685128937 absolute error = 3.108624468950438e-15 relative error = 1.625161401637764e-13 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.91280968512894 y1[1] (numeric) = 1.912809685128948 absolute error = 7.105427357601002e-15 relative error = 3.714654632314889e-13 % Desired digits = 10 Estimated correct digits = 10 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] = 1.160095999999972 y2[1] (analytic) = 1.916841441141891 y2[1] (numeric) = 1.91684144114189 absolute error = 8.881784197001252e-16 relative error = 4.633551845430804e-14 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 16 h = 0.000128 y1[1] (analytic) = 1.916841441141891 y1[1] (numeric) = 1.916841441141901 absolute error = 9.992007221626409e-15 relative error = 5.212745826109654e-13 % Desired digits = 10 Estimated correct digits = 10 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] = 1.170079999999965 y2[1] (analytic) = 1.920781806924431 y2[1] (numeric) = 1.920781806924432 absolute error = 8.881784197001252e-16 relative error = 4.624046398702008e-14 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 16 h = 0.000128 y1[1] (analytic) = 1.920781806924431 y1[1] (numeric) = 1.920781806924444 absolute error = 1.265654248072678e-14 relative error = 6.589266118150362e-13 % Desired digits = 10 Estimated correct digits = 10 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] = 1.180063999999957 y2[1] (analytic) = 1.924630389703154 y2[1] (numeric) = 1.924630389703156 absolute error = 2.442490654175344e-15 relative error = 1.269069982082151e-13 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.924630389703154 y1[1] (numeric) = 1.924630389703168 absolute error = 1.443289932012704e-14 relative error = 7.499049894121801e-13 % Desired digits = 10 Estimated correct digits = 10 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] = 1.19004799999995 y2[1] (analytic) = 1.928386805853529 y2[1] (numeric) = 1.928386805853533 absolute error = 4.440892098500626e-15 relative error = 2.302905249621343e-13 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.928386805853529 y1[1] (numeric) = 1.928386805853546 absolute error = 1.731947918415244e-14 relative error = 8.98133047352324e-13 % Desired digits = 10 Estimated correct digits = 10 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] = 1.200031999999943 y2[1] (analytic) = 1.932050680938143 y2[1] (numeric) = 1.932050680938148 absolute error = 5.551115123125783e-15 relative error = 2.873172623210037e-13 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.932050680938143 y1[1] (numeric) = 1.932050680938162 absolute error = 1.909583602355269e-14 relative error = 9.883713823842528e-13 % Desired digits = 10 Estimated correct digits = 10 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] = 1.210015999999935 y2[1] (analytic) = 1.935621649744024 y2[1] (numeric) = 1.935621649744031 absolute error = 7.327471962526033e-15 relative error = 3.78559103402003e-13 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.935621649744024 y1[1] (numeric) = 1.935621649744045 absolute error = 2.153832667772804e-14 relative error = 1.112734334242251e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 1.220127999999928 y2[1] (analytic) = 1.939143335281349 y2[1] (numeric) = 1.939143335281359 absolute error = 9.103828801926284e-15 relative error = 4.694768373378348e-13 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.939143335281349 y1[1] (numeric) = 1.939143335281373 absolute error = 2.398081733190338e-14 relative error = 1.236670693475272e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 1.230111999999921 y2[1] (analytic) = 1.942526230645741 y2[1] (numeric) = 1.942526230645752 absolute error = 1.088018564132653e-14 relative error = 5.601049535228004e-13 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.942526230645741 y1[1] (numeric) = 1.942526230645767 absolute error = 2.620126338115369e-14 relative error = 1.348824173789601e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 1.240095999999913 y2[1] (analytic) = 1.945815175534596 y2[1] (numeric) = 1.945815175534608 absolute error = 1.221245327087672e-14 relative error = 6.276265816213225e-13 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.945815175534596 y1[1] (numeric) = 1.945815175534624 absolute error = 2.775557561562891e-14 relative error = 1.426424049139369e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 1.250079999999906 y2[1] (analytic) = 1.94900984210777 y2[1] (numeric) = 1.949009842107783 absolute error = 1.310063169057685e-14 relative error = 6.721685754243846e-13 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.94900984210777 y1[1] (numeric) = 1.949009842107799 absolute error = 2.90878432451791e-14 relative error = 1.492442091196515e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 1.260063999999899 y2[1] (analytic) = 1.952109911922727 y2[1] (numeric) = 1.95210991192274 absolute error = 1.376676550535194e-14 relative error = 7.052249169613813e-13 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.952109911922727 y1[1] (numeric) = 1.952109911922757 absolute error = 3.042011087472929e-14 relative error = 1.558319574575955e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 1.270047999999891 y2[1] (analytic) = 1.955115075966279 y2[1] (numeric) = 1.955115075966294 absolute error = 1.48769885299771e-14 relative error = 7.609264903562991e-13 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.955115075966279 y1[1] (numeric) = 1.955115075966311 absolute error = 3.219646771412954e-14 relative error = 1.646781210472588e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 1.280031999999884 y2[1] (analytic) = 1.958025034685394 y2[1] (numeric) = 1.95802503468541 absolute error = 1.598721155460225e-14 relative error = 8.164967899489089e-13 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.958025034685394 y1[1] (numeric) = 1.958025034685428 absolute error = 3.33066907387547e-14 relative error = 1.701034979060227e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 1.290015999999877 y2[1] (analytic) = 1.960839498017052 y2[1] (numeric) = 1.960839498017069 absolute error = 1.665334536937735e-14 relative error = 8.492967112412035e-13 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.960839498017052 y1[1] (numeric) = 1.960839498017087 absolute error = 3.463895836830488e-14 relative error = 1.766537159381703e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 1.300127999999869 y2[1] (analytic) = 1.96359241737366 y2[1] (numeric) = 1.963592417373676 absolute error = 1.620925615952729e-14 relative error = 8.254898529913584e-13 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.96359241737366 y1[1] (numeric) = 1.963592417373696 absolute error = 3.61932706027801e-14 relative error = 1.843217069008102e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 1.310111999999862 y2[1] (analytic) = 1.96621382475637 y2[1] (numeric) = 1.966213824756386 absolute error = 1.665334536937735e-14 relative error = 8.469752963638549e-13 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.96621382475637 y1[1] (numeric) = 1.966213824756407 absolute error = 3.708144902248023e-14 relative error = 1.885931659903517e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 1.320095999999854 y2[1] (analytic) = 1.968738920497712 y2[1] (numeric) = 1.968738920497728 absolute error = 1.576516694967722e-14 relative error = 8.007748912533141e-13 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.968738920497712 y1[1] (numeric) = 1.96873892049775 absolute error = 3.796962744218035e-14 relative error = 1.928626850765024e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 1.330079999999847 y2[1] (analytic) = 1.971167452897588 y2[1] (numeric) = 1.971167452897603 absolute error = 1.532107773982716e-14 relative error = 7.772590663114591e-13 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.971167452897588 y1[1] (numeric) = 1.971167452897626 absolute error = 3.796962744218035e-14 relative error = 1.926250729554485e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 1.34006399999984 y2[1] (analytic) = 1.973499179881276 y2[1] (numeric) = 1.973499179881291 absolute error = 1.48769885299771e-14 relative error = 7.538380903138802e-13 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.973499179881276 y1[1] (numeric) = 1.973499179881314 absolute error = 3.796962744218035e-14 relative error = 1.923974827517515e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 1.350047999999832 y2[1] (analytic) = 1.975733869023566 y2[1] (numeric) = 1.975733869023579 absolute error = 1.332267629550188e-14 relative error = 6.743153267948039e-13 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.975733869023566 y1[1] (numeric) = 1.975733869023603 absolute error = 3.774758283725532e-14 relative error = 1.910560092585278e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 1.360031999999825 y2[1] (analytic) = 1.97787129757192 y2[1] (numeric) = 1.977871297571933 absolute error = 1.287858708565182e-14 relative error = 6.511337265201159e-13 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.97787129757192 y1[1] (numeric) = 1.977871297571958 absolute error = 3.774758283725532e-14 relative error = 1.908495405317581e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 1.370015999999818 y2[1] (analytic) = 1.979911252468685 y2[1] (numeric) = 1.979911252468698 absolute error = 1.243449787580175e-14 relative error = 6.280330929125026e-13 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.979911252468685 y1[1] (numeric) = 1.979911252468723 absolute error = 3.774758283725532e-14 relative error = 1.906529032055811e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 1.38012799999981 y2[1] (analytic) = 1.98187779635532 y2[1] (numeric) = 1.981877796355331 absolute error = 1.176836406102666e-14 relative error = 5.937986732920023e-13 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.98187779635532 y1[1] (numeric) = 1.981877796355357 absolute error = 3.774758283725532e-14 relative error = 1.904637253955479e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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] = 1.390111999999803 y2[1] (analytic) = 1.983720947694927 y2[1] (numeric) = 1.983720947694938 absolute error = 1.088018564132653e-14 relative error = 5.484735972551609e-13 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 15 h = 0.000128 y1[1] (analytic) = 1.983720947694927 y1[1] (numeric) = 1.983720947694964 absolute error = 3.708144902248023e-14 relative error = 1.869287566155344e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 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 , 4 ) = y1 - 1.0 ; diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ; Iterations = 10157 Total Elapsed Time = 15.0 Seconds Elapsed Time(since restart) = 15.0 Seconds Time to Timeout = 9 Minutes 45.0 Seconds Percent Done = 100 %