##############ECHO OF PROBLEM################# ##############temp/sub_full_linpostode.ode################# diff ( y , x , 1 ) = sin ( 0.3 * x + 0.1 ) - ( 0.1 * x + 0.2 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=40; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=0.1; x_end=5.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=3; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=16; glob_max_minutes=3.0; glob_subiter_method=3; glob_max_iter=100000000; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(-0.05 * x * x - 0.2 * x - cos(0.3 * x + 0.1) / 0.3); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 4900000.000000001 step_error = 1.129384878631564e-21 est_needed_step_err = 1.129384878631564e-21 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 min_size = 3.325706312382627 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 3.325706312382627 desired_abs_gbl_error = 3.325706312382627e-16 range = 4.9 estimated_steps = 4900000.000000001 step_error = 3.756002419974479e-21 est_needed_step_err = 3.756002419974479e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.333609234489469e-276 estimated_step_error = 1.333609234489469e-276 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 min_size = 3.325706312382627 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 3.325706312382627 desired_abs_gbl_error = 3.325706312382627e-16 range = 4.9 estimated_steps = 2450000 step_error = 5.311789562634075e-21 est_needed_step_err = 5.311789562634075e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.164492871584052e-266 estimated_step_error = 9.164492871584052e-266 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 min_size = 3.325706312382627 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 3.325706312382627 desired_abs_gbl_error = 3.325706312382627e-16 range = 4.9 estimated_steps = 1225000 step_error = 7.512004839948959e-21 est_needed_step_err = 7.512004839948959e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.297791540184716e-255 estimated_step_error = 6.297791540184716e-255 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 min_size = 3.325706312382627 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 3.325706312382627 desired_abs_gbl_error = 3.325706312382627e-16 range = 4.9 estimated_steps = 612500.0000000001 step_error = 1.062357912526815e-20 est_needed_step_err = 1.062357912526815e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.327809383163773e-244 estimated_step_error = 4.327809383163773e-244 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 min_size = 3.325706312382627 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 3.325706312382627 desired_abs_gbl_error = 3.325706312382627e-16 range = 4.9 estimated_steps = 306250.0000000001 step_error = 1.502400967989792e-20 est_needed_step_err = 1.502400967989792e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.974047949631297e-233 estimated_step_error = 2.974047949631297e-233 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 min_size = 3.325706312382627 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 3.325706312382627 desired_abs_gbl_error = 3.325706312382627e-16 range = 4.9 estimated_steps = 153125 step_error = 2.12471582505363e-20 est_needed_step_err = 2.12471582505363e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.043750171532809e-222 estimated_step_error = 2.043750171532809e-222 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 min_size = 3.325706312382627 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 3.325706312382627 desired_abs_gbl_error = 3.325706312382627e-16 range = 4.9 estimated_steps = 76562.50000000001 step_error = 3.004801935979583e-20 est_needed_step_err = 3.004801935979583e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.404454399848107e-211 estimated_step_error = 1.404454399848107e-211 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 min_size = 3.325706312382627 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 3.325706312382627 desired_abs_gbl_error = 3.325706312382627e-16 range = 4.9 estimated_steps = 38281.25000000001 step_error = 4.24943165010726e-20 est_needed_step_err = 4.24943165010726e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.651336818328237e-201 estimated_step_error = 9.651336818328237e-201 Double H and LOOP opt_iter = 9 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 min_size = 3.325706312382627 glob_desired_digits_correct = 16 estimated_h = 0.000256 estimated_answer = 3.325706312382627 desired_abs_gbl_error = 3.325706312382627e-16 range = 4.9 estimated_steps = 19140.625 step_error = 6.009603871959167e-20 est_needed_step_err = 6.009603871959167e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.632347709626615e-190 estimated_step_error = 6.632347709626615e-190 Double H and LOOP opt_iter = 10 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 min_size = 3.325706312382627 glob_desired_digits_correct = 16 estimated_h = 0.000512 estimated_answer = 3.325706312382627 desired_abs_gbl_error = 3.325706312382627e-16 range = 4.9 estimated_steps = 9570.312500000002 step_error = 8.49886330021452e-20 est_needed_step_err = 8.49886330021452e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.557714022943496e-179 estimated_step_error = 4.557714022943496e-179 Double H and LOOP opt_iter = 11 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4285 Order of pole (three term test) = 32.02 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE ACCURACY START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = -3.325706312382627 y[1] (numeric) = -3.325706312382627 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 0.2003520000000018 y[1] (closed_form) = -3.332778959090454 y[1] (numeric) = -3.332778959090456 absolute error = 1.77635683940025e-15 relative error = 5.329956955456279e-14 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 16 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 0.3001920000000042 y[1] (closed_form) = -3.337855345896195 y[1] (numeric) = -3.337855345896196 absolute error = 8.881784197001252e-16 relative error = 2.660925437623045e-14 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 16 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 0.4000320000000066 y[1] (closed_form) = -3.340992194322049 y[1] (numeric) = -3.340992194322049 absolute error = 4.440892098500626e-16 relative error = 1.329213551006744e-14 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 16 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 0.500384000000009 y[1] (closed_form) = -3.34220905519068 y[1] (numeric) = -3.342209055190679 absolute error = 1.332267629550188e-15 relative error = 3.986188797738684e-14 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 16 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 0.6002240000000006 y[1] (closed_form) = -3.341514459312851 y[1] (numeric) = -3.341514459312848 absolute error = 2.664535259100376e-15 relative error = 7.974034802316286e-14 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 16 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 0.7000639999999922 y[1] (closed_form) = -3.338942988819334 y[1] (numeric) = -3.33894298881933 absolute error = 3.996802888650564e-15 relative error = 1.197026394890274e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 0.8004159999999838 y[1] (closed_form) = -3.334493285311582 y[1] (numeric) = -3.334493285311578 absolute error = 4.440892098500626e-15 relative error = 1.331804180881912e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 0.9002559999999754 y[1] (closed_form) = -3.328239479247941 y[1] (numeric) = -3.328239479247934 absolute error = 6.661338147750939e-15 relative error = 2.001459987866064e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 1.000095999999967 y[1] (closed_form) = -3.320194728369622 y[1] (numeric) = -3.320194728369612 absolute error = 9.325873406851315e-15 relative error = 2.808833267267663e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 1.10044799999998 y[1] (closed_form) = -3.310337936800934 y[1] (numeric) = -3.310337936800926 absolute error = 7.993605777301127e-15 relative error = 2.414740105061914e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 1.200287999999994 y[1] (closed_form) = -3.298805954362645 y[1] (numeric) = -3.29880595436264 absolute error = 4.884981308350689e-15 relative error = 1.480833179014467e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 1.300128000000007 y[1] (closed_form) = -3.285591527237512 y[1] (numeric) = -3.285591527237507 absolute error = 4.440892098500626e-15 relative error = 1.351626354550067e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 1.39996800000002 y[1] (closed_form) = -3.27073561900781 y[1] (numeric) = -3.270735619007804 absolute error = 5.773159728050814e-15 relative error = 1.765095195863652e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 1.500320000000033 y[1] (closed_form) = -3.254193138977236 y[1] (numeric) = -3.254193138977234 absolute error = 2.220446049250313e-15 relative error = 6.823338242143118e-14 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 16 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 1.600160000000047 y[1] (closed_form) = -3.236178747288745 y[1] (numeric) = -3.236178747288744 absolute error = 1.332267629550188e-15 relative error = 4.116792469100649e-14 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 16 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 1.70000000000006 y[1] (closed_form) = -3.21666005948492 y[1] (numeric) = -3.216660059484923 absolute error = 2.664535259100376e-15 relative error = 8.283546317689052e-14 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 16 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 1.800352000000073 y[1] (closed_form) = -3.19557606477376 y[1] (numeric) = -3.195576064773765 absolute error = 5.773159728050814e-15 relative error = 1.80661001679506e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 1.900192000000086 y[1] (closed_form) = -3.173194534469013 y[1] (numeric) = -3.173194534469022 absolute error = 9.325873406851315e-15 relative error = 2.938954200742648e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 2.0000320000001 y[1] (closed_form) = -3.149466142582666 y[1] (numeric) = -3.149466142582678 absolute error = 1.199040866595169e-14 relative error = 3.807124167437202e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 2.100384000000113 y[1] (closed_form) = -3.124316027434332 y[1] (numeric) = -3.124316027434349 absolute error = 1.687538997430238e-14 relative error = 5.401306982431076e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 2.200224000000126 y[1] (closed_form) = -3.098059794452789 y[1] (numeric) = -3.098059794452809 absolute error = 1.953992523340276e-14 relative error = 6.307149161029701e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 2.300064000000139 y[1] (closed_form) = -3.070633109337007 y[1] (numeric) = -3.07063310933703 absolute error = 2.264854970235319e-14 relative error = 7.375856670562422e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 2.400416000000153 y[1] (closed_form) = -3.04194956523772 y[1] (numeric) = -3.041949565237748 absolute error = 2.842170943040401e-14 relative error = 9.343254653264749e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 2.500256000000166 y[1] (closed_form) = -3.012366688621933 y[1] (numeric) = -3.012366688621967 absolute error = 3.375077994860476e-14 relative error = 1.120407421715473e-12 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 14 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 2.600096000000179 y[1] (closed_form) = -2.981807315976183 y[1] (numeric) = -2.981807315976222 absolute error = 3.863576125695545e-14 relative error = 1.295716227200512e-12 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 14 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 2.700448000000192 y[1] (closed_form) = -2.950176018846343 y[1] (numeric) = -2.950176018846389 absolute error = 4.574118861455645e-14 relative error = 1.550456254893001e-12 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 14 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 2.800288000000206 y[1] (closed_form) = -2.917865743513593 y[1] (numeric) = -2.917865743513644 absolute error = 5.10702591327572e-14 relative error = 1.750260759813444e-12 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 14 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 2.900128000000219 y[1] (closed_form) = -2.884788904593079 y[1] (numeric) = -2.884788904593136 absolute error = 5.639932965095795e-14 relative error = 1.955059157401796e-12 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 14 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 2.999968000000232 y[1] (closed_form) = -2.851018613266776 y[1] (numeric) = -2.851018613266836 absolute error = 5.950795411990839e-14 relative error = 2.087252389128478e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 3.100320000000246 y[1] (closed_form) = -2.816451678102696 y[1] (numeric) = -2.816451678102763 absolute error = 6.616929226765933e-14 relative error = 2.349384964851742e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 3.200160000000259 y[1] (closed_form) = -2.781517228727277 y[1] (numeric) = -2.781517228727346 absolute error = 6.883382752675971e-14 relative error = 2.474686362387035e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 3.300000000000272 y[1] (closed_form) = -2.74611788958424 y[1] (numeric) = -2.746117889584315 absolute error = 7.549516567451064e-14 relative error = 2.749159675950422e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 3.400352000000285 y[1] (closed_form) = -2.710148063664994 y[1] (numeric) = -2.710148063665074 absolute error = 7.993605777301127e-14 relative error = 2.949508879043012e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 3.500192000000299 y[1] (closed_form) = -2.674055151855077 y[1] (numeric) = -2.674055151855164 absolute error = 8.659739592076221e-14 relative error = 3.238429688358778e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 3.600032000000312 y[1] (closed_form) = -2.637737747156452 y[1] (numeric) = -2.637737747156543 absolute error = 9.103828801926284e-14 relative error = 3.451377534305843e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 3.700384000000325 y[1] (closed_form) = -2.601090940418422 y[1] (numeric) = -2.601090940418518 absolute error = 9.592326932761353e-14 relative error = 3.687809135661474e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 3.800224000000338 y[1] (closed_form) = -2.564572345910999 y[1] (numeric) = -2.564572345911104 absolute error = 1.048050535246148e-13 relative error = 4.086648352569108e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 3.900064000000352 y[1] (closed_form) = -2.528079543318945 y[1] (numeric) = -2.528079543319055 absolute error = 1.101341240428155e-13 relative error = 4.356434287594759e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 4.000416000000365 y[1] (closed_form) = -2.491511523586691 y[1] (numeric) = -2.491511523586808 absolute error = 1.163513729807164e-13 relative error = 4.669911091288918e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 4.100256000000291 y[1] (closed_form) = -2.455327725060287 y[1] (numeric) = -2.455327725060376 absolute error = 8.837375276016246e-14 relative error = 3.599265053629147e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 4.200096000000218 y[1] (closed_form) = -2.419427864807714 y[1] (numeric) = -2.419427864807778 absolute error = 6.350475700855895e-14 relative error = 2.624784062888606e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 4.300448000000144 y[1] (closed_form) = -2.383718138901394 y[1] (numeric) = -2.383718138901433 absolute error = 3.819167204710538e-14 relative error = 1.60218909374525e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 4.400288000000071 y[1] (closed_form) = -2.348651156943069 y[1] (numeric) = -2.348651156943082 absolute error = 1.332267629550188e-14 relative error = 5.672479821499869e-13 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 15 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 4.500127999999997 y[1] (closed_form) = -2.314132031151454 y[1] (numeric) = -2.314132031151443 absolute error = 1.110223024625157e-14 relative error = 4.797578572354567e-13 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 15 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 4.599967999999924 y[1] (closed_form) = -2.280249496438688 y[1] (numeric) = -2.280249496438652 absolute error = 3.641531520770513e-14 relative error = 1.596988192063143e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 4.70031999999985 y[1] (closed_form) = -2.246924599460703 y[1] (numeric) = -2.246924599460641 absolute error = 6.261657858885883e-14 relative error = 2.786768127594837e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 4.800159999999777 y[1] (closed_form) = -2.21458707397055 y[1] (numeric) = -2.214587073970464 absolute error = 8.615330671091215e-14 relative error = 3.8902650396332e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000512 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 TOP MAIN SOLVE Loop x[1] = 4.899999999999704 y[1] (closed_form) = -2.183154422369202 y[1] (numeric) = -2.183154422369097 absolute error = 1.056932319443149e-13 relative error = 4.841308102686319e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000512 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 Finished! diff ( y , x , 1 ) = sin ( 0.3 * x + 0.1 ) - ( 0.1 * x + 0.2 ) ; Iterations = 9571 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100 %