##############ECHO OF PROBLEM################# ##############temp/subpostode.ode################# diff ( y , x , 1 ) = sin ( x ) - cos ( x ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=40; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=0.0; x_end=10.0; 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(2.0 - cos(x) - sin(x)); } // 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 = 10 estimated_steps = 10000000 step_error = 7.905694150420948e-22 est_needed_step_err = 7.905694150420948e-22 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 = 1 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 10 estimated_steps = 10000000 step_error = 7.905694150420948e-22 est_needed_step_err = 7.905694150420948e-22 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.688220302613934e-258 estimated_step_error = 2.688220302613934e-258 Double H and LOOP opt_iter = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 10 estimated_steps = 5000000 step_error = 1.118033988749895e-21 est_needed_step_err = 1.118033988749895e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.847330950431141e-247 estimated_step_error = 1.847330950431141e-247 Double H and LOOP opt_iter = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 10 estimated_steps = 2500000 step_error = 1.58113883008419e-21 est_needed_step_err = 1.58113883008419e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.269476197028619e-236 estimated_step_error = 1.269476197028619e-236 Double H and LOOP opt_iter = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 10 estimated_steps = 1250000 step_error = 2.236067977499789e-21 est_needed_step_err = 2.236067977499789e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.723774470416644e-226 estimated_step_error = 8.723774470416644e-226 Double H and LOOP opt_iter = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 10 estimated_steps = 625000 step_error = 3.162277660168379e-21 est_needed_step_err = 3.162277660168379e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.994932815799572e-215 estimated_step_error = 5.994932815799572e-215 Double H and LOOP opt_iter = 6 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 10 estimated_steps = 312500 step_error = 4.472135954999579e-21 est_needed_step_err = 4.472135954999579e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.119687352434481e-204 estimated_step_error = 4.119687352434481e-204 Double H and LOOP opt_iter = 7 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 10 estimated_steps = 156250 step_error = 6.324555320336758e-21 est_needed_step_err = 6.324555320336758e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.831028815978219e-193 estimated_step_error = 2.831028815978219e-193 Double H and LOOP opt_iter = 8 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 10 estimated_steps = 78125 step_error = 8.944271909999158e-21 est_needed_step_err = 8.944271909999158e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.945469871146985e-182 estimated_step_error = 1.945469871146985e-182 Double H and LOOP opt_iter = 9 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5 Order of pole (three term test) = 32.5 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE ACCURACY START of Soultion TOP MAIN SOLVE Loop x[1] = 0 y[1] (closed_form) = 1 y[1] (numeric) = 1 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 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 TOP MAIN SOLVE Loop x[1] = 0.1000960000000016 y[1] (closed_form) = 0.9050764867284197 y[1] (numeric) = 0.905076486728421 absolute error = 1.332267629550188e-15 relative error = 1.471994521000027e-13 % Desired digits = 16 Estimated correct digits = 12 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 TOP MAIN SOLVE Loop x[1] = 0.2000639999999959 y[1] (closed_form) = 0.8212140843539748 y[1] (numeric) = 0.821214084353972 absolute error = 2.775557561562891e-15 relative error = 3.37982216141159e-13 % Desired digits = 16 Estimated correct digits = 12 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 TOP MAIN SOLVE Loop x[1] = 0.3000319999999983 y[1] (closed_form) = 0.7491221907324588 y[1] (numeric) = 0.7491221907324581 absolute error = 6.661338147750939e-16 relative error = 8.892191728078132e-14 % Desired digits = 16 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 TOP MAIN SOLVE Loop x[1] = 0.4000000000000116 y[1] (closed_form) = 0.6895206636884582 y[1] (numeric) = 0.6895206636884649 absolute error = 6.661338147750939e-15 relative error = 9.660824538770733e-13 % Desired digits = 16 Estimated correct digits = 12 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 TOP MAIN SOLVE Loop x[1] = 0.5000960000000249 y[1] (closed_form) = 0.642953682684331 y[1] (numeric) = 0.6429536826843425 absolute error = 1.154631945610163e-14 relative error = 1.795824453154348e-12 % Desired digits = 16 Estimated correct digits = 12 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 TOP MAIN SOLVE Loop x[1] = 0.6000640000000381 y[1] (closed_form) = 0.610005230180906 y[1] (numeric) = 0.6100052301809218 absolute error = 1.576516694967722e-14 relative error = 2.584431439219272e-12 % Desired digits = 16 Estimated correct digits = 12 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 TOP MAIN SOLVE Loop x[1] = 0.7000320000000514 y[1] (closed_form) = 0.5909362662152521 y[1] (numeric) = 0.5909362662152707 absolute error = 1.865174681370263e-14 relative error = 3.156304305565944e-12 % Desired digits = 16 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 TOP MAIN SOLVE Loop x[1] = 0.8000000000000647 y[1] (closed_form) = 0.5859371997533132 y[1] (numeric) = 0.5859371997533335 absolute error = 2.031708135064036e-14 relative error = 3.467450327303696e-12 % Desired digits = 16 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 TOP MAIN SOLVE Loop x[1] = 0.9000960000000779 y[1] (closed_form) = 0.5950786534021603 y[1] (numeric) = 0.5950786534021798 absolute error = 1.953992523340276e-14 relative error = 3.283586988323285e-12 % Desired digits = 16 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 TOP MAIN SOLVE Loop x[1] = 1.000064000000091 y[1] (closed_form) = 0.6182459869493019 y[1] (numeric) = 0.6182459869493175 absolute error = 1.565414464721471e-14 relative error = 2.532025274350612e-12 % Desired digits = 16 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 TOP MAIN SOLVE Loop x[1] = 1.100032000000018 y[1] (closed_form) = 0.6552105227611684 y[1] (numeric) = 0.6552105227612098 absolute error = 4.141131881851834e-14 relative error = 6.320307348545626e-12 % Desired digits = 16 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 TOP MAIN SOLVE Loop x[1] = 1.199999999999944 y[1] (closed_form) = 0.7056031595560682 y[1] (numeric) = 0.7056031595561456 absolute error = 7.738254481637341e-14 relative error = 1.096686484015446e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 1.300095999999871 y[1] (closed_form) = 0.7690098133289898 y[1] (numeric) = 0.7690098133291143 absolute error = 1.245670233629426e-13 relative error = 1.61983658990905e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 1.400063999999797 y[1] (closed_form) = 0.8446353203629654 y[1] (numeric) = 0.8446353203631463 absolute error = 1.80855330711438e-13 relative error = 2.141223867286523e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 1.500031999999724 y[1] (closed_form) = 0.9317974685240344 y[1] (numeric) = 0.9317974685242798 absolute error = 2.453592884421596e-13 relative error = 2.633182603842102e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 1.59999999999965 y[1] (closed_form) = 1.029625919259424 y[1] (numeric) = 1.029625919259739 absolute error = 3.150812943886194e-13 relative error = 3.060153095361537e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 1.700095999999577 y[1] (closed_form) = 1.137287256711549 y[1] (numeric) = 1.13728725671194 absolute error = 3.916866830877552e-13 relative error = 3.444043541121811e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 1.800063999999503 y[1] (closed_form) = 1.25343133252581 y[1] (numeric) = 1.253431332526289 absolute error = 4.793943020331426e-13 relative error = 3.824655484454082e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 1.90003199999943 y[1] (closed_form) = 1.377030106363285 y[1] (numeric) = 1.377030106363853 absolute error = 5.679900993982301e-13 relative error = 4.124747140774452e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 1.999999999999357 y[1] (closed_form) = 1.506849409720608 y[1] (numeric) = 1.506849409721271 absolute error = 6.632472349110685e-13 relative error = 4.401549555201037e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 2.100095999999457 y[1] (closed_form) = 1.641768072926616 y[1] (numeric) = 1.641768072927147 absolute error = 5.306866057708248e-13 relative error = 3.232409099202561e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 2.200063999999557 y[1] (closed_form) = 1.780094121726974 y[1] (numeric) = 1.780094121727368 absolute error = 3.934630399271555e-13 relative error = 2.210349638958606e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 2.300031999999657 y[1] (closed_form) = 1.92061599254275 y[1] (numeric) = 1.920615992543 absolute error = 2.504663143554353e-13 relative error = 1.304093662282989e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 2.399999999999757 y[1] (closed_form) = 2.061930534989751 y[1] (numeric) = 2.061930534989863 absolute error = 1.127986593019159e-13 relative error = 5.470536343867501e-12 % Desired digits = 16 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 TOP MAIN SOLVE Loop x[1] = 2.500095999999857 y[1] (closed_form) = 2.202805833621587 y[1] (numeric) = 2.202805833621564 absolute error = 2.264854970235319e-14 relative error = 1.028168227842269e-12 % Desired digits = 16 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 TOP MAIN SOLVE Loop x[1] = 2.600063999999957 y[1] (closed_form) = 2.341475213816214 y[1] (numeric) = 2.34147521381605 absolute error = 1.647570968543732e-13 relative error = 7.036465553092344e-12 % Desired digits = 16 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 TOP MAIN SOLVE Loop x[1] = 2.700032000000057 y[1] (closed_form) = 2.476734868003945 y[1] (numeric) = 2.476734868003645 absolute error = 2.997602166487923e-13 relative error = 1.210304019704683e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 2.800000000000157 y[1] (closed_form) = 2.607234190512953 y[1] (numeric) = 2.607234190512522 absolute error = 4.312106227644108e-13 relative error = 1.65390061365977e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 2.900096000000257 y[1] (closed_form) = 2.731825012483485 y[1] (numeric) = 2.731825012482928 absolute error = 5.568878691519785e-13 relative error = 2.038519548679713e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 3.000064000000357 y[1] (closed_form) = 2.848944878002739 y[1] (numeric) = 2.848944878002067 absolute error = 6.723510637129948e-13 relative error = 2.360000254495441e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 3.100032000000457 y[1] (closed_form) = 2.957587790256197 y[1] (numeric) = 2.957587790255416 absolute error = 7.807088309164101e-13 relative error = 2.639681004528296e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 3.200000000000557 y[1] (closed_form) = 3.056668919222856 y[1] (numeric) = 3.056668919221976 absolute error = 8.806289031326742e-13 relative error = 2.881008465112309e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 3.300096000000657 y[1] (closed_form) = 3.14530511324661 y[1] (numeric) = 3.145305113245641 absolute error = 9.690026558928366e-13 relative error = 3.080790641937513e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 3.400064000000757 y[1] (closed_form) = 3.222384812557244 y[1] (numeric) = 3.222384812556201 absolute error = 1.043165553937797e-12 relative error = 3.237246991336066e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 3.500032000000857 y[1] (closed_form) = 3.287258655872555 y[1] (numeric) = 3.287258655871451 absolute error = 1.104005775687256e-12 relative error = 3.358439025523574e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 3.600000000000957 y[1] (closed_form) = 3.339278859629434 y[1] (numeric) = 3.339278859628278 absolute error = 1.155964213239713e-12 relative error = 3.461718118887479e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 3.700096000001057 y[1] (closed_form) = 3.377966719603178 y[1] (numeric) = 3.377966719601981 absolute error = 1.196376331336069e-12 relative error = 3.54170550110278e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 3.800064000001157 y[1] (closed_form) = 3.40283706301289 y[1] (numeric) = 3.402837063011664 absolute error = 1.226130308396023e-12 relative error = 3.603258944494981e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 3.900032000001257 y[1] (closed_form) = 3.413699683976989 y[1] (numeric) = 3.413699683975751 absolute error = 1.237676627852125e-12 relative error = 3.625616610803387e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 4.000000000001356 y[1] (closed_form) = 3.4104461161714 y[1] (numeric) = 3.410446116170169 absolute error = 1.231015289704374e-12 relative error = 3.609543290736178e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 4.100096000001456 y[1] (closed_form) = 3.393077679674156 y[1] (numeric) = 3.393077679672946 absolute error = 1.209699007631571e-12 relative error = 3.565196915113775e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 4.200064000001556 y[1] (closed_form) = 3.3618121868078 y[1] (numeric) = 3.361812186806621 absolute error = 1.179056852151916e-12 relative error = 3.507206193072571e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 4.300032000001656 y[1] (closed_form) = 3.316948616417824 y[1] (numeric) = 3.316948616416682 absolute error = 1.142197447734361e-12 relative error = 3.443518666767561e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 4.400000000001756 y[1] (closed_form) = 3.258934943866804 y[1] (numeric) = 3.258934943865715 absolute error = 1.089350831762204e-12 relative error = 3.3426590297923e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 4.500096000001856 y[1] (closed_form) = 3.18825230512421 y[1] (numeric) = 3.18825230512319 absolute error = 1.019628825815744e-12 relative error = 3.198080729611581e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 4.600064000001956 y[1] (closed_form) = 3.105787109839557 y[1] (numeric) = 3.105787109838622 absolute error = 9.348077867343818e-13 relative error = 3.009890097659249e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 4.700032000002056 y[1] (closed_form) = 3.012280319399651 y[1] (numeric) = 3.012280319398812 absolute error = 8.388845174067683e-13 relative error = 2.784881977962656e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 4.800000000002156 y[1] (closed_form) = 2.908665625394057 y[1] (numeric) = 2.908665625393322 absolute error = 7.358558207215538e-13 relative error = 2.529874229258862e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 4.900096000002256 y[1] (closed_form) = 2.795828018893323 y[1] (numeric) = 2.7958280188927 absolute error = 6.226130722097878e-13 relative error = 2.226936234998595e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 5.000064000002356 y[1] (closed_form) = 2.675182562280654 y[1] (numeric) = 2.675182562280158 absolute error = 4.951594689828198e-13 relative error = 1.850937113468193e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 5.100032000002456 y[1] (closed_form) = 2.547795217973462 y[1] (numeric) = 2.547795217973098 absolute error = 3.645972412869014e-13 relative error = 1.431030401167426e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 5.200000000002556 y[1] (closed_form) = 2.41493798441632 y[1] (numeric) = 2.414937984416086 absolute error = 2.34035013590983e-13 relative error = 9.691139693905979e-12 % Desired digits = 16 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 TOP MAIN SOLVE Loop x[1] = 5.300096000002656 y[1] (closed_form) = 2.277759987150003 y[1] (numeric) = 2.277759987149902 absolute error = 1.003641614261142e-13 relative error = 4.40626589246976e-12 % Desired digits = 16 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 TOP MAIN SOLVE Loop x[1] = 5.400064000002756 y[1] (closed_form) = 2.1379815340555 y[1] (numeric) = 2.137981534055538 absolute error = 3.819167204710538e-14 relative error = 1.786342465487074e-12 % Desired digits = 16 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 TOP MAIN SOLVE Loop x[1] = 5.500032000002856 y[1] (closed_form) = 1.996825296553507 y[1] (numeric) = 1.996825296553685 absolute error = 1.780797731498751e-13 relative error = 8.918144890153304e-12 % Desired digits = 16 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 TOP MAIN SOLVE Loop x[1] = 5.600000000002956 y[1] (closed_form) = 1.855700759357912 y[1] (numeric) = 1.855700759358232 absolute error = 3.199662756969701e-13 relative error = 1.724234223020316e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 5.700096000003056 y[1] (closed_form) = 1.715839760823812 y[1] (numeric) = 1.715839760824273 absolute error = 4.616307336391401e-13 relative error = 2.690407019228306e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 5.800064000003156 y[1] (closed_form) = 1.578996255541707 y[1] (numeric) = 1.578996255542307 absolute error = 5.997424779025096e-13 relative error = 3.798251425851263e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 5.900032000003256 y[1] (closed_form) = 1.446356591002356 y[1] (numeric) = 1.446356591003087 absolute error = 7.316369732279782e-13 relative error = 5.058482657592332e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 6.000000000003356 y[1] (closed_form) = 1.319245211544399 y[1] (numeric) = 1.31924521154526 absolute error = 8.602007994795713e-13 relative error = 6.520401150234693e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 6.100096000003457 y[1] (closed_form) = 1.19878218814665 y[1] (numeric) = 1.198782188147632 absolute error = 9.816591983735634e-13 relative error = 8.188803671593046e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 6.200064000003557 y[1] (closed_form) = 1.086478211245248 y[1] (numeric) = 1.086478211246341 absolute error = 1.093125590045929e-12 relative error = 1.006118280819514e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 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 TOP MAIN SOLVE Loop x[1] = 6.300032000003656 y[1] (closed_form) = 0.9832960062176336 y[1] (numeric) = 0.9832960062188283 absolute error = 1.194710996799131e-12 relative error = 1.215006457104133e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 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 TOP MAIN SOLVE Loop x[1] = 6.400000000003756 y[1] (closed_form) = 0.890265876388021 y[1] (numeric) = 0.8902658763893092 absolute error = 1.288191775472569e-12 relative error = 1.446974223811666e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 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 TOP MAIN SOLVE Loop x[1] = 6.500096000003857 y[1] (closed_form) = 0.8082192907795123 y[1] (numeric) = 0.8082192907808839 absolute error = 1.371680546924381e-12 relative error = 1.697163829882631e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 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 TOP MAIN SOLVE Loop x[1] = 6.600064000003957 y[1] (closed_form) = 0.738185170871086 y[1] (numeric) = 0.7381851708725291 absolute error = 1.443067887407778e-12 relative error = 1.954886042623837e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 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 TOP MAIN SOLVE Loop x[1] = 6.700032000004057 y[1] (closed_form) = 0.6807506267581821 y[1] (numeric) = 0.6807506267596815 absolute error = 1.499356194756274e-12 relative error = 2.202504317765217e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 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 TOP MAIN SOLVE Loop x[1] = 6.800000000004156 y[1] (closed_form) = 0.6364891585100065 y[1] (numeric) = 0.6364891585115513 absolute error = 1.544764316463443e-12 relative error = 2.42700805789005e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 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 TOP MAIN SOLVE Loop x[1] = 6.900096000004257 y[1] (closed_form) = 0.6058123625175496 y[1] (numeric) = 0.6058123625191231 absolute error = 1.573519092801234e-12 relative error = 2.597370390828978e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 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 TOP MAIN SOLVE Loop x[1] = 7.000064000004357 y[1] (closed_form) = 0.5891049472250289 y[1] (numeric) = 0.5891049472266207 absolute error = 1.591726750405087e-12 relative error = 2.701940898481493e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 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 TOP MAIN SOLVE Loop x[1] = 7.100032000004457 y[1] (closed_form) = 0.5864857156711933 y[1] (numeric) = 0.5864857156727873 absolute error = 1.593947196454337e-12 relative error = 2.717793722614663e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 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 TOP MAIN SOLVE Loop x[1] = 7.200000000004557 y[1] (closed_form) = 0.5979808216194367 y[1] (numeric) = 0.597980821621019 absolute error = 1.582289854695773e-12 relative error = 2.646054517953695e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 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 TOP MAIN SOLVE Loop x[1] = 7.300096000004657 y[1] (closed_form) = 0.6235170068086826 y[1] (numeric) = 0.6235170068102396 absolute error = 1.55697676973432e-12 relative error = 2.497087894528041e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 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 TOP MAIN SOLVE Loop x[1] = 7.400064000004757 y[1] (closed_form) = 0.662774029644018 y[1] (numeric) = 0.6627740296455351 absolute error = 1.517119763150276e-12 relative error = 2.289045278320781e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 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 TOP MAIN SOLVE Loop x[1] = 7.500032000004857 y[1] (closed_form) = 0.7153836297199236 y[1] (numeric) = 0.7153836297213866 absolute error = 1.462940879548569e-12 relative error = 2.044973939536914e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 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 TOP MAIN SOLVE Loop x[1] = 7.600000000004957 y[1] (closed_form) = 0.7808204853898105 y[1] (numeric) = 0.7808204853912081 absolute error = 1.397548743398147e-12 relative error = 1.789846410984525e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 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 TOP MAIN SOLVE Loop x[1] = 7.700096000005057 y[1] (closed_form) = 0.8585380496091564 y[1] (numeric) = 0.8585380496104762 absolute error = 1.319833131674386e-12 relative error = 1.537303014438593e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 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 TOP MAIN SOLVE Loop x[1] = 7.800064000005157 y[1] (closed_form) = 0.9475616898502808 y[1] (numeric) = 0.9475616898515111 absolute error = 1.230349155889598e-12 relative error = 1.298436997895092e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 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 TOP MAIN SOLVE Loop x[1] = 7.900032000005257 y[1] (closed_form) = 1.047094222484116 y[1] (numeric) = 1.047094222485248 absolute error = 1.13198339590781e-12 relative error = 1.081071188820337e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 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 TOP MAIN SOLVE Loop x[1] = 8.000000000005356 y[1] (closed_form) = 1.15614178719131 y[1] (numeric) = 1.156141787192333 absolute error = 1.023403584099469e-12 relative error = 8.851886467884618e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 8.100096000005456 y[1] (closed_form) = 1.273770835904747 y[1] (numeric) = 1.273770835905654 absolute error = 9.066081219089028e-13 relative error = 7.117513577432063e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 8.200064000005556 y[1] (closed_form) = 1.398506218209875 y[1] (numeric) = 1.398506218210654 absolute error = 7.793765632868599e-13 relative error = 5.57292168700174e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 8.300032000005656 y[1] (closed_form) = 1.529247685020628 y[1] (numeric) = 1.529247685021276 absolute error = 6.474820679613913e-13 relative error = 4.23399083290198e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 8.400000000005756 y[1] (closed_form) = 1.664689746036313 y[1] (numeric) = 1.664689746036825 absolute error = 5.120348589571222e-13 relative error = 3.075857589537606e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 8.500096000005856 y[1] (closed_form) = 1.803659238880155 y[1] (numeric) = 1.80365923888053 absolute error = 3.743672039036028e-13 relative error = 2.075598293921847e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 8.600064000005956 y[1] (closed_form) = 1.944413389065573 y[1] (numeric) = 1.944413389065806 absolute error = 2.327027459614328e-13 relative error = 1.19677609334537e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 8.700032000006056 y[1] (closed_form) = 2.085722587187912 y[1] (numeric) = 2.085722587187998 absolute error = 8.570921750106208e-14 relative error = 4.109329688787618e-12 % Desired digits = 16 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 TOP MAIN SOLVE Loop x[1] = 8.800000000006156 y[1] (closed_form) = 2.226175821178487 y[1] (numeric) = 2.22617582117844 absolute error = 4.618527782440651e-14 relative error = 2.07464645806624e-12 % Desired digits = 16 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 TOP MAIN SOLVE Loop x[1] = 8.900096000006256 y[1] (closed_form) = 2.364545530894659 y[1] (numeric) = 2.364545530894473 absolute error = 1.860733789271762e-13 relative error = 7.869308351054367e-12 % Desired digits = 16 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 TOP MAIN SOLVE Loop x[1] = 9.000064000006356 y[1] (closed_form) = 2.499096463549113 y[1] (numeric) = 2.499096463548796 absolute error = 3.161915174132446e-13 relative error = 1.265223339815393e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 9.100032000006456 y[1] (closed_form) = 2.62866377770694 y[1] (numeric) = 2.628663777706492 absolute error = 4.476419235288631e-13 relative error = 1.702925750052958e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 9.200000000006556 y[1] (closed_form) = 2.751953707311769 y[1] (numeric) = 2.751953707311198 absolute error = 5.710987238671805e-13 relative error = 2.075248294874318e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 9.300096000006656 y[1] (closed_form) = 2.86787809921002 y[1] (numeric) = 2.867878099209341 absolute error = 6.785683126508957e-13 relative error = 2.366098868838996e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 9.400064000006756 y[1] (closed_form) = 2.974983180574013 y[1] (numeric) = 2.974983180573231 absolute error = 7.811529201262601e-13 relative error = 2.625738946112426e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 9.500032000006856 y[1] (closed_form) = 3.072352780788618 y[1] (numeric) = 3.072352780787741 absolute error = 8.770761894538737e-13 relative error = 2.854737889926638e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 9.600000000006956 y[1] (closed_form) = 3.159014637022744 y[1] (numeric) = 3.159014637021785 absolute error = 9.592326932761353e-13 relative error = 3.03649334838213e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 9.700096000007056 y[1] (closed_form) = 3.234191798568501 y[1] (numeric) = 3.234191798567461 absolute error = 1.040501018678697e-12 relative error = 3.217190208506611e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 9.800064000007156 y[1] (closed_form) = 3.296941491321772 y[1] (numeric) = 3.296941491320671 absolute error = 1.101341240428155e-12 relative error = 3.340493737383912e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 9.900032000007256 y[1] (closed_form) = 3.346740858682571 y[1] (numeric) = 3.346740858681419 absolute error = 1.151967410351062e-12 relative error = 3.442057389542043e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 Finished! diff ( y , x , 1 ) = sin ( x ) - cos ( x ) ; Iterations = 78125 Total Elapsed Time = 1.0 Seconds Elapsed Time(since restart) = 1.0 Seconds Time to Timeout = 2 Minutes 59.0 Seconds Percent Done = 100 %