##############ECHO OF PROBLEM################# ##############temp/add_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=1.0; x_end=5.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_display_interval=0.1; 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 estimated_steps = 4000000 step_error = 1.25e-21 est_needed_step_err = 1.25e-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 = 2.82020331334295 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 2.82020331334295 desired_abs_gbl_error = 2.82020331334295e-16 range = 4 estimated_steps = 4000000 step_error = 3.525254141678689e-21 est_needed_step_err = 3.525254141678689e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.238788474488565e-276 estimated_step_error = 1.238788474488565e-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 = 2.82020331334295 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 2.82020331334295 desired_abs_gbl_error = 2.82020331334295e-16 range = 4 estimated_steps = 2000000 step_error = 4.985462217973925e-21 est_needed_step_err = 4.985462217973925e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.512889560752871e-266 estimated_step_error = 8.512889560752871e-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 = 2.82020331334295 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 2.82020331334295 desired_abs_gbl_error = 2.82020331334295e-16 range = 4 estimated_steps = 1000000 step_error = 7.050508283357377e-21 est_needed_step_err = 7.050508283357377e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.850013141208783e-255 estimated_step_error = 5.850013141208783e-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 = 2.82020331334295 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 2.82020331334295 desired_abs_gbl_error = 2.82020331334295e-16 range = 4 estimated_steps = 500000 step_error = 9.97092443594785e-21 est_needed_step_err = 9.97092443594785e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.020098392063689e-244 estimated_step_error = 4.020098392063689e-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 = 2.82020331334295 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 2.82020331334295 desired_abs_gbl_error = 2.82020331334295e-16 range = 4 estimated_steps = 250000 step_error = 1.410101656671475e-20 est_needed_step_err = 1.410101656671475e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.762590541417278e-233 estimated_step_error = 2.762590541417278e-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 = 2.82020331334295 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 2.82020331334295 desired_abs_gbl_error = 2.82020331334295e-16 range = 4 estimated_steps = 125000 step_error = 1.99418488718957e-20 est_needed_step_err = 1.99418488718957e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.898437712356594e-222 estimated_step_error = 1.898437712356594e-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 = 2.82020331334295 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 2.82020331334295 desired_abs_gbl_error = 2.82020331334295e-16 range = 4 estimated_steps = 62500 step_error = 2.820203313342951e-20 est_needed_step_err = 2.820203313342951e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.304596390534657e-211 estimated_step_error = 1.304596390534657e-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 = 2.82020331334295 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 2.82020331334295 desired_abs_gbl_error = 2.82020331334295e-16 range = 4 estimated_steps = 31250 step_error = 3.98836977437914e-20 est_needed_step_err = 3.98836977437914e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.96511714746688e-201 estimated_step_error = 8.96511714746688e-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 = 2.82020331334295 glob_desired_digits_correct = 16 estimated_h = 0.000256 estimated_answer = 2.82020331334295 desired_abs_gbl_error = 2.82020331334295e-16 range = 4 estimated_steps = 15625 step_error = 5.640406626685902e-20 est_needed_step_err = 5.640406626685902e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.160780240856365e-190 estimated_step_error = 6.160780240856365e-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 = 2.82020331334295 glob_desired_digits_correct = 16 estimated_h = 0.000512 estimated_answer = 2.82020331334295 desired_abs_gbl_error = 2.82020331334295e-16 range = 4 estimated_steps = 7812.5 step_error = 7.97673954875828e-20 est_needed_step_err = 7.97673954875828e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.23365408666796e-179 estimated_step_error = 4.23365408666796e-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 = 1.196 Order of pole (three term test) = 32.15 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE ACCURACY START of Soultion TOP MAIN SOLVE Loop x[1] = 1 y[1] (closed_form) = -2.82020331334295 y[1] (numeric) = -2.82020331334295 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] = 1.100352000000013 y[1] (closed_form) = -2.749129950638551 y[1] (numeric) = -2.749129950638562 absolute error = 1.06581410364015e-14 relative error = 3.876914233874573e-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] = 1.200192000000027 y[1] (closed_form) = -2.674694973583895 y[1] (numeric) = -2.674694973583917 absolute error = 2.220446049250313e-14 relative error = 8.301679523011472e-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] = 1.30003200000004 y[1] (closed_form) = -2.596583908485226 y[1] (numeric) = -2.596583908485258 absolute error = 3.286260152890463e-14 relative error = 1.265609072809658e-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] = 1.400384000000053 y[1] (closed_form) = -2.514409210385373 y[1] (numeric) = -2.514409210385415 absolute error = 4.218847493575595e-14 relative error = 1.677868294528316e-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] = 1.500224000000066 y[1] (closed_form) = -2.429052916000528 y[1] (numeric) = -2.429052916000582 absolute error = 5.417888360170764e-14 relative error = 2.230452998566782e-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] = 1.60006400000008 y[1] (closed_form) = -2.340150718799876 y[1] (numeric) = -2.340150718799941 absolute error = 6.572520305780927e-14 relative error = 2.808588460982369e-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] = 1.700416000000093 y[1] (closed_form) = -2.24726779669251 y[1] (numeric) = -2.247267796692588 absolute error = 7.815970093361102e-14 relative error = 3.477987850341874e-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] = 1.800256000000106 y[1] (closed_form) = -2.151402353086311 y[1] (numeric) = -2.151402353086401 absolute error = 9.015010959956271e-14 relative error = 4.190295203044524e-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] = 1.900096000000119 y[1] (closed_form) = -2.052141830070275 y[1] (numeric) = -2.052141830070379 absolute error = 1.039168751049147e-13 relative error = 5.063825198736681e-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] = 2.000448000000133 y[1] (closed_form) = -1.949006115030577 y[1] (numeric) = -1.949006115030693 absolute error = 1.167954621905665e-13 relative error = 5.992565199762554e-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] = 2.100288000000146 y[1] (closed_form) = -1.84310452260974 y[1] (numeric) = -1.843104522609872 absolute error = 1.323385845353187e-13 relative error = 7.180199652916814e-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] = 2.200128000000159 y[1] (closed_form) = -1.733978091257331 y[1] (numeric) = -1.733978091257478 absolute error = 1.467714838554457e-13 relative error = 8.464437041936305e-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] = 2.299968000000173 y[1] (closed_form) = -1.62168754331933 y[1] (numeric) = -1.621687543319492 absolute error = 1.623146062001979e-13 relative error = 1.000899383292828e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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] = 2.400320000000186 y[1] (closed_form) = -1.505695908694423 y[1] (numeric) = -1.505695908694601 absolute error = 1.778577285449501e-13 relative error = 1.181232727790096e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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] = 2.500160000000199 y[1] (closed_form) = -1.387251610937257 y[1] (numeric) = -1.387251610937449 absolute error = 1.922906278650771e-13 relative error = 1.386126542215089e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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] = 2.600000000000212 y[1] (closed_form) = -1.26583714732834 y[1] (numeric) = -1.265837147328549 absolute error = 2.091660178393795e-13 relative error = 1.652392792239055e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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] = 2.700352000000226 y[1] (closed_form) = -1.140875802044534 y[1] (numeric) = -1.140875802044761 absolute error = 2.26929586233382e-13 relative error = 1.989082298237086e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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] = 2.800192000000239 y[1] (closed_form) = -1.013712867177003 y[1] (numeric) = -1.013712867177247 absolute error = 2.440270208126094e-13 relative error = 2.407259774576781e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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] = 2.900032000000252 y[1] (closed_form) = -0.8837896940533265 y[1] (numeric) = -0.8837896940535885 absolute error = 2.620126338115369e-13 relative error = 2.964649119292938e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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] = 3.000384000000266 y[1] (closed_form) = -0.7504925420459019 y[1] (numeric) = -0.7504925420461822 absolute error = 2.80331313717852e-13 relative error = 3.735297794614277e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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] = 3.100224000000279 y[1] (closed_form) = -0.6152565352091703 y[1] (numeric) = -0.6152565352094682 absolute error = 2.978728375069295e-13 relative error = 4.841441260037342e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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] = 3.200064000000292 y[1] (closed_form) = -0.4774844949453221 y[1] (numeric) = -0.4774844949456383 absolute error = 3.162470285644758e-13 relative error = 6.623189483894971e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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] = 3.300416000000305 y[1] (closed_form) = -0.3365285521302699 y[1] (numeric) = -0.3365285521306047 absolute error = 3.34787753075716e-13 relative error = 9.948271876382125e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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] = 3.400256000000319 y[1] (closed_form) = -0.1939061476492117 y[1] (numeric) = -0.1939061476495651 absolute error = 3.534672554650342e-13 relative error = 1.822878025014857e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 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] = 3.500096000000332 y[1] (closed_form) = -0.04898437658295962 y[1] (numeric) = -0.04898437658333227 absolute error = 3.726463582154338e-13 relative error = 7.607453319005139e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 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] = 3.600448000000345 y[1] (closed_form) = 0.0989157104397218 y[1] (numeric) = 0.09891571043932977 absolute error = 3.920336277829506e-13 relative error = 3.963310034778063e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 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] = 3.700288000000358 y[1] (closed_form) = 0.2482022885502102 y[1] (numeric) = 0.2482022885497982 absolute error = 4.1197600886278e-13 relative error = 1.659839686689428e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 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] = 3.800128000000372 y[1] (closed_form) = 0.3995410205072984 y[1] (numeric) = 0.3995410205068666 absolute error = 4.318212454279546e-13 relative error = 1.080793268435041e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 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] = 3.899968000000385 y[1] (closed_form) = 0.5528476471188628 y[1] (numeric) = 0.5528476471184105 absolute error = 4.523048602322888e-13 relative error = 8.181365383201907e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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] = 4.000320000000398 y[1] (closed_form) = 0.7088375857663073 y[1] (numeric) = 0.7088375857658336 absolute error = 4.737321646075543e-13 relative error = 6.683225806873853e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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] = 4.100160000000325 y[1] (closed_form) = 0.8658328078242591 y[1] (numeric) = 0.8658328078239005 absolute error = 3.586020369539256e-13 relative error = 4.1417007268996e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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] = 4.200000000000252 y[1] (closed_form) = 1.024537780362338 y[1] (numeric) = 1.024537780362096 absolute error = 2.422506639732092e-13 relative error = 2.364487368025948e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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] = 4.300352000000178 y[1] (closed_form) = 1.185691439980258 y[1] (numeric) = 1.185691439980133 absolute error = 1.243449787580175e-13 relative error = 1.048712797994796e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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] = 4.400192000000104 y[1] (closed_form) = 1.347561137440134 y[1] (numeric) = 1.347561137440129 absolute error = 4.662936703425657e-15 relative error = 3.46027840509226e-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] = 4.500032000000031 y[1] (closed_form) = 1.510876668994251 y[1] (numeric) = 1.510876668994365 absolute error = 1.139088823265411e-13 relative error = 7.539257483032487e-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] = 4.600383999999957 y[1] (closed_form) = 1.676397119407332 y[1] (numeric) = 1.676397119407567 absolute error = 2.347011474057581e-13 relative error = 1.400033110822414e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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] = 4.700223999999884 y[1] (closed_form) = 1.842344065054954 y[1] (numeric) = 1.842344065055312 absolute error = 3.574918139293004e-13 relative error = 1.940418300306121e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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] = 4.800063999999811 y[1] (closed_form) = 2.009469292935002 y[1] (numeric) = 2.009469292935481 absolute error = 4.796163466380676e-13 relative error = 2.386781168163794e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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] = 4.900415999999737 y[1] (closed_form) = 2.178548626170935 y[1] (numeric) = 2.178548626171544 absolute error = 6.084022174945858e-13 relative error = 2.792695146602841e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 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 = 7813 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100 %