##############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; ELIMINATED in preodein.rb 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 # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $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 def exact_soln_y (x) return(0.05 * x * x + 0.2 * x - cos(0.3 * x + 0.1) / 0.3) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size 0.0 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 1.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.0 estimated_steps 4000000.0 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 2.8202033133429505 $glob_desired_digits_correct 16 estimated_h 1.0e-06 estimated_answer 2.8202033133429505 desired_abs_gbl_error 2.8202033133429505e-16 range 4.0 estimated_steps 4000000.0 step_error 3.5252541416786885e-21 est_needed_step_err 3.5252541416786885e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.2387884744885653e-276 estimated_step_error 1.2387884744885653e-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 2.8202033133429505 $glob_desired_digits_correct 16 estimated_h 2.0e-06 estimated_answer 2.8202033133429505 desired_abs_gbl_error 2.8202033133429505e-16 range 4.0 estimated_steps 2000000.0 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 8.51288956075287e-266 estimated_step_error 8.51288956075287e-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 2.8202033133429505 $glob_desired_digits_correct 16 estimated_h 4.0e-06 estimated_answer 2.8202033133429505 desired_abs_gbl_error 2.8202033133429505e-16 range 4.0 estimated_steps 1000000.0 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 2.8202033133429505 $glob_desired_digits_correct 16 estimated_h 8.0e-06 estimated_answer 2.8202033133429505 desired_abs_gbl_error 2.8202033133429505e-16 range 4.0 estimated_steps 500000.0 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 4.0200983920636885e-244 estimated_step_error 4.0200983920636885e-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 2.8202033133429505 $glob_desired_digits_correct 16 estimated_h 1.6e-05 estimated_answer 2.8202033133429505 desired_abs_gbl_error 2.8202033133429505e-16 range 4.0 estimated_steps 250000.0 step_error 1.4101016566714754e-20 est_needed_step_err 1.4101016566714754e-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 2.8202033133429505 $glob_desired_digits_correct 16 estimated_h 3.2e-05 estimated_answer 2.8202033133429505 desired_abs_gbl_error 2.8202033133429505e-16 range 4.0 estimated_steps 125000.0 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 2.8202033133429505 $glob_desired_digits_correct 16 estimated_h 6.4e-05 estimated_answer 2.8202033133429505 desired_abs_gbl_error 2.8202033133429505e-16 range 4.0 estimated_steps 62500.0 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 1.3045963905346566e-211 estimated_step_error 1.3045963905346566e-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 2.8202033133429505 $glob_desired_digits_correct 16 estimated_h 0.000128 estimated_answer 2.8202033133429505 desired_abs_gbl_error 2.8202033133429505e-16 range 4.0 estimated_steps 31250.0 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 2.8202033133429505 $glob_desired_digits_correct 16 estimated_h 0.000256 estimated_answer 2.8202033133429505 desired_abs_gbl_error 2.8202033133429505e-16 range 4.0 estimated_steps 15625.0 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 2.8202033133429505 $glob_desired_digits_correct 16 estimated_h 0.000512 estimated_answer 2.8202033133429505 desired_abs_gbl_error 2.8202033133429505e-16 range 4.0 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 4.2336540866679604e-179 estimated_step_error 4.2336540866679604e-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 1.1955934848325378 Order of pole (three term test) 32.151646645326416 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE ACCURACY START of Soultion TOP MAIN SOLVE Loop x[1] 1.0 y[1] (closed_form) -2.8202033133429505 y[1] (numeric) -2.8202033133429505 absolute error 0.0 relative error 0.0% 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] 1.1003520000000133 y[1] (closed_form) -2.7491299506385514 y[1] (numeric) -2.749129950638562 absolute error 1.0658141036401503e-14 relative error 3.8769142338745734e-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] 1.2001920000000266 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] 1.3000320000000398 y[1] (closed_form) -2.5965839084852256 y[1] (numeric) -2.5965839084852584 absolute error 3.2862601528904634e-14 relative error 1.2656090728096576e-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] 1.4003840000000531 y[1] (closed_form) -2.5144092103853732 y[1] (numeric) -2.5144092103854154 absolute error 4.218847493575595e-14 relative error 1.6778682945283156e-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] 1.5002240000000664 y[1] (closed_form) -2.4290529160005283 y[1] (numeric) -2.4290529160005825 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] 1.6000640000000796 y[1] (closed_form) -2.3401507187998756 y[1] (numeric) -2.3401507187999413 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) -2.2472677966925882 absolute error 7.815970093361102e-14 relative error 3.4779878503418738e-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] 1.8002560000001062 y[1] (closed_form) -2.1514023530863113 y[1] (numeric) -2.1514023530864015 absolute error 9.015010959956271e-14 relative error 4.1902952030445236e-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] 1.9000960000001195 y[1] (closed_form) -2.052141830070275 y[1] (numeric) -2.052141830070379 absolute error 1.0391687510491465e-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) -1.9490061150305766 y[1] (numeric) -1.9490061150306934 absolute error 1.1679546219056647e-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) -1.8431045226098723 absolute error 1.3233858453531866e-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] 2.2001280000001593 y[1] (closed_form) -1.7339780912573315 y[1] (numeric) -1.7339780912574783 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] 2.2999680000001725 y[1] (closed_form) -1.62168754331933 y[1] (numeric) -1.6216875433194924 absolute error 1.6231460620019789e-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) -1.5056959086944233 y[1] (numeric) -1.5056959086946011 absolute error 1.7785772854495008e-13 relative error 1.1812327277900959e-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) -1.3872516109372568 y[1] (numeric) -1.387251610937449 absolute error 1.9229062786507711e-13 relative error 1.3861265422150885e-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] 2.6000000000002124 y[1] (closed_form) -1.2658371473283396 y[1] (numeric) -1.2658371473285488 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] 2.7003520000002257 y[1] (closed_form) -1.1408758020445338 y[1] (numeric) -1.1408758020447607 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) -1.0137128671770028 y[1] (numeric) -1.0137128671772468 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 2.6201263381153694e-13 relative error 2.9646491192929376e-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] 3.0003840000002655 y[1] (closed_form) -0.7504925420459019 y[1] (numeric) -0.7504925420461822 absolute error 2.8033131371785203e-13 relative error 3.7352977946142773e-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] 3.1002240000002788 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 3.1624702856447584e-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] 3.3004160000003053 y[1] (closed_form) -0.3365285521302699 y[1] (numeric) -0.3365285521306047 absolute error 3.3478775307571595e-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] 3.4002560000003186 y[1] (closed_form) -0.19390614764921166 y[1] (numeric) -0.19390614764956512 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 3.9633100347780626e-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] 3.7002880000003584 y[1] (closed_form) 0.2482022885502102 y[1] (numeric) 0.24820228854979823 absolute error 4.1197600886277996e-13 relative error 1.6598396866894282e-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] 3.8001280000003717 y[1] (closed_form) 0.39954102050729845 y[1] (numeric) 0.39954102050686663 absolute error 4.3182124542795464e-13 relative error 1.0807932684350405e-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 4.5230486023228877e-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 3.5860203695392556e-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] 4.2000000000002515 y[1] (closed_form) 1.024537780362338 y[1] (numeric) 1.0245377803620956 absolute error 2.4225066397320916e-13 relative error 2.3644873680259484e-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) 1.1856914399802576 y[1] (numeric) 1.1856914399801333 absolute error 1.2434497875801753e-13 relative error 1.0487127979947965e-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] 4.4001920000001045 y[1] (closed_form) 1.3475611374401335 y[1] (numeric) 1.3475611374401288 absolute error 4.6629367034256575e-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) 1.5108766689942512 y[1] (numeric) 1.5108766689943651 absolute error 1.1390888232654106e-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) 1.6763971194073322 y[1] (numeric) 1.6763971194075669 absolute error 2.347011474057581e-13 relative error 1.4000331108224139e-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) 1.8423440650553116 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) 2.0094692929350018 y[1] (numeric) 2.0094692929354814 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) 2.1785486261709353 y[1] (numeric) 2.1785486261715437 absolute error 6.084022174945858e-13 relative error 2.7926951466028408e-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 1 Seconds Elapsed Time(since restart) 1 Seconds Time to Timeout 2 Minutes 59.0 Seconds Percent Done 100.01919999999159%