##############ECHO OF PROBLEM################# ##############temp/mtest6_rev_sm_hpostode.ode################# diff ( x2 , t , 2 ) = 3.0 * diff ( x2 , t , 1 ) - 2.0 * x2 - diff ( x1 , t , 2 ) - diff ( x1 , t , 1 ) + x1 ; diff ( x1 , t , 1 ) = 4.0 * x2 - 2.0 * diff ( x2 , t , 1 ) - 2.0 * x1 ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=64; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ t_start=0.5; t_end=0.8; array_x1_init[0 + 1] = exact_soln_x1(t_start); array_x2_init[0 + 1] = exact_soln_x2(t_start); array_x2_init[1 + 1] = exact_soln_x2p(t_start); glob_max_h=0.000001; glob_look_poles=true; glob_type_given_pole=0; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=100000000; glob_max_minutes=10.0; glob_subiter_method=3; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_x1 (double t) { double c1,c2,c3; c1 = 1.0; c2 = 0.0002; c3 = 0.0003; return(2.0 * c1 + 6.0 * c3 * exp(-t)); } double exact_soln_x1p (double t) { double c1,c2,c3; c1 = 1.0; c2 = 0.0002; c3 = 0.0003; return( - 6.0 * c3 * exp(-t)); } double exact_soln_x2 (double t) { double c1,c2,c3; c1 = 1.0; c2 = 0.0002; c3 = 0.0003; return(c1 + c2 * exp(2.0 * t) + c3 * exp(-t)); } double exact_soln_x2p (double t) { double c1,c2,c3; c1 = 1.0; c2 = 0.0002; c3 = 0.0003; return( 2.0 * c2 * exp(2.0 * t) - c3 * exp(-t)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.3 estimated_steps = 300000.0000000001 step_error = 6.085806194501845e-15 est_needed_step_err = 6.085806194501845e-15 opt_iter = 1 SETTING H FOR MAX H NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 START of Soultion TOP MAIN SOLVE Loop t[1] = 0.5 x2[1] (analytic) = 1.000725615563606 x2[1] (numeric) = 1.000725615563606 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 1e-06 x1[1] (analytic) = 2.001091755187483 x1[1] (numeric) = 2.001091755187483 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 0.5100000000002876 x2[1] (analytic) = 1.000734787626437 x2[1] (numeric) = 1.000734842946141 absolute error = 5.531970370675765e-08 relative error = 5.52790853188646e-06 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 8 h = 1e-06 x1[1] (analytic) = 2.001080892041862 x1[1] (numeric) = 2.001080782865435 absolute error = 1.091764270100271e-07 relative error = 5.455872745785188e-06 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 8 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 0.5200000000005751 x2[1] (analytic) = 1.000744199567262 x2[1] (numeric) = 1.000744423807083 absolute error = 2.242398207119578e-07 relative error = 2.240730656334783e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 1e-06 x1[1] (analytic) = 2.001070136986346 x1[1] (numeric) = 2.001069700269699 absolute error = 4.36716646401436e-07 relative error = 2.182415490239341e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 0.5300000000008627 x2[1] (analytic) = 1.000753855688758 x2[1] (numeric) = 1.000754366966274 absolute error = 5.112775156579374e-07 relative error = 5.108923765335445e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 1e-06 x1[1] (analytic) = 2.00105948894542 x1[1] (numeric) = 2.001058506292043 absolute error = 9.826533777790303e-07 relative error = 4.910665490993969e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 0.5400000000011502 x2[1] (analytic) = 1.000763760385927 x2[1] (numeric) = 1.000764681438614 absolute error = 9.210526870084834e-07 relative error = 9.203497603203538e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 1e-06 x1[1] (analytic) = 2.001048946854272 x1[1] (numeric) = 2.001047199813042 absolute error = 1.747041229904767e-06 relative error = 8.73062716757221e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 0.5500000000014378 x2[1] (analytic) = 1.000773918147905 x2[1] (numeric) = 1.000775376438144 absolute error = 1.458290238565141e-06 relative error = 0.000145716251405107 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 6 h = 1e-06 x1[1] (analytic) = 2.001038509658684 x1[1] (numeric) = 2.00103577970203 absolute error = 2.729956653624299e-06 relative error = 0.0001364269923066072 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 6 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 0.5600000000017253 x2[1] (analytic) = 1.000784333559815 x2[1] (numeric) = 1.000786461382278 absolute error = 2.127822463116047e-06 relative error = 0.0002126154848514993 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 6 h = 1e-06 x1[1] (analytic) = 2.001028176314926 x1[1] (numeric) = 2.001024244817006 absolute error = 3.931497919662519e-06 relative error = 0.0001964738910824698 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 6 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 0.5700000000020129 x2[1] (analytic) = 1.000795011304649 x2[1] (numeric) = 1.000797945896057 absolute error = 2.934591407433018e-06 relative error = 0.0002932260227404059 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 6 h = 1e-06 x1[1] (analytic) = 2.001017945789657 x1[1] (numeric) = 2.001012594004454 absolute error = 5.351785203000503e-06 relative error = 0.0002674531337543072 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 6 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 0.5800000000023005 x2[1] (analytic) = 1.000805956165195 x2[1] (numeric) = 1.000809839816517 absolute error = 3.883651322089676e-06 relative error = 0.0003880523790016924 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 6 h = 1e-06 x1[1] (analytic) = 2.001007817059815 x1[1] (numeric) = 2.00100082609929 absolute error = 6.990960525588008e-06 relative error = 0.0003493719747612075 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 6 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 0.590000000002588 x2[1] (analytic) = 1.000817173026001 x2[1] (numeric) = 1.00082215319717 absolute error = 4.980171168345038e-06 relative error = 0.0004976104829703649 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 6 h = 1e-06 x1[1] (analytic) = 2.00099778911252 x1[1] (numeric) = 2.000988939924704 absolute error = 8.849187815407333e-06 relative error = 0.0004422387602603057 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 6 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 0.6000000000028756 x2[1] (analytic) = 1.000828666875379 x2[1] (numeric) = 1.000834896312546 absolute error = 6.229437167215579e-06 relative error = 0.0006224279313125686 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 6 h = 1e-06 x1[1] (analytic) = 2.000987860944966 x1[1] (numeric) = 2.000976934292082 absolute error = 1.092665288426886e-05 relative error = 0.0005460629270938581 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 6 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 0.6100000000031631 x2[1] (analytic) = 1.00084044280745 x2[1] (numeric) = 1.000848079662803 absolute error = 7.636855352988192e-06 relative error = 0.0007630442402553303 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 6 h = 1e-06 x1[1] (analytic) = 2.000978031564331 x1[1] (numeric) = 2.000964808000847 absolute error = 1.32235634837663e-05 relative error = 0.0006608550056608237 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 6 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 0.6200000000034507 x2[1] (analytic) = 1.000852506024235 x2[1] (numeric) = 1.000861713978518 absolute error = 9.207954282830499e-06 relative error = 0.0009200111132666267 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 6 h = 1e-06 x1[1] (analytic) = 2.000968299987667 x1[1] (numeric) = 2.000952559838368 absolute error = 1.574014929861534e-05 relative error = 0.0007866266196577102 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 6 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 0.6300000000037382 x2[1] (analytic) = 1.00086486183778 x2[1] (numeric) = 1.000875810225497 absolute error = 1.094838771709128e-05 relative error = 0.001093892705653383 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 5 h = 1e-06 x1[1] (analytic) = 2.000958665241809 x1[1] (numeric) = 2.00094018857981 absolute error = 1.847666199905618e-05 relative error = 0.0009233904887697086 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 6 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 0.6400000000040258 x2[1] (analytic) = 1.000877515672332 x2[1] (numeric) = 1.000890379609735 absolute error = 1.286393740351777e-05 relative error = 0.001285265899381955 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 5 h = 1e-06 x1[1] (analytic) = 2.000949126363273 x1[1] (numeric) = 2.00092769298803 absolute error = 2.143337524307398e-05 relative error = 0.001071160428852539 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 5 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 0.6500000000043133 x2[1] (analytic) = 1.000890473066558 x2[1] (numeric) = 1.000905433582435 absolute error = 1.496051587679403e-05 relative error = 0.001494720579261541 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 5 h = 1e-06 x1[1] (analytic) = 2.000939682398166 x1[1] (numeric) = 2.000915071813465 absolute error = 2.461058470126787e-05 relative error = 0.001229951353244771 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 5 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 0.6600000000046009 x2[1] (analytic) = 1.000903739675806 x2[1] (numeric) = 1.000920983845141 absolute error = 1.724416933512884e-05 relative error = 0.001722859916650352 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 5 h = 1e-06 x1[1] (analytic) = 2.000930332402081 x1[1] (numeric) = 2.00090232379398 absolute error = 2.800860810037165e-05 relative error = 0.00139977927501093 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 5 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 0.6700000000048885 x2[1] (analytic) = 1.000917321274416 x2[1] (numeric) = 1.000937042355017 absolute error = 1.972108060122046e-05 relative error = 0.001970300661408341 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 5 h = 1e-06 x1[1] (analytic) = 2.000921075440011 x1[1] (numeric) = 2.000889447654767 absolute error = 3.162778524412602e-05 relative error = 0.00158066130805139 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 5 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 0.680000000005176 x2[1] (analytic) = 1.000931223758076 x2[1] (numeric) = 1.000953621330188 absolute error = 2.239757211186522e-05 relative error = 0.002237673436519619 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 5 h = 1e-06 x1[1] (analytic) = 2.000911910586253 x1[1] (numeric) = 2.000876442108211 absolute error = 3.546847804214437e-05 relative error = 0.001772615668610436 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 5 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 0.6900000000054636 x2[1] (analytic) = 1.000945453146227 x2[1] (numeric) = 1.000970733255203 absolute error = 2.528010897684396e-05 relative error = 0.00252562303943558 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 5 h = 1e-06 x1[1] (analytic) = 2.000902836924314 x1[1] (numeric) = 2.000863305853742 absolute error = 3.953107057164118e-05 relative error = 0.001975661678425442 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 5 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 0.7000000000057511 x2[1] (analytic) = 1.000960015584515 x2[1] (numeric) = 1.000988390886616 absolute error = 2.83753021006472e-05 relative error = 0.002834808749486095 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 5 h = 1e-06 x1[1] (analytic) = 2.000893853546819 x1[1] (numeric) = 2.000850037577774 absolute error = 4.381596904590168e-05 relative error = 0.002189819763213962 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 5 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 0.7100000000060387 x2[1] (analytic) = 1.000974917347298 x2[1] (numeric) = 1.0010066072587 absolute error = 3.168991140256594e-05 relative error = 0.003165904644898392 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 5 h = 1e-06 x1[1] (analytic) = 2.000884959555425 x1[1] (numeric) = 2.000836635953358 absolute error = 4.832360206696862e-05 relative error = 0.002415111465364086 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 5 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 0.7200000000063262 x2[1] (analytic) = 1.000990164840197 x2[1] (numeric) = 1.001025395689212 absolute error = 3.523084901502216e-05 relative error = 0.003519599917412433 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 5 h = 1e-06 x1[1] (analytic) = 2.000876154060722 x1[1] (numeric) = 2.000823099640382 absolute error = 5.305442034009289e-05 relative error = 0.002651559429723845 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 5 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 0.7300000000066138 x2[1] (analytic) = 1.001005764602707 x2[1] (numeric) = 1.001044769785384 absolute error = 3.900518267774267e-05 relative error = 0.003896599206221714 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 5 h = 1e-06 x1[1] (analytic) = 2.000867436182157 x1[1] (numeric) = 2.00080942728519 absolute error = 5.800889696638833e-05 relative error = 0.002899187418286679 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 5 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 0.7400000000069014 x2[1] (analytic) = 1.001021723310851 x2[1] (numeric) = 1.001064743449923 absolute error = 4.302013907175883e-05 relative error = 0.004297622925651496 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 5 h = 1e-06 x1[1] (analytic) = 2.000858805047932 x1[1] (numeric) = 2.000795617520552 absolute error = 6.318752738021516e-05 relative error = 0.003158020307120145 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 5 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 0.7500000000071889 x2[1] (analytic) = 1.001038047779902 x2[1] (numeric) = 1.001085330887211 absolute error = 4.728310730883756e-05 relative error = 0.004723407608102594 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 5 h = 1e-06 x1[1] (analytic) = 2.000850259794928 x1[1] (numeric) = 2.000781668965467 absolute error = 6.859082946064632e-05 relative error = 0.003428084091993789 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 5 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 0.7600000000074765 x2[1] (analytic) = 1.001054744967144 x2[1] (numeric) = 1.00110654660962 absolute error = 5.18016424755352e-05 relative error = 0.005174706252177587 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 5 h = 1e-06 x1[1] (analytic) = 2.000841799568612 x1[1] (numeric) = 2.000767580225074 absolute error = 7.421934353768478e-05 relative error = 0.003709405888745763 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 5 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 0.770000000007764 x2[1] (analytic) = 1.001071821974704 x2[1] (numeric) = 1.001128405443905 absolute error = 5.658346920056623e-05 relative error = 0.00565228867284969 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 5 h = 1e-06 x1[1] (analytic) = 2.000833423522954 x1[1] (numeric) = 2.000753349890482 absolute error = 8.007363247175547e-05 relative error = 0.004002013937310502 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 5 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 0.7800000000080516 x2[1] (analytic) = 1.001089286052433 x2[1] (numeric) = 1.001150922537832 absolute error = 6.163648539869726e-05 relative error = 0.006156941868966218 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 5 h = 1e-06 x1[1] (analytic) = 2.000825130820343 x1[1] (numeric) = 2.000738976538661 absolute error = 8.615428168212702e-05 relative error = 0.004305937603192917 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 5 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 0.7900000000083391 x2[1] (analytic) = 1.001107144600847 x2[1] (numeric) = 1.001174113366783 absolute error = 6.69687659360374e-05 relative error = 0.006689470382587131 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 5 h = 1e-06 x1[1] (analytic) = 2.000816920631502 x1[1] (numeric) = 2.000724458732245 absolute error = 9.246189925615766e-05 relative error = 0.00462120738298108 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 5 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 Finished! diff ( x2 , t , 2 ) = 3.0 * diff ( x2 , t , 1 ) - 2.0 * x2 - diff ( x1 , t , 2 ) - diff ( x1 , t , 1 ) + x1 ; diff ( x1 , t , 1 ) = 4.0 * x2 - 2.0 * diff ( x2 , t , 1 ) - 2.0 * x1 ; Iterations = 300000 Total Elapsed Time = 1 Minutes 10.0 Seconds Elapsed Time(since restart) = 1 Minutes 10.0 Seconds Time to Timeout = 8 Minutes 50.0 Seconds Percent Done = 100 %