##############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 */ /* # problem from Boyce DePrima - */ /* # _Elementary Differential Equations and Boundary Value Problems_ */ /* # page 269 */ /* # */ t_start=0.5; t_end=0.8; array_x1_init[0 + 1] = exact_soln_x1(t_start); /* # I think following line should be omitted */ /* # diff(x1,1,exact_soln_x1p(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=0.00001; glob_look_poles=true; glob_max_iter=100; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=1000000000; glob_max_minutes=30.0; 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 = 3.333333333333333e-16 est_needed_step_err = 3.333333333333333e-16 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.077953242000188e-178 estimated_step_error = 2.077953242000188e-178 best_h = 2e-06 opt_iter = 2 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.394490866805309e-170 estimated_step_error = 1.394490866805309e-170 best_h = 4e-06 opt_iter = 3 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.35827048617323e-163 estimated_step_error = 9.35827048617323e-163 best_h = 8e-06 opt_iter = 4 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.280229943722694e-155 estimated_step_error = 6.280229943722694e-155 best_h = 1.6e-05 opt_iter = 5 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.214592220588539e-147 estimated_step_error = 4.214592220588539e-147 best_h = 1e-05 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 % Correct digits = 16 h = 1e-05 x1[1] (analytic) = 2.001091755187483 x1[1] (numeric) = 2.001091755187483 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.5 Order of pole (ratio test) = 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] = 0.5100099999999544 x2[1] (analytic) = 1.000734796917849 x2[1] (numeric) = 1.000734852348989 absolute error = 5.543114012240835e-08 relative error = 5.539043939826022e-06 % Correct digits = 8 h = 1e-05 x1[1] (analytic) = 2.001080881232996 x1[1] (numeric) = 2.001080771838112 absolute error = 1.093948838182257e-07 relative error = 5.466789715707064e-06 % Correct digits = 8 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.5 Order of pole (ratio test) = 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] = 0.5200099999999089 x2[1] (analytic) = 1.00074420910069 x2[1] (numeric) = 1.000744433567788 absolute error = 2.244670984641317e-07 relative error = 2.243001722346684e-05 % Correct digits = 7 h = 1e-05 x1[1] (analytic) = 2.00107012628503 x1[1] (numeric) = 2.001069689131566 absolute error = 4.37153464094564e-07 relative error = 2.184598422375811e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.5 Order of pole (ratio test) = 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] = 0.5300099999998634 x2[1] (analytic) = 1.00075386546855 x2[1] (numeric) = 1.000754377093754 absolute error = 5.116252037584701e-07 relative error = 5.112397977288137e-05 % Correct digits = 7 h = 1e-05 x1[1] (analytic) = 2.001059478350585 x1[1] (numeric) = 2.001058495041968 absolute error = 9.833086163091309e-07 relative error = 4.913939975035843e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.5 Order of pole (ratio test) = 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] = 0.5400099999998179 x2[1] (analytic) = 1.000763770416525 x2[1] (numeric) = 1.000764691941979 absolute error = 9.215254539451934e-07 relative error = 9.208221572226259e-05 % Correct digits = 7 h = 1e-05 x1[1] (analytic) = 2.001048936364857 x1[1] (numeric) = 2.001047188449899 absolute error = 1.747914957661578e-06 relative error = 8.734993562110845e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.5 Order of pole (ratio test) = 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] = 0.5500099999997724 x2[1] (analytic) = 1.000773928433847 x2[1] (numeric) = 1.000775387326714 absolute error = 1.458892867400863e-06 relative error = 0.0001457764661879177 % Correct digits = 6 h = 1e-05 x1[1] (analytic) = 2.001038499273641 x1[1] (numeric) = 2.00103576822469 absolute error = 2.731048950987969e-06 relative error = 0.0001364815795387903 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.5 Order of pole (ratio test) = 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] = 0.5600099999997269 x2[1] (analytic) = 1.000784344105734 x2[1] (numeric) = 1.000786472665576 absolute error = 2.128559841718669e-06 relative error = 0.0002126891626807648 % Correct digits = 6 h = 1e-05 x1[1] (analytic) = 2.001028166033216 x1[1] (numeric) = 2.001024233224313 absolute error = 3.932808903428509e-06 relative error = 0.0001965394075998841 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.5 Order of pole (ratio test) = 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] = 0.5700099999996814 x2[1] (analytic) = 1.000795022115277 x2[1] (numeric) = 1.000797957583819 absolute error = 2.935468541132025e-06 relative error = 0.0002933136632641944 % Correct digits = 6 h = 1e-05 x1[1] (analytic) = 2.001017935610252 x1[1] (numeric) = 2.001012582295246 absolute error = 5.353315005951487e-06 relative error = 0.0002675295863512029 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.5 Order of pole (ratio test) = 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] = 0.5800099999996359 x2[1] (analytic) = 1.000805967245367 x2[1] (numeric) = 1.000809851918691 absolute error = 3.884673324794363e-06 relative error = 0.0003881544926722006 % Correct digits = 6 h = 1e-05 x1[1] (analytic) = 2.001007806981698 x1[1] (numeric) = 2.001000814272398 absolute error = 6.992709300046585e-06 relative error = 0.000349459371205269 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.5 Order of pole (ratio test) = 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] = 0.5900099999995904 x2[1] (analytic) = 1.000817184380651 x2[1] (numeric) = 1.000822165723919 absolute error = 4.981343267429494e-06 relative error = 0.0004977275915293325 % Correct digits = 6 h = 1e-05 x1[1] (analytic) = 2.000997779134681 x1[1] (numeric) = 2.000988927978954 absolute error = 8.851155727018778e-06 relative error = 0.0004423371089820202 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.5 Order of pole (ratio test) = 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] = 0.6000099999995449 x2[1] (analytic) = 1.000828678509549 x2[1] (numeric) = 1.000834909274242 absolute error = 6.230764693082591e-06 relative error = 0.0006225605667457044 % Correct digits = 6 h = 1e-05 x1[1] (analytic) = 2.00098785106641 x1[1] (numeric) = 2.000976922226284 absolute error = 1.092884012576789e-05 relative error = 0.0005461722378745806 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.5 Order of pole (ratio test) = 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] = 0.6100099999994993 x2[1] (analytic) = 1.000840454726288 x2[1] (numeric) = 1.000848093070066 absolute error = 7.638343778371137e-06 relative error = 0.0007631929487162955 % Correct digits = 6 h = 1e-05 x1[1] (analytic) = 2.000978021784068 x1[1] (numeric) = 2.000964795813787 absolute error = 1.322597028119432e-05 relative error = 0.0006609752899435683 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.5 Order of pole (ratio test) = 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] = 0.6200099999994538 x2[1] (analytic) = 1.000852518232997 x2[1] (numeric) = 1.000861727842197 absolute error = 9.209609199478663e-06 relative error = 0.0009201764527443273 % Correct digits = 6 h = 1e-05 x1[1] (analytic) = 2.00096829030472 x1[1] (numeric) = 2.000952547528819 absolute error = 1.574277590066231e-05 relative error = 0.0007867578900145841 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.5 Order of pole (ratio test) = 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] = 0.6300099999994083 x2[1] (analytic) = 1.000864874341834 x2[1] (numeric) = 1.000875824556686 absolute error = 1.095021485175707e-05 relative error = 0.001094075247566051 % Correct digits = 5 h = 1e-05 x1[1] (analytic) = 2.000958655655209 x1[1] (numeric) = 2.000940176146539 absolute error = 1.847950866951109e-05 relative error = 0.0009235327585246895 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.5 Order of pole (ratio test) = 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] = 0.6400099999993628 x2[1] (analytic) = 1.000877528477159 x2[1] (numeric) = 1.000890394419759 absolute error = 1.286594259997109e-05 relative error = 0.001285466226776686 % Correct digits = 5 h = 1e-05 x1[1] (analytic) = 2.000949116872062 x1[1] (numeric) = 2.000927680429794 absolute error = 2.143644226793029e-05 relative error = 0.001071313712436642 % Correct digits = 5 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.5 Order of pole (ratio test) = 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] = 0.6500099999993173 x2[1] (analytic) = 1.000890486177755 x2[1] (numeric) = 1.000905448882863 absolute error = 1.496270510781272e-05 relative error = 0.001494939288008717 % Correct digits = 5 h = 1e-05 x1[1] (analytic) = 2.000939673001394 x1[1] (numeric) = 2.000915059129018 absolute error = 2.46138723754008e-05 relative error = 0.001230115665530295 % Correct digits = 5 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.5 Order of pole (ratio test) = 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] = 0.6600099999992718 x2[1] (analytic) = 1.000903753099088 x2[1] (numeric) = 1.000920999647803 absolute error = 1.724654871559927e-05 relative error = 0.00172309761674876 % Correct digits = 5 h = 1e-05 x1[1] (analytic) = 2.000930323098808 x1[1] (numeric) = 2.000902310982063 absolute error = 2.801211674485771e-05 relative error = 0.001399954632177086 % Correct digits = 5 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.5 Order of pole (ratio test) = 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] = 0.6700099999992263 x2[1] (analytic) = 1.000917335015617 x2[1] (numeric) = 1.000937058671998 absolute error = 1.972365638103213e-05 relative error = 0.001970557976271276 % Correct digits = 5 h = 1e-05 x1[1] (analytic) = 2.000921066229308 x1[1] (numeric) = 2.000889434714096 absolute error = 3.163151521246022e-05 relative error = 0.001580847727895089 % Correct digits = 5 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.5 Order of pole (ratio test) = 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] = 0.6800099999991808 x2[1] (analytic) = 1.000931237823153 x2[1] (numeric) = 1.000953638173839 absolute error = 2.24003506852366e-05 relative error = 0.002237951003902462 % Correct digits = 5 h = 1e-05 x1[1] (analytic) = 2.000911901467199 x1[1] (numeric) = 2.000876429037485 absolute error = 3.547242971402298e-05 relative error = 0.001772813170235645 % Correct digits = 5 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.5 Order of pole (ratio test) = 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] = 0.6900099999991353 x2[1] (analytic) = 1.000945467541262 x2[1] (numeric) = 1.000970750638141 absolute error = 2.528309687854779e-05 relative error = 0.002525921511054301 % Correct digits = 5 h = 1e-05 x1[1] (analytic) = 2.000902827895996 x1[1] (numeric) = 2.000863292651654 absolute error = 3.953524434141542e-05 relative error = 0.001975870281666192 % Correct digits = 5 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.5 Order of pole (ratio test) = 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] = 0.7000099999990897 x2[1] (analytic) = 1.000960030315719 x2[1] (numeric) = 1.000988408821742 absolute error = 2.837850602332992e-05 relative error = 0.002835128792742992 % Correct digits = 5 h = 1e-05 x1[1] (analytic) = 2.000893844608334 x1[1] (numeric) = 2.000850024242944 absolute error = 4.382036539052336e-05 relative error = 0.002190039492030173 % Correct digits = 5 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.5 Order of pole (ratio test) = 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] = 0.7100099999990442 x2[1] (analytic) = 1.000974932421009 x2[1] (numeric) = 1.001006625759181 absolute error = 3.169333817165665e-05 relative error = 0.003166246940370577 % Correct digits = 5 h = 1e-05 x1[1] (analytic) = 2.000884950705879 x1[1] (numeric) = 2.000836622484517 absolute error = 4.83282213625813e-05 relative error = 0.00241534233867529 % Correct digits = 5 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.5 Order of pole (ratio test) = 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] = 0.7200099999989987 x2[1] (analytic) = 1.000990180262888 x2[1] (numeric) = 1.001025414768518 absolute error = 3.52345056298109e-05 relative error = 0.003519965162950681 % Correct digits = 5 h = 1e-05 x1[1] (analytic) = 2.000876145299232 x1[1] (numeric) = 2.000823086036168 absolute error = 5.305926306364839e-05 relative error = 0.00265180147148555 % Correct digits = 5 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.5 Order of pole (ratio test) = 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] = 0.7300099999989532 x2[1] (analytic) = 1.001005780380985 x2[1] (numeric) = 1.001044789457264 absolute error = 3.900907627918393e-05 relative error = 0.003896988113728672 % Correct digits = 5 h = 1e-05 x1[1] (analytic) = 2.000867427507845 x1[1] (numeric) = 2.000809413544264 absolute error = 5.80139635806276e-05 relative error = 0.002899440651742038 % Correct digits = 5 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.5 Order of pole (ratio test) = 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] = 0.7400099999989077 x2[1] (analytic) = 1.001021739451462 x2[1] (numeric) = 1.001064763728433 absolute error = 4.302427697067124e-05 relative error = 0.004298036223893359 % Correct digits = 5 h = 1e-05 x1[1] (analytic) = 2.000858796459931 x1[1] (numeric) = 2.000795603641525 absolute error = 6.319281840649893e-05 relative error = 0.003158284758439945 % Correct digits = 5 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.5 Order of pole (ratio test) = 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] = 0.7500099999988622 x2[1] (analytic) = 1.001038064289731 x2[1] (numeric) = 1.00108535178671 absolute error = 4.72874969792425e-05 relative error = 0.004723846042037824 % Correct digits = 5 h = 1e-05 x1[1] (analytic) = 2.000850251292379 x1[1] (numeric) = 2.000781654946956 absolute error = 6.859634542344395e-05 relative error = 0.003428359787502165 % Correct digits = 5 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.5 Order of pole (ratio test) = 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] = 0.7600099999988167 x2[1] (analytic) = 1.001054761853221 x2[1] (numeric) = 1.00110656814477 absolute error = 5.180629154954985e-05 relative error = 0.005175170582440716 % Correct digits = 5 h = 1e-05 x1[1] (analytic) = 2.000841791150665 x1[1] (numeric) = 2.000767566065672 absolute error = 7.422508499299596e-05 relative error = 0.003709692856340721 % Correct digits = 5 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.5 Order of pole (ratio test) = 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] = 0.7700099999987712 x2[1] (analytic) = 1.001071839244204 x2[1] (numeric) = 1.001128427629701 absolute error = 5.658838549615908e-05 relative error = 0.005652779678517631 % Correct digits = 5 h = 1e-05 x1[1] (analytic) = 2.000833415188768 x1[1] (numeric) = 2.000753335588789 absolute error = 8.007959997913261e-05 relative error = 0.004002312205065684 % Correct digits = 5 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.5 Order of pole (ratio test) = 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] = 0.7800099999987257 x2[1] (analytic) = 1.001089303712681 x2[1] (numeric) = 1.001150945389562 absolute error = 6.164167688127442e-05 relative error = 0.006157460343714347 % Correct digits = 5 h = 1e-05 x1[1] (analytic) = 2.000825122569084 x1[1] (numeric) = 2.000738962093224 absolute error = 8.616047585974229e-05 relative error = 0.004306247202109858 % Correct digits = 5 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.5 Order of pole (ratio test) = 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] = 0.7900099999986802 x2[1] (analytic) = 1.00110716265932 x2[1] (numeric) = 1.001174136900111 absolute error = 6.697424079082914e-05 relative error = 0.006690017141913179 % Correct digits = 5 h = 1e-05 x1[1] (analytic) = 2.000816912462344 x1[1] (numeric) = 2.000724444141627 absolute error = 9.246832071641009e-05 relative error = 0.004621528343770953 % Correct digits = 5 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.5 Order of pole (ratio test) = 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 = 30001 Total Elapsed Time = 5.0 Seconds Elapsed Time(since restart) = 5.0 Seconds Time to Timeout = 29 Minutes 55.0 Seconds Percent Done = 100 %