##############ECHO OF PROBLEM################# ##############temp/mtest6_sm_hpostode.ode################# diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1; diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + 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_look_poles=true; glob_max_h=0.0001; // END SECOND INPUT BLOCK // BEGIN OVERRIDE BLOCK glob_desired_digits_correct=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=10000000; glob_max_minutes=3; 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 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 = 2.115801377437761e-178 estimated_step_error = 2.115801377437761e-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 = 1.419890321483367e-170 estimated_step_error = 1.419890321483367e-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 = 9.528723353765765e-163 estimated_step_error = 9.528723353765765e-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 = 6.394618943765996e-155 estimated_step_error = 6.394618943765996e-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 = 4.291357401803811e-147 estimated_step_error = 4.291357401803811e-147 best_h = 3.2e-05 opt_iter = 6 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.879882909128652e-139 estimated_step_error = 2.879882909128652e-139 best_h = 6.4e-05 opt_iter = 7 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.932658995407646e-131 estimated_step_error = 1.932658995407646e-131 best_h = 0.000128 opt_iter = 8 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.296988571161699e-123 estimated_step_error = 1.296988571161699e-123 best_h = 0.0001 START of Soultion TOP MAIN SOLVE Loop t[1] = 0.5 x1[1] (analytic) = 2.001091755187483 x1[1] (numeric) = 2.001091755187483 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.0001 x2[1] (analytic) = 1.000725615563606 x2[1] (numeric) = 1.000725615563606 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 7092 Order of pole (six term test) = -3.392e+06 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 1.573e+04 Order of pole (six term test) = 1.303e+07 TOP MAIN SOLVE Loop t[1] = 0.5100999999999989 x1[1] (analytic) = 2.001080783958062 x1[1] (numeric) = 2.001080672587168 absolute error = 1.113708938405011e-07 relative error = 5.56553712040619e-06 % Correct digits = 8 h = 0.0001 x2[1] (analytic) = 1.000734880551354 x2[1] (numeric) = 1.000734936990498 absolute error = 5.643914446906706e-08 relative error = 5.639769889700654e-06 % Correct digits = 8 h = 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 1.581e+04 Order of pole (six term test) = 1.316e+07 TOP MAIN SOLVE Loop t[1] = 0.5200999999999978 x1[1] (analytic) = 2.001070029977998 x1[1] (numeric) = 2.001069588883132 absolute error = 4.410948664101966e-07 relative error = 2.204295001185173e-05 % Correct digits = 7 h = 0.0001 x2[1] (analytic) = 1.000744294912535 x2[1] (numeric) = 1.00074452143044 absolute error = 2.265179057658884e-07 relative error = 2.263494350329382e-05 % Correct digits = 7 h = 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6217 Order of pole (six term test) = -3.143e+05 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 1.589e+04 Order of pole (six term test) = 1.329e+07 TOP MAIN SOLVE Loop t[1] = 0.5300999999999967 x1[1] (analytic) = 2.001059383001824 x1[1] (numeric) = 2.001058393786021 absolute error = 9.892158030488929e-07 relative error = 4.943460506229222e-05 % Correct digits = 7 h = 0.0001 x2[1] (analytic) = 1.000753953497877 x2[1] (numeric) = 1.000754468257807 absolute error = 5.147599304589079e-07 relative error = 5.143721178014812e-05 % Correct digits = 7 h = 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 1.597e+04 Order of pole (six term test) = 1.342e+07 TOP MAIN SOLVE Loop t[1] = 0.5400999999999956 x1[1] (analytic) = 2.001048841964832 x1[1] (numeric) = 2.001047086176313 absolute error = 1.755788519464119e-06 relative error = 8.774341148715329e-05 % Correct digits = 7 h = 0.0001 x2[1] (analytic) = 1.000763860703313 x2[1] (numeric) = 1.000764786489465 absolute error = 9.25786151961816e-07 relative error = 9.250795200689953e-05 % Correct digits = 7 h = 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3504 Order of pole (six term test) = -1.821e+06 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 1.605e+04 Order of pole (six term test) = 1.356e+07 TOP MAIN SOLVE Loop t[1] = 0.5500999999999945 x1[1] (analytic) = 2.001038405812912 x1[1] (numeric) = 2.001035664923239 absolute error = 2.740889672558922e-06 relative error = 0.0001369733666578703 % Correct digits = 6 h = 0.0001 x2[1] (analytic) = 1.000774021018933 x2[1] (numeric) = 1.000775485341483 absolute error = 1.464322550104313e-06 relative error = 0.0001463190010281663 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 7081 Order of pole (six term test) = -2.086e+06 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 1.613e+04 Order of pole (six term test) = 1.37e+07 TOP MAIN SOLVE Loop t[1] = 0.5600999999999934 x1[1] (analytic) = 2.001028073502437 x1[1] (numeric) = 2.001024128884665 absolute error = 3.944617772422276e-06 relative error = 0.0001971295567841753 % Correct digits = 6 h = 0.0001 x2[1] (analytic) = 1.000784439030826 x2[1] (numeric) = 1.000786574233322 absolute error = 2.135202495479049e-06 relative error = 0.0002133528872158333 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 8533 Order of pole (six term test) = -3.277e+06 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 1.621e+04 Order of pole (six term test) = 1.383e+07 TOP MAIN SOLVE Loop t[1] = 0.5700999999999923 x1[1] (analytic) = 2.00101784400017 x1[1] (numeric) = 2.001012476906974 absolute error = 5.367093196095851e-06 relative error = 0.0002682181576835252 % Correct digits = 6 h = 0.0001 x2[1] (analytic) = 1.000795119422975 x2[1] (numeric) = 1.000798062792118 absolute error = 2.943369143526553e-06 relative error = 0.0002941030672914954 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6695 Order of pole (six term test) = -2.27e+06 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 1.629e+04 Order of pole (six term test) = 1.397e+07 TOP MAIN SOLVE Loop t[1] = 0.5800999999999912 x1[1] (analytic) = 2.001007716283151 x1[1] (numeric) = 2.001000707824959 absolute error = 7.008458192014899e-06 relative error = 0.0003502464350828707 % Correct digits = 6 h = 0.0001 x2[1] (analytic) = 1.000806066979173 x2[1] (numeric) = 1.000809960857059 absolute error = 3.893877885463581e-06 relative error = 0.0003890741687065145 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.526e+04 Order of pole (six term test) = -3.957e+05 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 1.637e+04 Order of pole (six term test) = 1.411e+07 TOP MAIN SOLVE Loop t[1] = 0.5900999999999901 x1[1] (analytic) = 2.000997689338599 x1[1] (numeric) = 2.000988820461703 absolute error = 8.868876896883648e-06 relative error = 0.0004432227455402573 % Correct digits = 6 h = 0.0001 x2[1] (analytic) = 1.000817286584998 x2[1] (numeric) = 1.000822278483835 absolute error = 4.991898837847231e-06 relative error = 0.0004987822357546057 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 7099 Order of pole (six term test) = -1.454e+06 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 1.646e+04 Order of pole (six term test) = 1.425e+07 TOP MAIN SOLVE Loop t[1] = 0.600099999999989 x1[1] (analytic) = 2.000987762163814 x1[1] (numeric) = 2.000976813628459 absolute error = 1.094853535432705e-05 relative error = 0.0005471565374536624 % Correct digits = 6 h = 0.0001 x2[1] (analytic) = 1.000828783229808 x2[1] (numeric) = 1.000835025949199 absolute error = 6.242719390980866e-06 relative error = 0.0006237549814299683 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5803 Order of pole (six term test) = -1.511e+06 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 1.654e+04 Order of pole (six term test) = 1.44e+07 TOP MAIN SOLVE Loop t[1] = 0.6100999999999879 x1[1] (analytic) = 2.000977933766068 x1[1] (numeric) = 2.000964686124536 absolute error = 1.324764153132207e-05 relative error = 0.0006620583519573606 % Correct digits = 6 h = 0.0001 x2[1] (analytic) = 1.000840562008795 x2[1] (numeric) = 1.000848213755607 absolute error = 7.651746811943028e-06 relative error = 0.0007645320446031034 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1029 Order of pole (six term test) = -1.961e+06 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 1.662e+04 Order of pole (six term test) = 1.454e+07 TOP MAIN SOLVE Loop t[1] = 0.6200999999999868 x1[1] (analytic) = 2.000968203162513 x1[1] (numeric) = 2.000952436737174 absolute error = 1.576642533862582e-05 relative error = 0.0007879398240165497 % Correct digits = 6 h = 0.0001 x2[1] (analytic) = 1.000852628125067 x2[1] (numeric) = 1.00086185263596 absolute error = 9.224510892913429e-06 relative error = 0.0009216652515759526 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5424 Order of pole (six term test) = -3.935e+05 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 1.671e+04 Order of pole (six term test) = 1.469e+07 TOP MAIN SOLVE Loop t[1] = 0.6300999999999857 x1[1] (analytic) = 2.000958569380082 x1[1] (numeric) = 2.00094006424142 absolute error = 1.850513866141767e-05 relative error = 0.0009248136840309875 % Correct digits = 6 h = 0.0001 x2[1] (analytic) = 1.000864986891782 x2[1] (numeric) = 1.000875953558446 absolute error = 1.096666666366986e-05 relative error = 0.001095718883895338 % Correct digits = 5 h = 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6294 Order of pole (six term test) = -1.546e+06 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 1.679e+04 Order of pole (six term test) = 1.484e+07 TOP MAIN SOLVE Loop t[1] = 0.6400999999999846 x1[1] (analytic) = 2.000949031455387 x1[1] (numeric) = 2.000927567400018 absolute error = 2.146405536818108e-05 relative error = 0.001072693758349719 % Correct digits = 5 h = 0.0001 x2[1] (analytic) = 1.000877643734322 x2[1] (numeric) = 1.00089052773148 absolute error = 1.288399715826394e-05 relative error = 0.00128726995141915 % Correct digits = 5 h = 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 7286 Order of pole (six term test) = -1.652e+06 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 1.687e+04 Order of pole (six term test) = 1.499e+07 TOP MAIN SOLVE Loop t[1] = 0.6500999999999835 x1[1] (analytic) = 2.000939588434628 x1[1] (numeric) = 2.00091494496327 absolute error = 2.464347135822109e-05 relative error = 0.00123159497171527 % Correct digits = 5 h = 0.0001 x2[1] (analytic) = 1.000890604192507 x2[1] (numeric) = 1.000905586608736 absolute error = 1.498241622943652e-05 relative error = 0.001496908469984485 % Correct digits = 5 h = 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 1.696e+04 Order of pole (six term test) = 1.514e+07 TOP MAIN SOLVE Loop t[1] = 0.6600999999999824 x1[1] (analytic) = 2.000930239373496 x1[1] (numeric) = 2.000902195668925 absolute error = 2.804370457187844e-05 relative error = 0.001401533347842206 % Correct digits = 5 h = 0.0001 x2[1] (analytic) = 1.000903873922865 x2[1] (numeric) = 1.0009211418943 absolute error = 1.726797143586367e-05 relative error = 0.001725237746176856 % Correct digits = 5 h = 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 1.704e+04 Order of pole (six term test) = 1.529e+07 TOP MAIN SOLVE Loop t[1] = 0.6700999999999813 x1[1] (analytic) = 2.000920983337077 x1[1] (numeric) = 2.000889318242042 absolute error = 3.166509503493842e-05 relative error = 0.001582526011703286 % Correct digits = 5 h = 0.0001 x2[1] (analytic) = 1.000917458700937 x2[1] (numeric) = 1.000937205547915 absolute error = 1.974684697847451e-05 relative error = 0.001972874666818521 % Correct digits = 5 h = 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4952 Order of pole (six term test) = -1.355e+06 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 1.713e+04 Order of pole (six term test) = 1.544e+07 TOP MAIN SOLVE Loop t[1] = 0.6800999999999802 x1[1] (analytic) = 2.000911819399759 x1[1] (numeric) = 2.000876311394864 absolute error = 3.550800489460215e-05 relative error = 0.001774591191392631 % Correct digits = 5 h = 0.0001 x2[1] (analytic) = 1.000931364423637 x2[1] (numeric) = 1.000953789790338 absolute error = 2.242536670116202e-05 relative error = 0.002240449994698203 % Correct digits = 5 h = 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 1.721e+04 Order of pole (six term test) = 1.56e+07 TOP MAIN SOLVE Loop t[1] = 0.6900999999999791 x1[1] (analytic) = 2.00090274664514 x1[1] (numeric) = 2.000863173826703 absolute error = 3.957281843725013e-05 relative error = 0.001977748219077655 % Correct digits = 5 h = 0.0001 x2[1] (analytic) = 1.000945597111655 x2[1] (numeric) = 1.000970907108816 absolute error = 2.53099971609938e-05 relative error = 0.002528608671043536 % Correct digits = 5 h = 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 1.73e+04 Order of pole (six term test) = 1.575e+07 TOP MAIN SOLVE Loop t[1] = 0.700099999999978 x1[1] (analytic) = 2.000893764165939 x1[1] (numeric) = 2.000849904223788 absolute error = 4.385994215150291e-05 relative error = 0.00219201753421355 % Correct digits = 5 h = 0.0001 x2[1] (analytic) = 1.000960162911913 x2[1] (numeric) = 1.000988570262652 absolute error = 2.840735073972311e-05 relative error = 0.002838010121909621 % Correct digits = 5 h = 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6414 Order of pole (six term test) = -1.553e+06 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 1.739e+04 Order of pole (six term test) = 1.591e+07 TOP MAIN SOLVE Loop t[1] = 0.7100999999999769 x1[1] (analytic) = 2.000884871063899 x1[1] (numeric) = 2.000836501259143 absolute error = 4.836980475575459e-05 relative error = 0.002417420684981024 % Correct digits = 5 h = 0.0001 x2[1] (analytic) = 1.000975068100067 x2[1] (numeric) = 1.001006792288917 absolute error = 3.172418884989092e-05 relative error = 0.00316932857379815 % Correct digits = 5 h = 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3989 Order of pole (six term test) = -1.972e+06 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 1.747e+04 Order of pole (six term test) = 1.607e+07 TOP MAIN SOLVE Loop t[1] = 0.7200999999999758 x1[1] (analytic) = 2.000876066449703 x1[1] (numeric) = 2.000822963592466 absolute error = 5.310285723636454e-05 relative error = 0.002653980330255473 % Correct digits = 5 h = 0.0001 x2[1] (analytic) = 1.000990319083066 x2[1] (numeric) = 1.001025586508248 absolute error = 3.526742518200621e-05 relative error = 0.003523253373150711 % Correct digits = 5 h = 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 1.756e+04 Order of pole (six term test) = 1.623e+07 TOP MAIN SOLVE Loop t[1] = 0.7300999999999747 x1[1] (analytic) = 2.000867349442881 x1[1] (numeric) = 2.000809289869977 absolute error = 5.805957290450081e-05 relative error = 0.002901720242507173 % Correct digits = 5 h = 0.0001 x2[1] (analytic) = 1.001005922401755 x2[1] (numeric) = 1.001044966530789 absolute error = 3.904412903343868e-05 relative error = 0.003900489313765344 % Correct digits = 5 h = 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 1.765e+04 Order of pole (six term test) = 1.64e+07 TOP MAIN SOLVE Loop t[1] = 0.7400999999999736 x1[1] (analytic) = 2.000858719171727 x1[1] (numeric) = 2.000795478724292 absolute error = 6.324044743477586e-05 relative error = 0.003160665309790328 % Correct digits = 5 h = 0.0001 x2[1] (analytic) = 1.001021884733539 x2[1] (numeric) = 1.001064946262237 absolute error = 4.306152869859581e-05 relative error = 0.004301756970084458 % Correct digits = 5 h = 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 1.774e+04 Order of pole (six term test) = 1.656e+07 TOP MAIN SOLVE Loop t[1] = 0.7500999999999725 x1[1] (analytic) = 2.000850174773205 x1[1] (numeric) = 2.000781528774283 absolute error = 6.864599892209e-05 relative error = 0.003430841538640991 % Correct digits = 5 h = 0.0001 x2[1] (analytic) = 1.001038212895093 x2[1] (numeric) = 1.001085539910027 absolute error = 4.732701493415092e-05 relative error = 0.004727793037718005 % Correct digits = 5 h = 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 1.783e+04 Order of pole (six term test) = 1.673e+07 TOP MAIN SOLVE Loop t[1] = 0.7600999999999714 x1[1] (analytic) = 2.00084171539287 x1[1] (numeric) = 2.000767438624948 absolute error = 7.427676792159943e-05 relative error = 0.003712276056130458 % Correct digits = 5 h = 0.0001 x2[1] (analytic) = 1.001054913845138 x2[1] (numeric) = 1.001106761989629 absolute error = 5.184814449110675e-05 relative error = 0.005179350680369129 % Correct digits = 5 h = 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 1.792e+04 Order of pole (six term test) = 1.69e+07 TOP MAIN SOLVE Loop t[1] = 0.7700999999999703 x1[1] (analytic) = 2.000833340184775 x1[1] (numeric) = 2.000753206867255 absolute error = 8.013331751977049e-05 relative error = 0.004004997113471243 % Correct digits = 5 h = 0.0001 x2[1] (analytic) = 1.001071994687264 x2[1] (numeric) = 1.001128627330992 absolute error = 5.663264372790522e-05 relative error = 0.005657199884569473 % Correct digits = 5 h = 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5043 Order of pole (six term test) = -2.156e+06 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 1.801e+04 Order of pole (six term test) = 1.707e+07 TOP MAIN SOLVE Loop t[1] = 0.7800999999999692 x1[1] (analytic) = 2.000825048311393 x1[1] (numeric) = 2.000738832078022 absolute error = 8.621623337123907e-05 relative error = 0.00430903408791297 % Correct digits = 5 h = 0.0001 x2[1] (analytic) = 1.001089462672813 x2[1] (numeric) = 1.001151151085101 absolute error = 6.168841228837429e-05 relative error = 0.006162127820591795 % Correct digits = 5 h = 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5466 Order of pole (six term test) = -1.616e+06 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 1.81e+04 Order of pole (six term test) = 1.724e+07 TOP MAIN SOLVE Loop t[1] = 0.7900999999999681 x1[1] (analytic) = 2.00081683894353 x1[1] (numeric) = 2.000724312819752 absolute error = 9.252612377741443e-05 relative error = 0.004624417486723573 % Correct digits = 5 h = 0.0001 x2[1] (analytic) = 1.001107325203823 x2[1] (numeric) = 1.001174348730683 absolute error = 6.702352686027702e-05 relative error = 0.006694939211101188 % Correct digits = 5 h = 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5857 Order of pole (six term test) = -1.671e+06 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 = 1.819e+04 Order of pole (six term test) = 1.741e+07 Finished! diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1; diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1; Iterations = 3001 Total Elapsed Time = 1 Seconds Elapsed Time(since restart) = 1 Seconds Time to Timeout = 2 Minutes 59 Seconds Percent Done = 100.1 %