##############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; ELIMINATED in preodein.rb 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=0.0001 $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=10000000 $glob_max_minutes=3 $glob_subiter_method=3 #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_x1 (t) c1 = 1.0; c2 = 0.0002; c3 = 0.0003; return(2.0 * c1 + 6.0 * c3 * exp(-t)) end def exact_soln_x1p (t) c1 = 1.0; c2 = 0.0002; c3 = 0.0003; return( - 6.0 * c3 * exp(-t)) end def exact_soln_x2 (t) c1 = 1.0; c2 = 0.0002; c3 = 0.0003; return(c1 + c2 * exp(2.0 * t) + c3 * exp(-t)) end def exact_soln_x2p (t) c1 = 1.0; c2 = 0.0002; c3 = 0.0003; return( 2.0 * c2 * exp(2.0 * t) - c3 * exp(-t)) 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 10 desired_abs_gbl_error 1.0e-10 range 0.30000000000000004 estimated_steps 300000.00000000006 step_error 3.3333333333333326e-16 est_needed_step_err 3.3333333333333326e-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 2.115801377437763e-178 estimated_step_error 2.115801377437763e-178 best_h 2.0e-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 1.4198903214833679e-170 estimated_step_error 1.4198903214833679e-170 best_h 4.0e-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 9.528723353765774e-163 estimated_step_error 9.528723353765774e-163 best_h 8.0e-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 6.394618943766002e-155 estimated_step_error 6.394618943766002e-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 4.2913574018038153e-147 estimated_step_error 4.2913574018038153e-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 2.8798829091286545e-139 estimated_step_error 2.8798829091286545e-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 1.9326589954076476e-131 estimated_step_error 1.9326589954076476e-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 1.2969885711617002e-123 estimated_step_error 1.2969885711617002e-123 best_h 0.0001 START of Soultion TOP MAIN SOLVE Loop t[1] 0.5 x2[1] (analytic) 1.0007256155636055 x2[1] (numeric) 1.0007256155636055 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.0001 x1[1] (analytic) 2.001091755187483 x1[1] (numeric) 2.001091755187483 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 8.999955781173066 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 15732.049286500394 Order of pole (six term test) 13026167.814560136 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 9021.974984962475 Order of pole (six term test) -2256853.6874961765 TOP MAIN SOLVE Loop t[1] 0.5100999999999989 x2[1] (analytic) 1.0007348805513538 x2[1] (numeric) 1.0007349369904983 absolute error 5.643914446906706e-08 relative error 5.639769889700654e-06% Correct digits 8 h 0.0001 x1[1] (analytic) 2.001080783958062 x1[1] (numeric) 2.001080672587168 absolute error 1.1137089384050114e-07 relative error 5.56553712040619e-06% Correct digits 8 h 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 8.999956225537577 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 15811.697995801662 Order of pole (six term test) 13158400.404657584 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 6444.108318646856 Order of pole (six term test) -356759.60351375624 TOP MAIN SOLVE Loop t[1] 0.5200999999999978 x2[1] (analytic) 1.0007442949125347 x2[1] (numeric) 1.0007445214304405 absolute error 2.2651790576588837e-07 relative error 2.2634943503293825e-05% Correct digits 7 h 0.0001 x1[1] (analytic) 2.001070029977998 x1[1] (numeric) 2.001069588883132 absolute error 4.4109486641019657e-07 relative error 2.204295001185173e-05% Correct digits 7 h 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 8.999956661102852 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 15890.959119067445 Order of pole (six term test) 13290651.810065588 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] 0.5300999999999967 x2[1] (analytic) 1.0007539534978767 x2[1] (numeric) 1.0007544682578071 absolute error 5.147599304589079e-07 relative error 5.143721178014812e-05% Correct digits 7 h 0.0001 x1[1] (analytic) 2.0010593830018237 x1[1] (numeric) 2.0010583937860207 absolute error 9.89215803048893e-07 relative error 4.9434605062292215e-05% Correct digits 7 h 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 8.999957092334135 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 15970.617536717944 Order of pole (six term test) 13424232.684430648 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] 0.5400999999999956 x2[1] (analytic) 1.0007638607033134 x2[1] (numeric) 1.0007647864894653 absolute error 9.25786151961816e-07 relative error 9.250795200689953e-05% Correct digits 7 h 0.0001 x1[1] (analytic) 2.0010488419648325 x1[1] (numeric) 2.001047086176313 absolute error 1.7557885194641187e-06 relative error 8.774341148715329e-05% Correct digits 7 h 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 8.999957519274556 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 16050.6614604691 Order of pole (six term test) 13559133.987329189 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 5972.478809754603 Order of pole (six term test) -2196329.540211804 TOP MAIN SOLVE Loop t[1] 0.5500999999999945 x2[1] (analytic) 1.0007740210189329 x2[1] (numeric) 1.000775485341483 absolute error 1.4643225501043133e-06 relative error 0.00014631900102816627% Correct digits 6 h 0.0001 x1[1] (analytic) 2.0010384058129116 x1[1] (numeric) 2.001035664923239 absolute error 2.7408896725589216e-06 relative error 0.00013697336665787028% Correct digits 6 h 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 8.999957941966818 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 16131.120690100104 Order of pole (six term test) 13695413.515193272 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 5438.25108701994 Order of pole (six term test) -1733391.2304868924 TOP MAIN SOLVE Loop t[1] 0.5600999999999934 x2[1] (analytic) 1.0007844390308265 x2[1] (numeric) 1.000786574233322 absolute error 2.1352024954790494e-06 relative error 0.0002133528872158333% Correct digits 6 h 0.0001 x1[1] (analytic) 2.0010280735024373 x1[1] (numeric) 2.001024128884665 absolute error 3.944617772422276e-06 relative error 0.0001971295567841753% Correct digits 6 h 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 8.999958360453178 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 16211.984625199711 Order of pole (six term test) 13833065.108761305 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] 0.5700999999999923 x2[1] (analytic) 1.0007951194229747 x2[1] (numeric) 1.0007980627921182 absolute error 2.943369143526553e-06 relative error 0.0002941030672914954% Correct digits 6 h 0.0001 x1[1] (analytic) 2.00101784400017 x1[1] (numeric) 2.0010124769069737 absolute error 5.367093196095851e-06 relative error 0.00026821815768352517% Correct digits 6 h 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 8.999958774775491 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 16293.230840779652 Order of pole (six term test) 13972063.050998107 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] 0.5800999999999912 x2[1] (analytic) 1.0008060669791734 x2[1] (numeric) 1.0008099608570589 absolute error 3.893877885463581e-06 relative error 0.00038907416870651447% Correct digits 6 h 0.0001 x1[1] (analytic) 2.0010077162831506 x1[1] (numeric) 2.0010007078249585 absolute error 7.008458192014899e-06 relative error 0.00035024643508287074% Correct digits 6 h 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 8.999959184975184 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 16374.915772186298 Order of pole (six term test) 14112508.02672316 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 23699.33867535051 Order of pole (six term test) -4492544.590083616 TOP MAIN SOLVE Loop t[1] 0.5900999999999901 x2[1] (analytic) 1.0008172865849976 x2[1] (numeric) 1.0008222784838354 absolute error 4.991898837847231e-06 relative error 0.0004987822357546057% Correct digits 6 h 0.0001 x1[1] (analytic) 2.0009976893385995 x1[1] (numeric) 2.0009888204617026 absolute error 8.868876896883648e-06 relative error 0.0004432227455402573% Correct digits 6 h 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 8.99995959109329 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 16456.987413978124 Order of pole (six term test) 14254328.7830513 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 23103.26041093388 Order of pole (six term test) -62786999.95105452 TOP MAIN SOLVE Loop t[1] 0.600099999999989 x2[1] (analytic) 1.000828783229808 x2[1] (numeric) 1.000835025949199 absolute error 6.2427193909808665e-06 relative error 0.0006237549814299683% Correct digits 6 h 0.0001 x1[1] (analytic) 2.0009877621638137 x1[1] (numeric) 2.0009768136284594 absolute error 1.094853535432705e-05 relative error 0.0005471565374536624% Correct digits 6 h 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 8.999959993170418 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 16539.474830503368 Order of pole (six term test) 14397581.32096293 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 5822.981806493776 Order of pole (six term test) -1602345.886681051 TOP MAIN SOLVE Loop t[1] 0.6100999999999879 x2[1] (analytic) 1.0008405620087946 x2[1] (numeric) 1.0008482137556065 absolute error 7.651746811943028e-06 relative error 0.0007645320446031034% Correct digits 6 h 0.0001 x1[1] (analytic) 2.000977933766068 x1[1] (numeric) 2.0009646861245365 absolute error 1.3247641531322074e-05 relative error 0.0006620583519573606% Correct digits 6 h 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 8.999960391246775 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 16622.38227746543 Order of pole (six term test) 14542284.260000704 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 4587.771844952825 Order of pole (six term test) -1341537.0416424866 TOP MAIN SOLVE Loop t[1] 0.6200999999999868 x2[1] (analytic) 1.0008526281250667 x2[1] (numeric) 1.0008618526359596 absolute error 9.224510892913429e-06 relative error 0.0009216652515759526% Correct digits 6 h 0.0001 x1[1] (analytic) 2.000968203162513 x1[1] (numeric) 2.0009524367371743 absolute error 1.5766425338625822e-05 relative error 0.0007879398240165497% Correct digits 6 h 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 8.999960785362173 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 16705.706797174713 Order of pole (six term test) 14688444.379669309 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 9289.300372297323 Order of pole (six term test) -4503747.377750388 TOP MAIN SOLVE Loop t[1] 0.6300999999999857 x2[1] (analytic) 1.000864986891782 x2[1] (numeric) 1.0008759535584457 absolute error 1.0966666663669855e-05 relative error 0.001095718883895338% Correct digits 5 h 0.0001 x1[1] (analytic) 2.0009585693800815 x1[1] (numeric) 2.00094006424142 absolute error 1.8505138661417675e-05 relative error 0.0009248136840309875% Correct digits 6 h 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 8.99996117555602 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 16789.43594229065 Order of pole (six term test) 14836051.498240668 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 5973.123930015814 Order of pole (six term test) -1507294.8758219637 TOP MAIN SOLVE Loop t[1] 0.6400999999999846 x2[1] (analytic) 1.0008776437343216 x2[1] (numeric) 1.00089052773148 absolute error 1.2883997158263938e-05 relative error 0.0012872699514191502% Correct digits 5 h 0.0001 x1[1] (analytic) 2.0009490314553866 x1[1] (numeric) 2.0009275674000184 absolute error 2.146405536818108e-05 relative error 0.0010726937583497185% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 8.999961561867341 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 16873.5989987049 Order of pole (six term test) 14985165.673264012 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 4837.155446008548 Order of pole (six term test) -3705622.1041132296 TOP MAIN SOLVE Loop t[1] 0.6500999999999835 x2[1] (analytic) 1.0008906041925067 x2[1] (numeric) 1.0009055866087362 absolute error 1.4982416229436524e-05 relative error 0.0014969084699844853% Correct digits 5 h 0.0001 x1[1] (analytic) 2.0009395884346284 x1[1] (numeric) 2.00091494496327 absolute error 2.4643471358221092e-05 relative error 0.0012315949717152696% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 8.999961944334773 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 16958.183511081967 Order of pole (six term test) 15135778.090705993 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 7142.062675714836 Order of pole (six term test) -1109681.9674654545 TOP MAIN SOLVE Loop t[1] 0.6600999999999824 x2[1] (analytic) 1.0009038739228646 x2[1] (numeric) 1.0009211418943005 absolute error 1.726797143586367e-05 relative error 0.001725237746176856% Correct digits 5 h 0.0001 x1[1] (analytic) 2.0009302393734965 x1[1] (numeric) 2.0009021956689246 absolute error 2.8043704571878436e-05 relative error 0.0014015333478422062% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 8.999962322996552 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 17043.185183419922 Order of pole (six term test) 15287892.708652696 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 11511.297195783265 Order of pole (six term test) -9647766.61602445 TOP MAIN SOLVE Loop t[1] 0.6700999999999813 x2[1] (analytic) 1.0009174587009366 x2[1] (numeric) 1.000937205547915 absolute error 1.9746846978474508e-05 relative error 0.001972874666818521% Correct digits 5 h 0.0001 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 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 8.999962697890556 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 17128.608504109237 Order of pole (six term test) 15441528.48745625 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 7365.098475738712 Order of pole (six term test) -1991232.5631660612 TOP MAIN SOLVE Loop t[1] 0.6800999999999802 x2[1] (analytic) 1.0009313644236368 x2[1] (numeric) 1.000953789790338 absolute error 2.242536670116202e-05 relative error 0.0022404499946982025% Correct digits 5 h 0.0001 x1[1] (analytic) 2.000911819399759 x1[1] (numeric) 2.0008763113948644 absolute error 3.550800489460215e-05 relative error 0.001774591191392631% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 8.99996306905427 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 17214.466268252076 Order of pole (six term test) 15596719.192629544 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 7862.250965348234 Order of pole (six term test) -915256.9553019406 TOP MAIN SOLVE Loop t[1] 0.6900999999999791 x2[1] (analytic) 1.0009455971116548 x2[1] (numeric) 1.0009709071088158 absolute error 2.5309997160993802e-05 relative error 0.002528608671043536% Correct digits 5 h 0.0001 x1[1] (analytic) 2.0009027466451403 x1[1] (numeric) 2.000863173826703 absolute error 3.9572818437250135e-05 relative error 0.0019777482190776545% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 8.999963436524808 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 17300.773608348783 Order of pole (six term test) 15753502.02140821 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] 0.700099999999978 x2[1] (analytic) 1.0009601629119127 x2[1] (numeric) 1.0009885702626524 absolute error 2.8407350739723114e-05 relative error 0.002838010121909621% Correct digits 5 h 0.0001 x1[1] (analytic) 2.000893764165939 x1[1] (numeric) 2.0008499042237875 absolute error 4.3859942151502906e-05 relative error 0.0021920175342135502% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 8.999963800338929 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 17387.469142785376 Order of pole (six term test) 15911784.583538232 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 4252.862247979717 Order of pole (six term test) -1151175.1967979164 TOP MAIN SOLVE Loop t[1] 0.7100999999999769 x2[1] (analytic) 1.0009750681000673 x2[1] (numeric) 1.0010067922889172 absolute error 3.172418884989092e-05 relative error 0.00316932857379815% Correct digits 5 h 0.0001 x1[1] (analytic) 2.000884871063899 x1[1] (numeric) 2.000836501259143 absolute error 4.8369804755754586e-05 relative error 0.002417420684981024% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 8.999964160533017 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 17474.627831932965 Order of pole (six term test) 16071707.107276715 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 7661.664176652707 Order of pole (six term test) -2202556.12310734 TOP MAIN SOLVE Loop t[1] 0.7200999999999758 x2[1] (analytic) 1.0009903190830665 x2[1] (numeric) 1.0010255865082485 absolute error 3.526742518200621e-05 relative error 0.0035232533731507113% Correct digits 5 h 0.0001 x1[1] (analytic) 2.0008760664497025 x1[1] (numeric) 2.000822963592466 absolute error 5.310285723636454e-05 relative error 0.0026539803302554734% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 8.999964517143074 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 17562.239527583708 Order of pole (six term test) 16233265.091388825 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] 0.7300999999999747 x2[1] (analytic) 1.0010059224017553 x2[1] (numeric) 1.0010449665307888 absolute error 3.904412903343868e-05 relative error 0.003900489313765344% Correct digits 5 h 0.0001 x1[1] (analytic) 2.0008673494428812 x1[1] (numeric) 2.0008092898699767 absolute error 5.805957290450081e-05 relative error 0.0029017202425071728% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 8.999964870204781 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 17650.2494637136 Order of pole (six term test) 16396375.293732515 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 5004.88983530022 Order of pole (six term test) 815592.3118429041 TOP MAIN SOLVE Loop t[1] 0.7400999999999736 x2[1] (analytic) 1.0010218847335386 x2[1] (numeric) 1.0010649462622372 absolute error 4.306152869859581e-05 relative error 0.004301756970084458% Correct digits 5 h 0.0001 x1[1] (analytic) 2.000858719171727 x1[1] (numeric) 2.0007954787242923 absolute error 6.324044743477586e-05 relative error 0.003160665309790328% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 8.999965219753433 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 17738.723135860626 Order of pole (six term test) 16561164.159026014 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 7401.774443143276 Order of pole (six term test) -1640086.2714385637 TOP MAIN SOLVE Loop t[1] 0.7500999999999725 x2[1] (analytic) 1.0010382128950925 x2[1] (numeric) 1.0010855399100267 absolute error 4.7327014934150924e-05 relative error 0.004727793037718005% Correct digits 5 h 0.0001 x1[1] (analytic) 2.0008501747732055 x1[1] (numeric) 2.0007815287742834 absolute error 6.864599892209e-05 relative error 0.003430841538640991% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 8.999965565823993 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 17827.654461544564 Order of pole (six term test) 16727634.030697716 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] 0.7600999999999714 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 x1[1] (analytic) 2.0008417153928697 x1[1] (numeric) 2.000767438624948 absolute error 7.427676792159943e-05 relative error 0.003712276056130458% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 8.999965908451065 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 17917.017269193133 Order of pole (six term test) 16895752.093217537 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] 0.7700999999999703 x2[1] (analytic) 1.001071994687264 x2[1] (numeric) 1.0011286273309918 absolute error 5.663264372790522e-05 relative error 0.005657199884569473% Correct digits 5 h 0.0001 x1[1] (analytic) 2.000833340184775 x1[1] (numeric) 2.0007532068672553 absolute error 8.013331751977049e-05 relative error 0.0040049971134712425% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 8.999966247668917 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 18006.818449887043 Order of pole (six term test) 17065542.719161917 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 Radius of convergence (six term test) for eq 2 8114.495304415933 Order of pole (six term test) -6763552.898253885 TOP MAIN SOLVE Loop t[1] 0.7800999999999692 x2[1] (analytic) 1.0010894626728126 x2[1] (numeric) 1.001151151085101 absolute error 6.16884122883743e-05 relative error 0.006162127820591795% Correct digits 5 h 0.0001 x1[1] (analytic) 2.000825048311393 x1[1] (numeric) 2.0007388320780217 absolute error 8.621623337123907e-05 relative error 0.00430903408791297% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 8.999966583511473 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 18097.094539645033 Order of pole (six term test) 17237084.18434364 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] 0.790099999999968 x2[1] (analytic) 1.0011073252038227 x2[1] (numeric) 1.001174348730683 absolute error 6.702352686027702e-05 relative error 0.006694939211101188% Correct digits 5 h 0.0001 x1[1] (analytic) 2.0008168389435297 x1[1] (numeric) 2.0007243128197523 absolute error 9.252612377741443e-05 relative error 0.004624417486723573% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 8.999966916012303 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 18187.79260060644 Order of pole (six term test) 17410294.232715115 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 3001 Total Elapsed Time 1 Minutes 1.0 Seconds Elapsed Time(since restart) 1 Minutes 1.0 Seconds Time to Timeout 1 Minutes 59.0 Seconds Percent Done 100.06666666665562%