##############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; 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_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=1000000000 $glob_max_minutes=30.0 $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 estimated_h 1.0e-06 estimated_answer 1.0 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 2.0779532420001884e-178 estimated_step_error 2.0779532420001884e-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 1.394490866805309e-170 estimated_step_error 1.394490866805309e-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 9.35827048617323e-163 estimated_step_error 9.35827048617323e-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 6.280229943722694e-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 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 2.8283666375393533e-139 estimated_step_error 2.8283666375393533e-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 1.898086969794602e-131 estimated_step_error 1.898086969794602e-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 1.2737876225160193e-123 estimated_step_error 1.2737876225160193e-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 0.0 relative error 0.0% Correct digits 16 h 0.0001 x2[1] (analytic) 1.0007256155636055 x2[1] (numeric) 1.0007256155636055 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.0001 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 Radius of convergence (ratio test) for eq 2 12.499999837152727 Order of pole (ratio test) 1.0 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 0.5100999999999989 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 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 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 Radius of convergence (ratio test) for eq 2 12.499999838818715 Order of pole (ratio test) 1.0 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 0.5200999999999978 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 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 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 Radius of convergence (ratio test) for eq 2 12.499999840451109 Order of pole (ratio test) 1.0 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 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 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 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 Radius of convergence (ratio test) for eq 2 12.49999984206669 Order of pole (ratio test) 1.0 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 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 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 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 Radius of convergence (ratio test) for eq 2 12.499999843665629 Order of pole (ratio test) 1.0 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 0.5500999999999945 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 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 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 Radius of convergence (ratio test) for eq 2 12.499999845248105 Order of pole (ratio test) 1.0 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 0.5600999999999934 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 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 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 Radius of convergence (ratio test) for eq 2 12.499999846814296 Order of pole (ratio test) 1.0 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 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 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 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 Radius of convergence (ratio test) for eq 2 12.499999848364375 Order of pole (ratio test) 1.0 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 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 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 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 Radius of convergence (ratio test) for eq 2 12.499999849898499 Order of pole (ratio test) 1.0 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 0.5900999999999901 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 x2[1] (analytic) 1.0008172865849976 x2[1] (numeric) 1.0008222784838352 absolute error 4.991898837625186e-06 relative error 0.0004987822357324194% Correct digits 6 h 0.0001 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 Radius of convergence (ratio test) for eq 2 12.499999851416858 Order of pole (ratio test) 1.0 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 0.600099999999989 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 x2[1] (analytic) 1.000828783229808 x2[1] (numeric) 1.0008350259491987 absolute error 6.242719390758822e-06 relative error 0.0006237549814077822% Correct digits 6 h 0.0001 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 Radius of convergence (ratio test) for eq 2 12.499999852919606 Order of pole (ratio test) 1.0 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 0.6100999999999879 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 x2[1] (analytic) 1.0008405620087946 x2[1] (numeric) 1.0008482137556063 absolute error 7.651746811720983e-06 relative error 0.0007645320445809176% Correct digits 6 h 0.0001 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 Radius of convergence (ratio test) for eq 2 12.499999854406912 Order of pole (ratio test) 1.0 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 0.6200999999999868 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 x2[1] (analytic) 1.0008526281250667 x2[1] (numeric) 1.0008618526359594 absolute error 9.224510892691384e-06 relative error 0.000921665251553767% Correct digits 6 h 0.0001 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 Radius of convergence (ratio test) for eq 2 12.499999855878942 Order of pole (ratio test) 1.0 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 0.6300999999999857 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 x2[1] (analytic) 1.000864986891782 x2[1] (numeric) 1.0008759535584455 absolute error 1.096666666344781e-05 relative error 0.0010957188838731527% Correct digits 5 h 0.0001 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 Radius of convergence (ratio test) for eq 2 12.49999985733585 Order of pole (ratio test) 1.0 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 0.6400999999999846 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 x2[1] (analytic) 1.0008776437343216 x2[1] (numeric) 1.0008905277314797 absolute error 1.2883997158041893e-05 relative error 0.0012872699513969653% Correct digits 5 h 0.0001 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 Radius of convergence (ratio test) for eq 2 12.4999998587778 Order of pole (ratio test) 1.0 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 0.6500999999999835 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 x2[1] (analytic) 1.0008906041925067 x2[1] (numeric) 1.000905586608736 absolute error 1.4982416229214479e-05 relative error 0.0014969084699623005% Correct digits 5 h 0.0001 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 Radius of convergence (ratio test) for eq 2 12.49999986020496 Order of pole (ratio test) 1.0 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 0.6600999999999824 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 x2[1] (analytic) 1.0009038739228646 x2[1] (numeric) 1.0009211418943 absolute error 1.7267971435419582e-05 relative error 0.0017252377461324873% Correct digits 5 h 0.0001 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 Radius of convergence (ratio test) for eq 2 12.499999861617468 Order of pole (ratio test) 1.0 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 0.6700999999999813 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) 1.0009174587009366 x2[1] (numeric) 1.0009372055479147 absolute error 1.974684697803042e-05 relative error 0.0019728746667741527% Correct digits 5 h 0.0001 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 Radius of convergence (ratio test) for eq 2 12.499999863015498 Order of pole (ratio test) 1.0 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 0.6800999999999802 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 x2[1] (analytic) 1.0009313644236368 x2[1] (numeric) 1.0009537897903376 absolute error 2.242536670071793e-05 relative error 0.0022404499946538353% Correct digits 5 h 0.0001 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 Radius of convergence (ratio test) for eq 2 12.49999986439919 Order of pole (ratio test) 1.0 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 0.6900999999999791 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 x2[1] (analytic) 1.0009455971116548 x2[1] (numeric) 1.0009709071088153 absolute error 2.5309997160549713e-05 relative error 0.0025286086709991693% Correct digits 5 h 0.0001 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 Radius of convergence (ratio test) for eq 2 12.499999865768695 Order of pole (ratio test) 1.0 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 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 x2[1] (analytic) 1.0009601629119127 x2[1] (numeric) 1.000988570262652 absolute error 2.8407350739279025e-05 relative error 0.0028380101218652546% Correct digits 5 h 0.0001 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 Radius of convergence (ratio test) for eq 2 12.499999867124169 Order of pole (ratio test) 1.0 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 0.7100999999999769 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 x2[1] (analytic) 1.0009750681000673 x2[1] (numeric) 1.0010067922889168 absolute error 3.172418884944683e-05 relative error 0.003169328573753784% Correct digits 5 h 0.0001 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 Radius of convergence (ratio test) for eq 2 12.499999868465762 Order of pole (ratio test) 1.0 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 0.7200999999999758 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 x2[1] (analytic) 1.0009903190830665 x2[1] (numeric) 1.001025586508248 absolute error 3.526742518156212e-05 relative error 0.0035232533731063462% Correct digits 5 h 0.0001 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 Radius of convergence (ratio test) for eq 2 12.499999869793607 Order of pole (ratio test) 1.0 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 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 x2[1] (analytic) 1.0010059224017553 x2[1] (numeric) 1.0010449665307883 absolute error 3.904412903299459e-05 relative error 0.00390048931372098% Correct digits 5 h 0.0001 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 Radius of convergence (ratio test) for eq 2 12.49999987110786 Order of pole (ratio test) 1.0 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 0.7400999999999736 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 x2[1] (analytic) 1.0010218847335386 x2[1] (numeric) 1.0010649462622367 absolute error 4.306152869815172e-05 relative error 0.004301756970040095% Correct digits 5 h 0.0001 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 Radius of convergence (ratio test) for eq 2 12.499999872408656 Order of pole (ratio test) 1.0 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 0.7500999999999725 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 x2[1] (analytic) 1.0010382128950925 x2[1] (numeric) 1.0010855399100262 absolute error 4.7327014933706835e-05 relative error 0.004727793037673642% Correct digits 5 h 0.0001 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 Radius of convergence (ratio test) for eq 2 12.499999873696149 Order of pole (ratio test) 1.0 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 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 x2[1] (analytic) 1.001054913845138 x2[1] (numeric) 1.0011067619896286 absolute error 5.184814449066266e-05 relative error 0.005179350680324767% Correct digits 5 h 0.0001 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 Radius of convergence (ratio test) for eq 2 12.49999987497047 Order of pole (ratio test) 1.0 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 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 x2[1] (analytic) 1.001071994687264 x2[1] (numeric) 1.0011286273309914 absolute error 5.663264372746113e-05 relative error 0.005657199884525112% Correct digits 5 h 0.0001 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 Radius of convergence (ratio test) for eq 2 12.499999876231756 Order of pole (ratio test) 1.0 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 0.7800999999999692 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 x2[1] (analytic) 1.0010894626728126 x2[1] (numeric) 1.0011511510851006 absolute error 6.16884122879302e-05 relative error 0.006162127820547434% Correct digits 5 h 0.0001 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 Radius of convergence (ratio test) for eq 2 12.499999877480146 Order of pole (ratio test) 1.0 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 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 x2[1] (analytic) 1.0011073252038227 x2[1] (numeric) 1.0011743487306826 absolute error 6.702352685983293e-05 relative error 0.006694939211056829% Correct digits 5 h 0.0001 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 Radius of convergence (ratio test) for eq 2 12.499999878715778 Order of pole (ratio test) 1.0 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 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 34 Seconds Elapsed Time(since restart) 34 Seconds Time to Timeout 29 Minutes 26.0 Seconds Percent Done 100.06666666665562%