##############ECHO OF PROBLEM################# ##############temp/mtest7_sm_hpostode.ode################# diff ( y2 , x , 5 ) = y1 ; diff ( y1 , x , 1 ) = m1 * y2 ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=30 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=0.0 x_end=0.5 $array_y1_init[0 + 1] = exact_soln_y1(x_start) $array_y2_init[0 + 1] = exact_soln_y2(x_start) $array_y2_init[1 + 1] = exact_soln_y2p(x_start) $array_y2_init[2 + 1] = exact_soln_y2pp(x_start) $array_y2_init[4 + 1] = exact_soln_y2pppp(x_start) $glob_look_poles=true $glob_max_iter=20 $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 def exact_soln_y1 (x) return( cos(x)) end def exact_soln_y2 (x) return( sin(x)) end def exact_soln_y2p (x) return( cos(x)) end def exact_soln_y2pp (x) return( -sin(x)) end def exact_soln_y2ppp (x) return( -cos(x)) end def exact_soln_y2pppp (x) return( sin(x)) 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 0.5 estimated_steps 500000.0 step_error 2.0e-16 est_needed_step_err 2.0e-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 2.4795962632247947e-183 estimated_step_error 2.4795962632247947e-183 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 1.6640288840366095e-175 estimated_step_error 1.6640288840366095e-175 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 1.116710880708846e-167 estimated_step_error 1.116710880708846e-167 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 7.494119862081017e-160 estimated_step_error 7.494119862081017e-160 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 5.029218706240937e-152 estimated_step_error 5.029218706240937e-152 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 3.37505154183379e-144 estimated_step_error 3.37505154183379e-144 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 2.2649587491391413e-136 estimated_step_error 2.2649587491391413e-136 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 1.5199880866158875e-128 estimated_step_error 1.5199880866158875e-128 best_h 0.0001 START of Soultion TOP MAIN SOLVE Loop x[1] 0.0 y2[1] (analytic) 0.0 y2[1] (numeric) 0.0 absolute error 0.0 relative error -1.0% Correct digits -1 h 0.0001 y1[1] (analytic) 1.0 y1[1] (numeric) 1.0 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 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 x[1] 0.010099999999999994 y2[1] (analytic) 0.010099828284042501 y2[1] (numeric) 0.010100000000875844 absolute error 1.7171683334288312e-07 relative error 0.0017001955727721809% Correct digits 5 h 0.0001 y1[1] (analytic) 0.9999489954335835 y1[1] (numeric) 0.9999489949999985 absolute error 4.335850567471766e-10 relative error 4.336071726930149e-08% Correct digits 10 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 Radius of convergence (six term test) for eq 1 0.010100379335234791 Order of pole (six term test) -9.500000000346873 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 x[1] 0.020099999999999934 y2[1] (analytic) 0.020098646593839704 y2[1] (numeric) 0.020100000027339793 absolute error 1.3534335000890685e-06 relative error 0.006733953422037382% Correct digits 5 h 0.0001 y1[1] (analytic) 0.9997980018009117 y1[1] (numeric) 0.9997979949999086 absolute error 6.801003094025759e-09 relative error 6.802377161961995e-07% Correct digits 9 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 Radius of convergence (six term test) for eq 1 0.020102839548730253 Order of pole (six term test) -9.500000005441041 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 x[1] 0.030099999999999873 y2[1] (analytic) 0.03009545505572634 y2[1] (numeric) 0.030100000205893148 absolute error 4.545150166807704e-06 relative error 0.015102447058506554% Correct digits 4 h 0.0001 y1[1] (analytic) 0.9995470292012221 y1[1] (numeric) 0.9995469949989674 absolute error 3.4202254695081535e-08 relative error 3.421775433859668e-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 Radius of convergence (six term test) for eq 1 0.030109543575607974 Order of pole (six term test) -9.50000002736449 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 x[1] 0.04000000000000012 y2[1] (analytic) 0.03998933418663428 y2[1] (numeric) 0.04000000085330085 absolute error 1.0666666666568625e-05 relative error 0.026673779105163917% Correct digits 4 h 0.0001 y1[1] (analytic) 0.9992001066609779 y1[1] (numeric) 0.9991999999943116 absolute error 1.0666666627745514e-07 relative error 1.067520565364055e-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 Radius of convergence (six term test) for eq 1 0.040022391221872664 Order of pole (six term test) -9.500000085348123 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 x[1] 0.050000000000000405 y2[1] (analytic) 0.04997916927067873 y2[1] (numeric) 0.050000002604011655 absolute error 2.0833333332921644e-05 relative error 0.04168403284194627% Correct digits 4 h 0.0001 y1[1] (analytic) 0.9987502603949662 y1[1] (numeric) 0.9987499999783 absolute error 2.604166661202001e-07 relative error 2.607425263821364e-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 Radius of convergence (six term test) for eq 1 0.050043724534228035 Order of pole (six term test) -9.500000208389752 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 x[1] 0.06000000000000069 y2[1] (analytic) 0.05996400647944529 y2[1] (numeric) 0.060000006479444555 absolute error 3.5999999999265786e-05 relative error 0.06003601512451643% Correct digits 4 h 0.0001 y1[1] (analytic) 0.9982005399352041 y1[1] (numeric) 0.9981999999352046 absolute error 5.399999994937232e-07 relative error 5.409734596304427e-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 Radius of convergence (six term test) for eq 1 0.06007553620224222 Order of pole (six term test) -9.500000432168457 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 x[1] 0.07000000000000098 y2[1] (analytic) 0.06994284733753374 y2[1] (numeric) 0.0700000140041993 absolute error 5.7166666665567356e-05 relative error 0.08173339925623782% Correct digits 4 h 0.0001 y1[1] (analytic) 0.9975510002532795 y1[1] (numeric) 0.9975499998366131 absolute error 1.0004166663968306e-06 relative error 0.0001002872701388524% 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 Radius of convergence (six term test) for eq 1 0.07011991211764515 Order of pole (six term test) -9.500000800758098 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 x[1] 0.08000000000000126 y2[1] (analytic) 0.07991469396917394 y2[1] (numeric) 0.08000002730250563 absolute error 8.533333333168858e-05 relative error 0.10678052945382585% Correct digits 3 h 0.0001 y1[1] (analytic) 0.9968017063026193 y1[1] (numeric) 0.996799999635953 absolute error 1.7066666663234642e-06 relative error 0.00017121426012139436% 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 Radius of convergence (six term test) for eq 1 0.08017893140721623 Order of pole (six term test) -9.500001366279735 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 x[1] 0.09000000000000155 y2[1] (analytic) 0.0898785491980126 y2[1] (numeric) 0.09000004919800998 absolute error 0.00012149999999738759 relative error 0.13518242237055847% Correct digits 3 h 0.0001 y1[1] (analytic) 0.9959527330119942 y1[1] (numeric) 0.9959499992619952 absolute error 2.733749998928836e-06 relative error 0.0002744859176862075% 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 Radius of convergence (six term test) for eq 1 0.09025466609537491 Order of pole (six term test) -9.5000021889185 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 x[1] 0.10000000000000184 y2[1] (analytic) 0.09983341664682999 y2[1] (numeric) 0.10000008331349204 absolute error 0.00016666666666205476 relative error 0.16694476885595694% Correct digits 3 h 0.0001 y1[1] (analytic) 0.9950041652780256 y1[1] (numeric) 0.9949999986113599 absolute error 4.166666665694763e-06 relative error 0.00041875871590251146% 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 Radius of convergence (six term test) for eq 1 0.10034918092059691 Order of pole (six term test) -9.500003336943067 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 x[1] 0.11000000000000212 y2[1] (analytic) 0.10977830083717692 y2[1] (numeric) 0.11000013417050161 absolute error 0.0002218333333246919 relative error 0.2020739359536225% Correct digits 3 h 0.0001 y1[1] (analytic) 0.9939560979566966 y1[1] (numeric) 0.9939499975400309 absolute error 6.100416665710817e-06 relative error 0.0006137511182085019% 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 Radius of convergence (six term test) for eq 1 0.11046453146200345 Order of pole (six term test) -9.50000488672768 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 x[1] 0.12000000000000241 y2[1] (analytic) 0.11971220728892175 y2[1] (numeric) 0.12000020728890513 absolute error 0.0002879999999833849 relative error 0.24057696913757984% Correct digits 3 h 0.0001 y1[1] (analytic) 0.9928086358538659 y1[1] (numeric) 0.9927999958538668 absolute error 8.639999999116021e-06 relative error 0.0008702583445686068% 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 Radius of convergence (six term test) for eq 1 0.1206027637017817 Order of pole (six term test) -9.500006922776775 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 x[1] 0.130000000000002 y2[1] (analytic) 0.12963414261969686 y2[1] (numeric) 0.13000030928633224 absolute error 0.0003661666666353869 relative error 0.2824615947895742% Correct digits 3 h 0.0001 y1[1] (analytic) 0.9915618937147878 y1[1] (numeric) 0.991549993298122 absolute error 1.1900416665766578e-05 relative error 0.001200168818628442% 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 Radius of convergence (six term test) for eq 1 0.13076591317522684 Order of pole (six term test) -9.500009537752176 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 x[1] 0.1400000000000009 y2[1] (analytic) 0.13954311464423738 y2[1] (numeric) 0.14000044797751293 absolute error 0.00045733333327555026 relative error 0.3277362229168478% Correct digits 3 h 0.0001 y1[1] (analytic) 0.990215996212637 y1[1] (numeric) 0.990199989545972 absolute error 1.6006666665013825e-05 relative error 0.0016164823357970259% 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 Radius of convergence (six term test) for eq 1 0.14095600360856617 Order of pole (six term test) -9.500012832502833 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 x[1] 0.1500999999999998 y2[1] (analytic) 0.14953700883403717 y2[1] (numeric) 0.15010063458409736 absolute error 0.0005636257500601927 relative error 0.3769138853684907% Correct digits 3 h 0.0001 y1[1] (analytic) 0.9887561291789645 y1[1] (numeric) 0.988734979122692 absolute error 2.1150056272456474e-05 relative error 0.002139056906784375% 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 Radius of convergence (six term test) for eq 1 0.1512773897166466 Order of pole (six term test) -9.500016961306773 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 x[1] 0.1600999999999987 y2[1] (analytic) 0.15941692854582665 y2[1] (numeric) 0.1601008760124708 absolute error 0.0006839474666441581 relative error 0.429030638642337% Correct digits 3 h 0.0001 y1[1] (analytic) 0.9872113466188559 y1[1] (numeric) 0.9871839716214994 absolute error 2.737499735649962e-05 relative error 0.002772962187910164% 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 Radius of convergence (six term test) for eq 1 0.1615277021719851 Order of pole (six term test) -9.500021960749585 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 x[1] 0.1700999999999976 y2[1] (analytic) 0.1692809066976086 y2[1] (numeric) 0.1701011858807824 absolute error 0.0008202791831738165 relative error 0.4845668653223279% Correct digits 3 h 0.0001 y1[1] (analytic) 0.9855678437467588 y1[1] (numeric) 0.9855329613744868 absolute error 3.488237227200486e-05 relative error 0.0035393172061494193% 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 Radius of convergence (six term test) for eq 1 0.17181096820476646 Order of pole (six term test) -9.500027993271273 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 x[1] 0.18009999999999649 y2[1] (analytic) 0.1791279568997877 y2[1] (numeric) 0.18010157779940855 absolute error 0.0009736208996208584 relative error 0.5435337489867905% Correct digits 3 h 0.0001 y1[1] (analytic) 0.9838257849115909 y1[1] (numeric) 0.983781947630571 absolute error 4.383728101986506e-05 relative error 0.004455797123044949% 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 Radius of convergence (six term test) for eq 1 0.18212915607557195 Order of pole (six term test) -9.500035192901361 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 x[1] 0.19009999999999538 y2[1] (analytic) 0.18895709445554962 y2[1] (numeric) 0.19010206707149435 absolute error 0.0011449726159447338 relative error 0.6059431741601413% Correct digits 3 h 0.0001 y1[1] (analytic) 0.9819853443177838 y1[1] (numeric) 0.9819309294941861 absolute error 5.4414823597692674e-05 relative error 0.005541307099190606% 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 Radius of convergence (six term test) for eq 1 0.192484217978257 Order of pole (six term test) -9.500043702043872 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 x[1] 0.20009999999999428 y2[1] (analytic) 0.19876733645932973 y2[1] (numeric) 0.20010267079141852 absolute error 0.0013353343320887945 relative error 0.671807730523179% Correct digits 3 h 0.0001 y1[1] (analytic) 0.9800467060078635 y1[1] (numeric) 0.9799799059078591 absolute error 6.680010000437164e-05 relative error 0.006816011889522709% 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 Radius of convergence (six term test) for eq 1 0.20287808918061834 Order of pole (six term test) -9.500053671522299 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 x[1] 0.21009999999999318 y2[1] (analytic) 0.2085577018951028 y2[1] (numeric) 0.21010340794307836 absolute error 0.001545706047975548 relative error 0.7411407173794923% Correct digits 3 h 0.0001 y1[1] (analytic) 0.9780100638440452 y1[1] (numeric) 0.9779288756338063 absolute error 8.118821023894718e-05 relative error 0.00830136756669342% 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 Radius of convergence (six term test) for eq 1 0.21331268712522433 Order of pole (six term test) -9.500065260627062 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 x[1] 0.22009999999999208 y2[1] (analytic) 0.21832721173448388 y2[1] (numeric) 0.22010429949798488 absolute error 0.0017770877635009952 relative error 0.8139561483807066% Correct digits 3 h 0.0001 y1[1] (analytic) 0.9758756214888482 y1[1] (numeric) 0.975777837234551 absolute error 9.778425429718407e-05 relative error 0.01002015545259745% Correct digits 4 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 Radius of convergence (six term test) for eq 1 0.2237899106627485 Order of pole (six term test) -9.500078637165451 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 x[1] 0.23009999999999098 y2[1] (analytic) 0.22807488903463025 y2[1] (numeric) 0.23010536851315658 absolute error 0.0020304794785263314 relative error 0.8902687565127037% Correct digits 3 h 0.0001 y1[1] (analytic) 0.9736435923847294 y1[1] (numeric) 0.9735267890525545 absolute error 0.00011680333217489736 relative error 0.011996518344953399% Correct digits 4 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 Radius of convergence (six term test) for eq 1 0.23431163916179046 Order of pole (six term test) -9.500093977514036 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 x[1] 0.24009999999998988 y2[1] (analytic) 0.23779975903593495 y2[1] (numeric) 0.24010664022880437 absolute error 0.0023068811928694255 relative error 0.9700939993470821% Correct digits 3 h 0.0001 y1[1] (analytic) 0.971314199732739 y1[1] (numeric) 0.9711757291888732 absolute error 0.0001384705438658429 relative error 0.014255999130244737% Correct digits 4 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 Radius of convergence (six term test) for eq 1 0.24487973172060543 Order of pole (six term test) -9.500111466673491 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 x[1] 0.2500999999999888 y2[1] (analytic) 0.24750084925950183 y2[1] (numeric) 0.2501081421657963 absolute error 0.002607292906294467 relative error 1.0534480645602755% Correct digits 3 h 0.0001 y1[1] (analytic) 0.9688876764702012 y1[1] (numeric) 0.9687246554808381 absolute error 0.00016302098936316067 relative error 0.01682558188345112% Correct digits 4 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 Radius of convergence (six term test) for eq 1 0.25549602637253316 Order of pole (six term test) -9.500131298325881 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 x[1] 0.2600999999999877 y2[1] (analytic) 0.25717718960439284 y2[1] (numeric) 0.260109904222891 absolute error 0.0029327146184981445 relative error 1.1403478757231318% Correct digits 3 h 0.0001 y1[1] (analytic) 0.9663642652474201 y1[1] (numeric) 0.9661735654787651 absolute error 0.0001906997686550449 relative error 0.019733735560494847% Correct digits 4 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 Radius of convergence (six term test) for eq 1 0.26616233928031824 Order of pole (six term test) -9.500153674894317 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 x[1] 0.2700999999999866 y2[1] (analytic) 0.266827812444637 y2[1] (numeric) 0.2701119587737328 absolute error 0.003284146329095794 relative error 1.2308110983659952% Correct digits 3 h 0.0001 y1[1] (analytic) 0.9637442184034152 y1[1] (numeric) 0.9635224564216872 absolute error 0.00022176198172796369 relative error 0.02301046039947666% Correct digits 4 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 Radius of convergence (six term test) for eq 1 0.27688046398482496 Order of pole (six term test) -9.500178807605021 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 x[1] 0.28009999999998547 y2[1] (analytic) 0.27645175272599243 y2[1] (numeric) 0.2801143407635949 absolute error 0.003662588037602499 relative error 1.32485614632102% Correct digits 3 h 0.0001 y1[1] (analytic) 0.9610277979406874 y1[1] (numeric) 0.9607713252121233 absolute error 0.0002564727285641055 relative error 0.026687337152336406% Correct digits 4 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 Radius of convergence (six term test) for eq 1 0.28765217061813814 Order of pole (six term test) -9.500206916551715 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 x[1] 0.29009999999998437 y2[1] (analytic) 0.286048048062451 y2[1] (numeric) 0.29011708780586454 absolute error 0.0040690397434135495 relative error 1.4225021883474565% Correct digits 3 h 0.0001 y1[1] (analytic) 0.9582152754990194 y1[1] (numeric) 0.9579201683898808 absolute error 0.0002951071091386037 relative error 0.030797579279344907% Correct digits 4 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 Radius of convergence (six term test) for eq 1 0.29847920517404475 Order of pole (six term test) -9.50023823076237 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 x[1] 0.30009999999998327 y2[1] (analytic) 0.2956157388324759 y2[1] (numeric) 0.3001202402782549 absolute error 0.004504501445779019 relative error 1.5237691550420798% Correct digits 3 h 0.0001 y1[1] (analytic) 0.9553069323283117 y1[1] (numeric) 0.9549689821048901 absolute error 0.0003379502234215348 relative error 0.03537608824818943% Correct digits 4 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 Radius of convergence (six term test) for eq 1 0.30936328876627894 Order of pole (six term test) -9.500272988268236 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 x[1] 0.31009999999998217 y2[1] (analytic) 0.3051538682749632 y2[1] (numeric) 0.31012384141874166 absolute error 0.00496997314377845 relative error 1.628677746041281% Correct digits 3 h 0.0001 y1[1] (analytic) 0.9523030592604574 y1[1] (numeric) 0.9519177620890837 absolute error 0.0003852971713736997 relative error 0.040459512087771196% Correct digits 4 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 Radius of convergence (six term test) for eq 1 0.32030611690203475 Order of pole (six term test) -9.50031143617515 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 x[1] 0.32009999999998107 y2[1] (analytic) 0.31466148258491705 y2[1] (numeric) 0.3201279374212036 absolute error 0.0054664548362865495 relative error 1.7372494375161818% Correct digits 3 h 0.0001 y1[1] (analytic) 0.9492039566802606 y1[1] (numeric) 0.9487665036273145 absolute error 0.0004374530529460685 relative error 0.046086307359696835% Correct digits 4 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 Radius of convergence (six term test) for eq 1 0.3313093587739293 Order of pole (six term test) -9.50035383073707 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 x[1] 0.33009999999997997 y2[1] (analytic) 0.3241376310088294 y2[1] (numeric) 0.33013257753076874 absolute error 0.005994946521939326 relative error 1.8495064899687705% Correct digits 3 h 0.0001 y1[1] (analytic) 0.9460099344953963 y1[1] (numeric) 0.9455152015273193 absolute error 0.0004947329680770052 relative error 0.05229680472022705% Correct digits 4 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 Radius of convergence (six term test) for eq 1 0.342374656563258 Order of pole (six term test) -9.500400437431834 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 x[1] 0.34009999999997886 y2[1] (analytic) 0.33358136593975474 y2[1] (numeric) 0.34013781413884525 absolute error 0.006556448199090514 relative error 1.9654719563306238% Correct digits 3 h 0.0001 y1[1] (analytic) 0.9427213121054214 y1[1] (numeric) 0.9421638500887313 absolute error 0.0005574620166901578 relative error 0.059133278258571786% Correct digits 4 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 Radius of convergence (six term test) for eq 1 0.35350362474761404 Order of pole (six term test) -9.500451531039044 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 x[1] 0.35009999999997776 y2[1] (analytic) 0.3429917430120696 y2[1] (numeric) 0.3501437028778371 absolute error 0.007151959865767499 relative error 2.0851696903723504% Correct digits 3 h 0.0001 y1[1] (analytic) 0.9393384183698346 y1[1] (numeric) 0.9387124430711429 absolute error 0.0006259752986916833 relative error 0.06664001881004994% Correct digits 4 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 Radius of convergence (six term test) for eq 1 0.3646978494358015 Order of pole (six term test) -9.500507395720108 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 x[1] 0.36009999999997666 y2[1] (analytic) 0.35236782119590876 y2[1] (numeric) 0.3601503027155253 absolute error 0.007782481519616524 relative error 2.2086243554259273% Correct digits 3 h 0.0001 y1[1] (analytic) 0.9358615915751902 y1[1] (numeric) 0.9351609736612261 absolute error 0.0007006179139641411 relative error 0.0748634114564847% Correct digits 4 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 Radius of convergence (six term test) for eq 1 0.3759588876845492 Order of pole (six term test) -9.500568325100327 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 x[1] 0.37009999999997556 y2[1] (analytic) 0.36170866289126724 y2[1] (numeric) 0.3701576760491121 absolute error 0.008449013157844854 relative error 2.335861433427902% Correct digits 3 h 0.0001 y1[1] (analytic) 0.9322911794012703 y1[1] (numeric) 0.9315094344389042 absolute error 0.0007817449623660488 relative error 0.08385201744245782% Correct digits 4 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 Radius of convergence (six term test) for eq 1 0.3872882668593295 Order of pole (six term test) -9.500634622353028 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 x[1] 0.38009999999997446 y2[1] (analytic) 0.37101333402175946 y2[1] (numeric) 0.3801658887989131 absolute error 0.009152554777153654 relative error 2.4669072342873988% Correct digits 3 h 0.0001 y1[1] (analytic) 0.9286275388863171 y1[1] (numeric) 0.9277578173425913 absolute error 0.0008697215437257766 relative error 0.093656660749994% Correct digits 4 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 Radius of convergence (six term test) for eq 1 0.39868748398066994 Order of pole (six term test) -9.50070660028567 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 x[1] 0.39009999999997336 y2[1] (analytic) 0.3802809041280263 y2[1] (numeric) 0.3901750105016902 absolute error 0.009894106373663891 relative error 2.6017889055856767% Correct digits 3 h 0.0001 y1[1] (analytic) 0.924871036391329 y1[1] (numeric) 0.9239061136334942 absolute error 0.0009649227578347741 relative error 0.10433051959327426% Correct digits 3 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 Radius of convergence (six term test) for eq 1 0.41015800509090744 Order of pole (six term test) -9.500784581427864 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 x[1] 0.40009999999997226 y2[1] (analytic) 0.38951044646078 y2[1] (numeric) 0.40018511440361426 absolute error 0.010674667942834282 relative error 2.7405344426132405% Correct digits 3 h 0.0001 y1[1] (analytic) 0.921022047563425 y1[1] (numeric) 0.9199543138589829 absolute error 0.001067733704442131 relative error 0.11592922311326134% Correct digits 3 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 Radius of convergence (six term test) for eq 1 0.421701264619852 Order of pole (six term test) -9.500868898121265 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 x[1] 0.41009999999997115 y2[1] (analytic) 0.3987010380734786 y2[1] (numeric) 0.4101962775528468 absolute error 0.011495239479368202 relative error 2.8831726987502067% Correct digits 3 h 0.0001 y1[1] (analytic) 0.9170809572982805 y1[1] (numeric) 0.9159024078150307 absolute error 0.0011785494832498022 relative error 0.12851095357184253% Correct digits 3 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 Radius of convergence (six term test) for eq 1 0.43331866477127545 Order of pole (six term test) -9.500959892611258 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 x[1] 0.42009999999997005 y2[1] (analytic) 0.40785175991461964 y2[1] (numeric) 0.4202085808917336 absolute error 0.012356820977113936 relative error 3.029733396197857% Correct digits 3 h 0.0001 y1[1] (analytic) 0.9130481597016378 y1[1] (numeric) 0.9117503845077368 absolute error 0.0012977751939009519 relative error 0.14213655436587636% Correct digits 3 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 Radius of convergence (six term test) for eq 1 0.44501157490100507 Order of pole (six term test) -9.501057917140372 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 x[1] 0.43009999999996895 y2[1] (analytic) 0.4169616969196445 y2[1] (numeric) 0.4302221093485951 absolute error 0.013260412428950596 relative error 3.1802471370664294% Correct digits 3 h 0.0001 y1[1] (analytic) 0.9089240580498958 y1[1] (numeric) 0.9074982321139229 absolute error 0.0014258259359729575 relative error 0.15686964420680855% Correct digits 3 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 Radius of convergence (six term test) for eq 1 0.4567813309138974 Order of pole (six term test) -9.501163334043365 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 x[1] 0.44009999999996785 y2[1] (analytic) 0.4260299381024444 y2[1] (numeric) 0.4402369519291095 absolute error 0.014207013826665116 relative error 3.3347454148278324% Correct digits 3 h 0.0001 y1[1] (analytic) 0.9047090647497832 y1[1] (numeric) 0.9031459379408162 absolute error 0.0015631268089669748 relative error 0.17277673783442096% Correct digits 3 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 Radius of convergence (six term test) for eq 1 0.4686292346563725 Order of pole (six term test) -9.501276515843887 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 x[1] 0.45009999999996675 y2[1] (analytic) 0.4350555766464578 y2[1] (numeric) 0.45025320180727285 absolute error 0.015197625160815076 relative error 3.493260626139549% Correct digits 3 h 0.0001 y1[1] (analytic) 0.9004036012971173 y1[1] (numeric) 0.8986934883848217 absolute error 0.0017101129122956138 relative error 0.18992737366132623% Correct digits 3 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 Radius of convergence (six term test) for eq 1 0.4805565533199793 Order of pole (six term test) -9.501397845352642 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 x[1] 0.46009999999996565 y2[1] (analytic) 0.44403770999535164 y2[1] (numeric) 0.46027095641593185 absolute error 0.016233246420580216 relative error 3.655826083048251% Correct digits 3 h 0.0001 y1[1] (analytic) 0.8960080982346554 y1[1] (numeric) 0.8941408688893857 absolute error 0.0018672293452697275 relative error 0.20839424877393453% Correct digits 3 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 Radius of convergence (six term test) for eq 1 0.4925645188440618 Order of pole (six term test) -9.501527715766962 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 x[1] 0.47009999999996455 y2[1] (analytic) 0.4529754399432762 y2[1] (numeric) 0.4702903175368751 absolute error 0.0173148775935989 relative error 3.822476025580361% Correct digits 3 h 0.0001 y1[1] (analytic) 0.8915229951090411 y1[1] (numeric) 0.8894880639019555 absolute error 0.002034931207085644 relative error 0.2282533617471924% Correct digits 3 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 Radius of convergence (six term test) for eq 1 0.504654327322962 Order of pole (six term test) -9.50166653077172 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 x[1] 0.48009999999996344 y2[1] (analytic) 0.4618678727246847 y2[1] (numeric) 0.48031139139047296 absolute error 0.01844351866578825 relative error 3.993245634727719% Correct digits 3 h 0.0001 y1[1] (analytic) 0.8869487404268492 y1[1] (numeric) 0.8847350568300428 absolute error 0.002213683596806404 relative error 0.24958416376363032% Correct digits 3 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 Radius of convergence (six term test) for eq 1 0.5168271384130791 Order of pole (six term test) -9.501814704641447 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 x[1] 0.49009999999996234 y2[1] (analytic) 0.4707141191037093 y2[1] (numeric) 0.4903342887248574 absolute error 0.019620169621148098 relative error 4.168171045837127% Correct digits 3 h 0.0001 y1[1] (analytic) 0.8822857916097363 y1[1] (numeric) 0.8798818299963901 absolute error 0.002403961613346217 relative error 0.27246971856592783% Correct digits 3 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 Radius of convergence (six term test) for eq 1 0.5290840747417613 Order of pole (six term test) -9.501972662343572 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 ( y2 , x , 5 ) = y1 ; diff ( y1 , x , 1 ) = m1 * y2 ; Iterations 5001 Total Elapsed Time 2 Minutes 47.0 Seconds Elapsed Time(since restart) 2 Minutes 46.0 Seconds Time to Timeout 13.0 Seconds Percent Done 100.03999999999225%