##############ECHO OF PROBLEM################# ##############temp/mtest7postode.ode################# diff ( y2 , x , 5 ) = y1 ; diff ( y1 , x , 1 ) = neg ( diff ( y2 , x , 4 ) ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=64; ELIMINATED in preodein.rb max_terms=40 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=c(0.1) x_end=c(0.7) # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $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[3 + 1] = exact_soln_y2ppp(x_start) $array_y2_init[4 + 1] = exact_soln_y2pppp(x_start) $glob_look_poles=true $glob_max_h=c(0.1) # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $glob_type_given_pole=3 #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=8 $glob_max_minutes=(3.0) $glob_subiter_method=3 $glob_max_iter=100000 $glob_upper_ratio_limit=c(1.000001) $glob_lower_ratio_limit=c(0.999999) $glob_look_poles=true $glob_h=c(0.001) $glob_display_interval=c(0.01) #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y1 (x) x = c(x) return( cos(c(x)) ) end def exact_soln_y2 (x) x = c(x) return( sin(c(x)) + c(10.0) * c(x) + c(10.0)) end def exact_soln_y2p (x) x = c(x) return( cos(c(x)) + c(10.0)) end def exact_soln_y2pp (x) x = c(x) return( neg(sin(c(x)))) end def exact_soln_y2ppp (x) x = c(x) return( neg(cos(c(x)))) end def exact_soln_y2pppp (x) x = c(x) return( sin(c(x))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] 0.1 y2[1] (closed_form) 11.099833416646828 y2[1] (numeric) 11.099833416646828 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 y1[1] (closed_form) 0.9950041652780258 y1[1] (numeric) 0.9950041652780258 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.09933466539753058 Order of pole (three term test) 32.99003328892062 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.09933466539753061 Order of pole (three term test) 32.00996671107938 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.11000000000000001 y2[1] (closed_form) 11.209778300837176 y2[1] (numeric) 11.209778300837176 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 y1[1] (closed_form) 0.9939560979566968 y1[1] (numeric) 0.9939560979566969 absolute error 1.1102230246251565e-16 relative error 1.1169739054948934e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.10911481154043456 Order of pole (three term test) 32.98794872466531 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.10911481154043458 Order of pole (three term test) 32.0120512753347 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.12000000000000002 y2[1] (closed_form) 11.31971220728892 y2[1] (numeric) 11.319712207288921 absolute error 1.7763568394002505e-15 relative error 1.5692597186847467e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 y1[1] (closed_form) 0.9928086358538663 y1[1] (numeric) 0.9928086358538663 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.11885131321356719 Order of pole (three term test) 32.98566898742602 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.11885131321356715 Order of pole (three term test) 32.01433101257398 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.13000000000000003 y2[1] (closed_form) 11.429634142619696 y2[1] (numeric) 11.429634142619694 absolute error 1.7763568394002505e-15 relative error 1.5541677163369866e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 y1[1] (closed_form) 0.9915618937147881 y1[1] (numeric) 0.9915618937147881 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.1285402759460775 Order of pole (three term test) 32.98319498906726 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.1285402759460775 Order of pole (three term test) 32.01680501093274 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.14000000000000004 y2[1] (closed_form) 11.539543114644237 y2[1] (numeric) 11.539543114644236 absolute error 1.7763568394002505e-15 relative error 1.539364965971632e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 y1[1] (closed_form) 0.9902159962126371 y1[1] (numeric) 0.9902159962126372 absolute error 1.1102230246251565e-16 relative error 1.1211927790214665e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.13817782428205697 Order of pole (three term test) 32.98052771915538 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.1381778242820571 Order of pole (three term test) 32.01947228084462 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.15000000000000005 y2[1] (closed_form) 11.6494381324736 y2[1] (numeric) 11.6494381324736 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.9887710779360422 y1[1] (numeric) 0.9887710779360421 absolute error 1.1102230246251565e-16 relative error 1.1228312087592942e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.1477601033306699 Order of pole (three term test) 32.9776682445628 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.14776010333067002 Order of pole (three term test) 32.0223317554372 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.16000000000000006 y2[1] (closed_form) 11.759318206614246 y2[1] (numeric) 11.759318206614248 absolute error 1.7763568394002505e-15 relative error 1.5105950941961122e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.9872272833756269 y1[1] (numeric) 0.9872272833756267 absolute error 2.220446049250313e-16 relative error 2.249174112832397e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.157283280308059 Order of pole (three term test) 32.974617709041226 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.15728328030805896 Order of pole (three term test) 32.02538229095879 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.17000000000000007 y2[1] (closed_form) 11.869182349066996 y2[1] (numeric) 11.869182349066996 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.9855847669095607 y1[1] (numeric) 0.9855847669095603 absolute error 3.3306690738754696e-16 relative error 3.379383677285567e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.1667435460704072 Order of pole (three term test) 32.97137733276418 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.16674354607040726 Order of pole (three term test) 32.02862266723582 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.18000000000000008 y2[1] (closed_form) 11.979029573425825 y2[1] (numeric) 11.979029573425825 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.9838436927881214 y1[1] (numeric) 0.9838436927881212 absolute error 2.220446049250313e-16 relative error 2.2569093703876637e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.17613711663754503 Order of pole (three term test) 32.96794841183897 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.17613711663754503 Order of pole (three term test) 32.03205158816103 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.19000000000000009 y2[1] (closed_form) 12.088858894976502 y2[1] (numeric) 12.088858894976502 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.9820042351172703 y1[1] (numeric) 0.9820042351172701 absolute error 2.220446049250313e-16 relative error 2.2611369379533774e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.18546023470649128 Order of pole (three term test) 32.964332317788255 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.18546023470649142 Order of pole (three term test) 32.03566768221175 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.2000000000000001 y2[1] (closed_form) 12.198669330795063 y2[1] (numeric) 12.198669330795061 absolute error 1.7763568394002505e-15 relative error 1.456189024581482e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.9800665778412416 y1[1] (numeric) 0.9800665778412414 absolute error 2.220446049250313e-16 relative error 2.265607357146299e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.19470917115432537 Order of pole (three term test) 32.96053049700144 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.19470917115432534 Order of pole (three term test) 32.03946950299856 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.2100000000000001 y2[1] (closed_form) 12.3084598998461 y2[1] (numeric) 12.3084598998461 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.9780309147241483 y1[1] (numeric) 0.978030914724148 absolute error 2.220446049250313e-16 relative error 2.2703229681411303e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.20388022652978538 Order of pole (three term test) 32.95654447015616 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.20388022652978527 Order of pole (three term test) 32.04345552984385 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.2200000000000001 y2[1] (closed_form) 12.41822962308087 y2[1] (numeric) 12.418229623080869 absolute error 1.7763568394002505e-15 relative error 1.430442899927268e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.9758974493306055 y1[1] (numeric) 0.9758974493306055 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.21296973253299953 Order of pole (three term test) 32.95237583160999 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.21296973253299967 Order of pole (three term test) 32.047624168390016 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.23000000000000012 y2[1] (closed_form) 12.52797752353519 y2[1] (numeric) 12.527977523535188 absolute error 1.7763568394002505e-15 relative error 1.4179118984394471e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.9736663950053748 y1[1] (numeric) 0.9736663950053749 absolute error 1.1102230246251565e-16 relative error 1.1402499154949555e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.22197405348276 Order of pole (three term test) 32.94802624876276 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.22197405348276011 Order of pole (three term test) 32.051973751237234 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.24000000000000013 y2[1] (closed_form) 12.637702626427135 y2[1] (numeric) 12.637702626427133 absolute error 1.7763568394002505e-15 relative error 1.4056010747441149e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.9713379748520296 y1[1] (numeric) 0.9713379748520296 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.23088958777074145 Order of pole (three term test) 32.94349746138964 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.2308895877707413 Order of pole (three term test) 32.05650253861036 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.2500000000000001 y2[1] (closed_form) 12.747403959254523 y2[1] (numeric) 12.747403959254521 absolute error 1.7763568394002505e-15 relative error 1.3935047834666196e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.9689124217106447 y1[1] (numeric) 0.9689124217106446 absolute error 1.1102230246251565e-16 relative error 1.1458445569982719e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2397127693021014 Order of pole (three term test) 32.93879128094519 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.23971276930210159 Order of pole (three term test) 32.06120871905482 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.2600000000000001 y2[1] (closed_form) 12.857080551892157 y2[1] (numeric) 12.857080551892151 absolute error 5.329070518200751e-15 relative error 4.14485271107404e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.9663899781345132 y1[1] (numeric) 0.9663899781345132 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24844006892186835 Order of pole (three term test) 32.93390958983882 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.2484400689218684 Order of pole (three term test) 32.06609041016117 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.27000000000000013 y2[1] (closed_form) 12.966731436688832 y2[1] (numeric) 12.96673143668883 absolute error 1.7763568394002505e-15 relative error 1.3699341642675825e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.9637708963658905 y1[1] (numeric) 0.9637708963658905 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2570679958265565 Order of pole (three term test) 32.928854340681916 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.2570679958265564 Order of pole (three term test) 32.071145659318084 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.28000000000000014 y2[1] (closed_form) 13.076355648564116 y2[1] (numeric) 13.076355648564114 absolute error 1.7763568394002505e-15 relative error 1.3584494695166142e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.9610554383107709 y1[1] (numeric) 0.961055438310771 absolute error 1.1102230246251565e-16 relative error 1.1552122597387043e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.26559309896044137 Order of pole (three term test) 32.92362755550671 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.2655930989604414 Order of pole (three term test) 32.076372444493295 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.29000000000000015 y2[1] (closed_form) 13.185952225104836 y2[1] (numeric) 13.185952225104833 absolute error 3.552713678800501e-15 relative error 2.694317117300381e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.9582438755126971 y1[1] (numeric) 0.9582438755126974 absolute error 3.3306690738754696e-16 relative error 3.4758052297422036e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.27401196839593694 Order of pole (three term test) 32.918231324957596 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.274011968395937 Order of pole (three term test) 32.08176867504241 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.30000000000000016 y2[1] (closed_form) 13.295520206661342 y2[1] (numeric) 13.295520206661337 absolute error 5.329070518200751e-15 relative error 4.0081699966359886e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.955336489125606 y1[1] (numeric) 0.9553364891256064 absolute error 4.440892098500626e-16 relative error 4.6485109163633603e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2823212366975171 Order of pole (three term test) 32.91266780745484 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.2823212366975171 Order of pole (three term test) 32.08733219254516 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.31000000000000016 y2[1] (closed_form) 13.405058636443446 y2[1] (numeric) 13.405058636443442 absolute error 3.552713678800501e-15 relative error 2.6502783577104046e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.9523335698857134 y1[1] (numeric) 0.9523335698857137 absolute error 3.3306690738754696e-16 relative error 3.49737652771725e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.29051758026865243 Order of pole (three term test) 32.90693922833126 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.29051758026865243 Order of pole (three term test) 32.09306077166873 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.3200000000000002 y2[1] (closed_form) 13.514566560616121 y2[1] (numeric) 13.514566560616117 absolute error 3.552713678800501e-15 relative error 2.6288032715409074e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.9492354180824408 y1[1] (numeric) 0.9492354180824413 absolute error 4.440892098500626e-16 relative error 4.678388536609509e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2985977206811958 Order of pole (three term test) 32.901047878942144 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.2985977206811957 Order of pole (three term test) 32.09895212105785 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.3300000000000002 y2[1] (closed_form) 13.624043028394869 y2[1] (numeric) 13.624043028394867 absolute error 1.7763568394002505e-15 relative error 1.3038397160798851e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.9460423435283869 y1[1] (numeric) 0.9460423435283875 absolute error 5.551115123125783e-16 relative error 5.86772374524187e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3065584259867167 Order of pole (three term test) 32.894996115748675 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.3065584259867167 Order of pole (three term test) 32.10500388425132 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.3400000000000002 y2[1] (closed_form) 13.733487092140816 y2[1] (numeric) 13.733487092140814 absolute error 1.7763568394002505e-15 relative error 1.293449236513861e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.9427546655283462 y1[1] (numeric) 0.9427546655283467 absolute error 5.551115123125783e-16 relative error 5.888186318351214e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3143965120092338 Order of pole (three term test) 32.888786359375466 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.3143965120092338 Order of pole (three term test) 32.111213640624534 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.3500000000000002 y2[1] (closed_form) 13.842897807455454 y2[1] (numeric) 13.842897807455453 absolute error 1.7763568394002505e-15 relative error 1.2832261453548743e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.9393727128473789 y1[1] (numeric) 0.9393727128473793 absolute error 4.440892098500626e-16 relative error 4.727508088924171e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3221088436188454 Order of pole (three term test) 32.88242109364224 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.32210884361884534 Order of pole (three term test) 32.11757890635776 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.3600000000000002 y2[1] (closed_form) 13.952274233275093 y2[1] (numeric) 13.952274233275093 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.9358968236779348 y1[1] (numeric) 0.9358968236779351 absolute error 3.3306690738754696e-16 relative error 3.558799420631045e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3296923359857366 Order of pole (three term test) 32.87590286457045 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.3296923359857369 Order of pole (three term test) 32.12409713542955 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.3700000000000002 y2[1] (closed_form) 14.061615431964963 y2[1] (numeric) 14.061615431964963 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.9323273456060344 y1[1] (numeric) 0.9323273456060348 absolute error 4.440892098500626e-16 relative error 4.7632326987190785e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.33714395581407214 Order of pole (three term test) 32.8692342793648 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.33714395581407214 Order of pole (three term test) 32.1307657206352 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.3800000000000002 y2[1] (closed_form) 14.170920469412986 y2[1] (numeric) 14.170920469412986 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.9286646355765101 y1[1] (numeric) 0.9286646355765106 absolute error 4.440892098500626e-16 relative error 4.7820191793388836e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.34446072255527543 Order of pole (three term test) 32.86241800537046 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.3444607225552753 Order of pole (three term test) 32.13758199462955 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.39000000000000024 y2[1] (closed_form) 14.280188415123163 y2[1] (numeric) 14.280188415123163 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.924909059857313 y1[1] (numeric) 0.9249090598573132 absolute error 2.220446049250313e-16 relative error 2.4007182388210842e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.35163970960020474 Order of pole (three term test) 32.85545676900614 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.35163970960020474 Order of pole (three term test) 32.14454323099387 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.40000000000000024 y2[1] (closed_form) 14.389418342308653 y2[1] (numeric) 14.389418342308652 absolute error 1.7763568394002505e-15 relative error 1.2344882865607547e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.921060994002885 y1[1] (numeric) 0.9210609940028852 absolute error 2.220446049250313e-16 relative error 2.4107481086571322e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.35867804544976095 Order of pole (three term test) 32.848353354673584 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.3586780454497608 Order of pole (three term test) 32.151646645326416 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.41000000000000025 y2[1] (closed_form) 14.498609327984425 y2[1] (numeric) 14.498609327984422 absolute error 3.552713678800501e-15 relative error 2.4503823769795954e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.917120822816605 y1[1] (numeric) 0.9171208228166053 absolute error 3.3306690738754696e-16 relative error 3.6316578917557706e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3655729148634473 Order of pole (three term test) 32.841110603643806 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.36557291486344723 Order of pole (three term test) 32.158889396356194 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.42000000000000026 y2[1] (closed_form) 14.607760453059573 y2[1] (numeric) 14.607760453059567 absolute error 5.329070518200751e-15 relative error 3.648109191908734e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.9130889403123081 y1[1] (numeric) 0.9130889403123086 absolute error 4.440892098500626e-16 relative error 4.863592036260659e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3723215599854296 Order of pole (three term test) 32.83373141292066 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.3723215599854296 Order of pole (three term test) 32.166268587079344 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.43000000000000027 y2[1] (closed_form) 14.716870802429213 y2[1] (numeric) 14.716870802429208 absolute error 5.329070518200751e-15 relative error 3.621062241927896e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.908965749674885 y1[1] (numeric) 0.9089657496748855 absolute error 5.551115123125783e-16 relative error 6.107067428130578e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.37892128144763826 Order of pole (three term test) 32.826218734082026 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.37892128144763837 Order of pole (three term test) 32.173781265917974 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.4400000000000003 y2[1] (closed_form) 14.825939465066003 y2[1] (numeric) 14.825939465065998 absolute error 5.329070518200751e-15 relative error 3.5944234972478534e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.9047516632199633 y1[1] (numeric) 0.9047516632199637 absolute error 4.440892098500626e-16 relative error 4.908409985891296e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3853694394494846 Order of pole (three term test) 32.81857557209929 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.38536943944948454 Order of pole (three term test) 32.18142442790071 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.4500000000000003 y2[1] (closed_form) 14.934965534111234 y2[1] (numeric) 14.934965534111228 absolute error 5.329070518200751e-15 relative error 3.5681840082116264e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.9004471023526768 y1[1] (numeric) 0.9004471023526771 absolute error 3.3306690738754696e-16 relative error 3.6989058715088755e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.39166345481374176 Order of pole (three term test) 32.81080498413534 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.3916634548137418 Order of pole (three term test) 32.18919501586467 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.4600000000000003 y2[1] (closed_form) 15.043948106965523 y2[1] (numeric) 15.043948106965516 absolute error 7.105427357601002e-15 relative error 4.723113445406732e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.8960524975255251 y1[1] (numeric) 0.8960524975255255 absolute error 4.440892098500626e-16 relative error 4.9560624079105615e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3978008100181829 Order of pole (three term test) 32.80291007832172 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.39780081001818257 Order of pole (three term test) 32.19708992167826 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.4700000000000003 y2[1] (closed_form) 15.152886285379072 y2[1] (numeric) 15.152886285379065 absolute error 7.105427357601002e-15 relative error 4.6891577114631855e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.8915682881953289 y1[1] (numeric) 0.8915682881953292 absolute error 3.3306690738754696e-16 relative error 3.7357419706091785e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.403779050202557 Order of pole (three term test) 32.794894012515556 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.40377905020255705 Order of pole (three term test) 32.20510598748445 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.4800000000000003 y2[1] (closed_form) 15.261779175541488 y2[1] (numeric) 15.261779175541475 absolute error 1.2434497875801753e-14 relative error 8.147475948105229e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.886994922779284 y1[1] (numeric) 0.8869949227792844 absolute error 3.3306690738754696e-16 relative error 3.755003538734188e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.40959578415049885 Order of pole (three term test) 32.78675999303623 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4095957841504988 Order of pole (three term test) 32.21324000696377 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.4900000000000003 y2[1] (closed_form) 15.370625888171162 y2[1] (numeric) 15.370625888171151 absolute error 1.0658141036401503e-14 relative error 6.934096967777828e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.8823328586101213 y1[1] (numeric) 0.8823328586101219 absolute error 5.551115123125783e-16 relative error 6.2914070001542e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4152486852459848 Order of pole (three term test) 32.77851127338311 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.41524868524598474 Order of pole (three term test) 32.22148872661689 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.5000000000000003 y2[1] (closed_form) 15.479425538604207 y2[1] (numeric) 15.479425538604199 absolute error 8.881784197001252e-15 relative error 5.737799619792693e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.8775825618903725 y1[1] (numeric) 0.8775825618903731 absolute error 5.551115123125783e-16 relative error 6.325461972681297e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.42073549240394814 Order of pole (three term test) 32.77015115293407 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.42073549240394803 Order of pole (three term test) 32.22984884706593 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.5100000000000003 y2[1] (closed_form) 15.58817724688291 y2[1] (numeric) 15.588177246882903 absolute error 7.105427357601002e-15 relative error 4.5582156560490984e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.8727445076457511 y1[1] (numeric) 0.8727445076457516 absolute error 5.551115123125783e-16 relative error 6.360527135369831e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.42605401097468104 Order of pole (three term test) 32.76168297562583 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4260540109746809 Order of pole (three term test) 32.238317024374176 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.5200000000000004 y2[1] (closed_form) 15.696880137843742 y2[1] (numeric) 15.696880137843735 absolute error 7.105427357601002e-15 relative error 4.5266494330108734e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.8678191796776498 y1[1] (numeric) 0.8678191796776501 absolute error 3.3306690738754696e-16 relative error 3.8379758731682357e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4312021136216691 Order of pole (three term test) 32.75311012861639 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4312021136216693 Order of pole (three term test) 32.24688987138361 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.5300000000000004 y2[1] (closed_form) 15.80553334120485 y2[1] (numeric) 15.805533341204846 absolute error 3.552713678800501e-15 relative error 2.2477657679153516e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.8628070705147608 y1[1] (numeric) 0.8628070705147614 absolute error 5.551115123125783e-16 relative error 6.433784924611156e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4361777411724929 Order of pole (three term test) 32.74443604093026 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4361777411724932 Order of pole (three term test) 32.25556395906973 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.5400000000000004 y2[1] (closed_form) 15.914135991653117 y2[1] (numeric) 15.914135991653115 absolute error 1.7763568394002505e-15 relative error 1.116213183255403e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.8577086813638239 y1[1] (numeric) 0.8577086813638244 absolute error 4.440892098500626e-16 relative error 5.177622886408542e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.440978903442474 Order of pole (three term test) 32.73566418208687 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.44097890344247404 Order of pole (three term test) 32.26433581791313 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.5500000000000004 y2[1] (closed_form) 16.022687228930664 y2[1] (numeric) 16.022687228930664 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.8525245220595056 y1[1] (numeric) 0.852524522059506 absolute error 4.440892098500626e-16 relative error 5.2091077541939084e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4456036800307177 Order of pole (three term test) 32.72679806071279 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4456036800307178 Order of pole (three term test) 32.27320193928721 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.5600000000000004 y2[1] (closed_form) 16.13118619792089 y2[1] (numeric) 16.131186197920886 absolute error 3.552713678800501e-15 relative error 2.202388364507504e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.8472551110134159 y1[1] (numeric) 0.8472551110134163 absolute error 4.440892098500626e-16 relative error 5.2415052335167403e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4500502210882523 Order of pole (three term test) 32.71784122313835 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4500502210882524 Order of pole (three term test) 32.28215877686164 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.5700000000000004 y2[1] (closed_form) 16.239632048733974 y2[1] (numeric) 16.23963204873397 absolute error 3.552713678800501e-15 relative error 2.187681142121362e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.8419009751622685 y1[1] (numeric) 0.841900975162269 absolute error 5.551115123125783e-16 relative error 6.59354875085619e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.45431674805794126 Order of pole (three term test) 32.708797251979185 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.45431674805794126 Order of pole (three term test) 32.29120274802082 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.5800000000000004 y2[1] (closed_form) 16.34802393679188 y2[1] (numeric) 16.348023936791876 absolute error 3.552713678800501e-15 relative error 2.173176215386483e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.8364626499151867 y1[1] (numeric) 0.8364626499151873 absolute error 5.551115123125783e-16 relative error 6.636417207258015e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.45840155438588365 Order of pole (three term test) 32.69966976470314 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4584015543858837 Order of pole (three term test) 32.30033023529686 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.5900000000000004 y2[1] (closed_form) 16.456361022912787 y2[1] (numeric) 16.456361022912784 absolute error 3.552713678800501e-15 relative error 2.1588695543649833e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.8309406791001632 y1[1] (numeric) 0.8309406791001639 absolute error 6.661338147750939e-16 relative error 8.01662298560782e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4623030062040101 Order of pole (three term test) 32.69046241218344 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.46230300620401005 Order of pole (three term test) 32.30953758781656 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.6000000000000004 y2[1] (closed_form) 16.56464247339504 y2[1] (numeric) 16.564642473395036 absolute error 3.552713678800501e-15 relative error 2.144757234879424e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.8253356149096781 y1[1] (numeric) 0.8253356149096787 absolute error 5.551115123125783e-16 relative error 6.725888260296725e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.46601954298361314 Order of pole (three term test) 32.68117887723833 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4660195429836131 Order of pole (three term test) 32.31882112276167 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.6100000000000004 y2[1] (closed_form) 16.672867460100484 y2[1] (numeric) 16.672867460100484 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.8196480178454792 y1[1] (numeric) 0.8196480178454798 absolute error 5.551115123125783e-16 relative error 6.772559686921958e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.46954967815953397 Order of pole (three term test) 32.67182287315802 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.46954967815953386 Order of pole (three term test) 32.32817712684198 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.6200000000000004 y2[1] (closed_form) 16.78103516053731 y2[1] (numeric) 16.781035160537307 absolute error 3.552713678800501e-15 relative error 2.117100432013365e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.8138784566625337 y1[1] (numeric) 0.8138784566625342 absolute error 5.551115123125783e-16 relative error 6.820570169517947e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.47289199972476975 Order of pole (three term test) 32.66239814221939 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.47289199972476964 Order of pole (three term test) 32.33760185778061 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.6300000000000004 y2[1] (closed_form) 16.889144757942276 y2[1] (numeric) 16.889144757942265 absolute error 1.0658141036401503e-14 relative error 6.310645795956846e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.8080275083121516 y1[1] (numeric) 0.8080275083121521 absolute error 4.440892098500626e-16 relative error 5.4959664773999887e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.476045170795258 Order of pole (three term test) 32.652908454189145 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.47604517079525815 Order of pole (three term test) 32.34709154581086 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.6400000000000005 y2[1] (closed_form) 16.997195441362397 y2[1] (numeric) 16.997195441362383 absolute error 1.4210854715202004e-14 relative error 8.360705602419633e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 0.8020957578842923 y1[1] (numeric) 0.8020957578842927 absolute error 3.3306690738754696e-16 relative error 4.1524581586877575e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4790079301446125 Order of pole (three term test) 32.643357604815975 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4790079301446126 Order of pole (three term test) 32.356642395184025 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.6500000000000005 y2[1] (closed_form) 17.105186405736045 y2[1] (numeric) 17.105186405736028 absolute error 1.7763568394002505e-14 relative error 1.0384901966368328e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 0.7960837985490555 y1[1] (numeric) 0.7960837985490558 absolute error 2.220446049250313e-16 relative error 2.7892114539917832e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4817790927085966 Order of pole (three term test) 32.6337494143123 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.48177909270859665 Order of pole (three term test) 32.36625058568771 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.6600000000000005 y2[1] (closed_form) 17.21311685197344 y2[1] (numeric) 17.21311685197342 absolute error 1.7763568394002505e-14 relative error 1.0319786094966269e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 0.7899922314973647 y1[1] (numeric) 0.7899922314973651 absolute error 3.3306690738754696e-16 relative error 4.216078261380448e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.48435755005913284 Order of pole (three term test) 32.624087725826186 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4843575500591329 Order of pole (three term test) 32.375912274173814 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.6700000000000005 y2[1] (closed_form) 17.320985987036565 y2[1] (numeric) 17.320985987036547 absolute error 1.7763568394002505e-14 relative error 1.0255518021489758e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 0.783821665880849 y1[1] (numeric) 0.7838216658808493 absolute error 3.3306690738754696e-16 relative error 4.2492689585615184e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.48674227084765964 Order of pole (three term test) 32.61437640390423 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4867422708476595 Order of pole (three term test) 32.38562359609577 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.6800000000000005 y2[1] (closed_form) 17.428793024018475 y2[1] (numeric) 17.428793024018457 absolute error 1.7763568394002505e-14 relative error 1.0192081786456859e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 0.7775727187509276 y1[1] (numeric) 0.777572718750928 absolute error 4.440892098500626e-16 relative error 5.711224161303343e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4889323012176579 Order of pole (three term test) 32.60461933294571 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.48893230121765796 Order of pole (three term test) 32.39538066705429 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.6900000000000005 y2[1] (closed_form) 17.536537182221974 y2[1] (numeric) 17.536537182221952 absolute error 2.1316282072803006e-14 relative error 1.2155354190685277e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 0.7712460149971063 y1[1] (numeric) 0.7712460149971067 absolute error 3.3306690738754696e-16 relative error 4.3185559589412806e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4909267651861797 Order of pole (three term test) 32.59482041564892 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4909267651861797 Order of pole (three term test) 32.40517958435109 NO COMPLEX POLE (six term test) for Equation 2 Finished! diff ( y2 , x , 5 ) = y1 ; diff ( y1 , x , 1 ) = neg ( diff ( y2 , x , 4 ) ) ; Iterations 600 Total Elapsed Time 4 Seconds Elapsed Time(since restart) 4 Seconds Time to Timeout 2 Minutes 56.0 Seconds Percent Done 100.16666666666676%