##############ECHO OF PROBLEM################# ##############R:Temp/h3sinpostode.ode################# diff ( y , x , 3 ) = sin ( x ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=40 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=c(0.1) x_end=c(1.5) # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $array_y_init[0 + 1] = exact_soln_y(x_start) $array_y_init[1 + 1] = exact_soln_yp(x_start) $array_y_init[2 + 1] = exact_soln_ypp(x_start) $glob_look_poles=true # 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=12 $glob_max_minutes=(3.0) $glob_subiter_method=2 $glob_max_iter=1000000 $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) $glob_h_reason=1 #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) x = c(x) return(c(1.0) + cos(c(x))) end def exact_soln_yp (x) x = c(x) return(neg(sin(c(x)))) end def exact_soln_ypp (x) x = c(x) return(neg(cos(c(x)))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] 0.1 y[1] (closed_form) 1.9950041652780257 y[1] (numeric) 1.9950041652780257 absolute error 0.0 relative error 0.0% Desired digits 12 Estimated correct digits 14 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 0.09933466539753055 Order of pole (three term test) 32.009966711079386 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.11000000000000001 y[1] (closed_form) 1.9939560979566968 y[1] (numeric) 1.993956097956697 absolute error 2.220446049250313e-16 relative error 1.1135882337257634e-14% Desired digits 12 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 0.10911481154043462 Order of pole (three term test) 32.0120512753347 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.12000000000000002 y[1] (closed_form) 1.9928086358538661 y[1] (numeric) 1.9928086358538664 absolute error 2.220446049250313e-16 relative error 1.1142294394458554e-14% Desired digits 12 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 0.11885131321356739 Order of pole (three term test) 32.01433101257399 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.13000000000000003 y[1] (closed_form) 1.991561893714788 y[1] (numeric) 1.9915618937147883 absolute error 2.220446049250313e-16 relative error 1.1149269607225692e-14% Desired digits 12 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 0.12854027594607761 Order of pole (three term test) 32.01680501093275 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.14000000000000004 y[1] (closed_form) 1.9902159962126371 y[1] (numeric) 1.9902159962126371 absolute error 0.0 relative error 0.0% Desired digits 12 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 0.13817782428205685 Order of pole (three term test) 32.01947228084462 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.15000000000000005 y[1] (closed_form) 1.9887710779360424 y[1] (numeric) 1.9887710779360424 absolute error 0.0 relative error 0.0% Desired digits 12 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 0.14776010333066983 Order of pole (three term test) 32.0223317554372 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.16000000000000006 y[1] (closed_form) 1.9872272833756268 y[1] (numeric) 1.9872272833756266 absolute error 2.220446049250313e-16 relative error 1.1173588787884023e-14% Desired digits 12 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 0.15728328030805888 Order of pole (three term test) 32.025382290958774 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.17000000000000007 y[1] (closed_form) 1.9855847669095605 y[1] (numeric) 1.9855847669095605 absolute error 0.0 relative error 0.0% Desired digits 12 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 0.1667435460704072 Order of pole (three term test) 32.02862266723583 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.18000000000000008 y[1] (closed_form) 1.9838436927881213 y[1] (numeric) 1.9838436927881213 absolute error 0.0 relative error 0.0% Desired digits 12 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 0.17613711663754503 Order of pole (three term test) 32.03205158816103 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.19000000000000009 y[1] (closed_form) 1.9820042351172704 y[1] (numeric) 1.98200423511727 absolute error 4.440892098500626e-16 relative error 2.2406067655238234e-14% Desired digits 12 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 0.18546023470649142 Order of pole (three term test) 32.03566768221175 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2000000000000001 y[1] (closed_form) 1.9800665778412416 y[1] (numeric) 1.980066577841241 absolute error 6.661338147750939e-16 relative error 3.364199074060142e-14% Desired digits 12 Estimated correct digits 13 Correct digits 15 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 0.19470917115432546 Order of pole (three term test) 32.03946950299856 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2100000000000001 y[1] (closed_form) 1.9780309147241484 y[1] (numeric) 1.9780309147241475 absolute error 8.881784197001252e-16 relative error 4.49021505725045e-14% Desired digits 12 Estimated correct digits 13 Correct digits 15 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 0.20388022652978513 Order of pole (three term test) 32.04345552984385 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2200000000000001 y[1] (closed_form) 1.9758974493306054 y[1] (numeric) 1.9758974493306043 absolute error 1.1102230246251565e-15 relative error 5.6188291806403105e-14% Desired digits 12 Estimated correct digits 13 Correct digits 15 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 0.21296973253299986 Order of pole (three term test) 32.047624168390016 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.23000000000000012 y[1] (closed_form) 1.9736663950053748 y[1] (numeric) 1.9736663950053734 absolute error 1.3322676295501878e-15 relative error 6.750216920760612e-14% Desired digits 12 Estimated correct digits 13 Correct digits 15 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 0.22197405348275995 Order of pole (three term test) 32.051973751237234 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.24000000000000013 y[1] (closed_form) 1.9713379748520294 y[1] (numeric) 1.9713379748520279 absolute error 1.5543122344752192e-15 relative error 7.88455482673836e-14% Desired digits 12 Estimated correct digits 13 Correct digits 15 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 0.23088958777074156 Order of pole (three term test) 32.05650253861036 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2500000000000001 y[1] (closed_form) 1.9689124217106446 y[1] (numeric) 1.9689124217106433 absolute error 1.3322676295501878e-15 relative error 6.766515436947051e-14% Desired digits 12 Estimated correct digits 13 Correct digits 15 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 0.23971276930210164 Order of pole (three term test) 32.06120871905482 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2600000000000001 y[1] (closed_form) 1.9663899781345133 y[1] (numeric) 1.966389978134512 absolute error 1.3322676295501878e-15 relative error 6.775195380186445e-14% Desired digits 12 Estimated correct digits 13 Correct digits 15 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 0.24844006892186837 Order of pole (three term test) 32.06609041016117 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.27000000000000013 y[1] (closed_form) 1.9637708963658906 y[1] (numeric) 1.9637708963658895 absolute error 1.1102230246251565e-15 relative error 5.653526216727775e-14% Desired digits 12 Estimated correct digits 13 Correct digits 15 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 0.2570679958265568 Order of pole (three term test) 32.071145659318084 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.28000000000000014 y[1] (closed_form) 1.9610554383107708 y[1] (numeric) 1.9610554383107697 absolute error 1.1102230246251565e-15 relative error 5.661354610053702e-14% Desired digits 12 Estimated correct digits 13 Correct digits 15 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 0.26559309896044175 Order of pole (three term test) 32.07637244449329 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.29000000000000015 y[1] (closed_form) 1.958243875512697 y[1] (numeric) 1.9582438755126956 absolute error 1.3322676295501878e-15 relative error 6.80337952902511e-14% Desired digits 12 Estimated correct digits 13 Correct digits 15 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) 32.081768675042404 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.30000000000000016 y[1] (closed_form) 1.955336489125606 y[1] (numeric) 1.9553364891256044 absolute error 1.5543122344752192e-15 relative error 7.949078039096389e-14% Desired digits 12 Estimated correct digits 13 Correct digits 15 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 0.2823212366975178 Order of pole (three term test) 32.08733219254517 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.31000000000000016 y[1] (closed_form) 1.9523335698857134 y[1] (numeric) 1.952333569885712 absolute error 1.3322676295501878e-15 relative error 6.823975421516604e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.29051758026865276 Order of pole (three term test) 32.09306077166873 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3200000000000002 y[1] (closed_form) 1.949235418082441 y[1] (numeric) 1.9492354180824398 absolute error 1.1102230246251565e-15 relative error 5.695684648072616e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.29859772068119617 Order of pole (three term test) 32.098952121057856 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3300000000000002 y[1] (closed_form) 1.946042343528387 y[1] (numeric) 1.946042343528386 absolute error 8.881784197001252e-16 relative error 4.5640241213341786e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.30655842598671695 Order of pole (three term test) 32.10500388425132 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3400000000000002 y[1] (closed_form) 1.942754665528346 y[1] (numeric) 1.942754665528345 absolute error 1.1102230246251565e-15 relative error 5.714684639932255e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.3143965120092345 Order of pole (three term test) 32.111213640624534 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3500000000000002 y[1] (closed_form) 1.939372712847379 y[1] (numeric) 1.9393727128473779 absolute error 1.1102230246251565e-15 relative error 5.724650126664574e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.3221088436188457 Order of pole (three term test) 32.11757890635776 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3600000000000002 y[1] (closed_form) 1.9358968236779348 y[1] (numeric) 1.935896823677934 absolute error 8.881784197001252e-16 relative error 4.587942956653597e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.32969233598573683 Order of pole (three term test) 32.12409713542955 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3700000000000002 y[1] (closed_form) 1.9323273456060344 y[1] (numeric) 1.932327345606034 absolute error 4.440892098500626e-16 relative error 2.2982090009743315e-14% Desired digits 12 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 0.33714395581407286 Order of pole (three term test) 32.1307657206352 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3800000000000002 y[1] (closed_form) 1.92866463557651 y[1] (numeric) 1.9286646355765096 absolute error 4.440892098500626e-16 relative error 2.3025735094547266e-14% Desired digits 12 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 0.3444607225552759 Order of pole (three term test) 32.13758199462955 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.39000000000000024 y[1] (closed_form) 1.9249090598573129 y[1] (numeric) 1.9249090598573122 absolute error 6.661338147750939e-16 relative error 3.460598885770075e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.3516397096002052 Order of pole (three term test) 32.14454323099386 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.40000000000000024 y[1] (closed_form) 1.921060994002885 y[1] (numeric) 1.9210609940028847 absolute error 4.440892098500626e-16 relative error 2.311687193880923e-14% Desired digits 12 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 0.3586780454497616 Order of pole (three term test) 32.151646645326416 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.41000000000000025 y[1] (closed_form) 1.917120822816605 y[1] (numeric) 1.9171208228166048 absolute error 2.220446049250313e-16 relative error 1.1582191496872205e-14% Desired digits 12 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 0.36557291486344823 Order of pole (three term test) 32.158889396356194 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.42000000000000026 y[1] (closed_form) 1.9130889403123081 y[1] (numeric) 1.913088940312308 absolute error 2.220446049250313e-16 relative error 1.1606601253404505e-14% Desired digits 12 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 0.3723215599854297 Order of pole (three term test) 32.166268587079344 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.43000000000000027 y[1] (closed_form) 1.908965749674885 y[1] (numeric) 1.9089657496748849 absolute error 2.220446049250313e-16 relative error 1.1631670445781838e-14% Desired digits 12 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 0.3789212814476387 Order of pole (three term test) 32.173781265917974 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4400000000000003 y[1] (closed_form) 1.9047516632199633 y[1] (numeric) 1.904751663219963 absolute error 2.220446049250313e-16 relative error 1.1657404438207297e-14% Desired digits 12 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 0.3853694394494845 Order of pole (three term test) 32.18142442790071 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4500000000000003 y[1] (closed_form) 1.9004471023526768 y[1] (numeric) 1.9004471023526766 absolute error 2.220446049250313e-16 relative error 1.1683808754800333e-14% Desired digits 12 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 0.3916634548137418 Order of pole (three term test) 32.18919501586466 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4600000000000003 y[1] (closed_form) 1.896052497525525 y[1] (numeric) 1.8960524975255244 absolute error 6.661338147750939e-16 relative error 3.5132667246526294e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.3978008100181832 Order of pole (three term test) 32.19708992167827 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4700000000000003 y[1] (closed_form) 1.8915682881953289 y[1] (numeric) 1.8915682881953282 absolute error 6.661338147750939e-16 relative error 3.5215953816323813e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.4037790502025573 Order of pole (three term test) 32.20510598748445 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4800000000000003 y[1] (closed_form) 1.8869949227792842 y[1] (numeric) 1.8869949227792835 absolute error 6.661338147750939e-16 relative error 3.530130403286779e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.4095957841504994 Order of pole (three term test) 32.21324000696377 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4900000000000003 y[1] (closed_form) 1.8823328586101213 y[1] (numeric) 1.8823328586101207 absolute error 6.661338147750939e-16 relative error 3.538873646752118e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.41524868524598524 Order of pole (three term test) 32.22148872661689 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5000000000000003 y[1] (closed_form) 1.8775825618903725 y[1] (numeric) 1.8775825618903719 absolute error 6.661338147750939e-16 relative error 3.547827021275818e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.42073549240394853 Order of pole (three term test) 32.22984884706593 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5100000000000003 y[1] (closed_form) 1.8727445076457512 y[1] (numeric) 1.8727445076457503 absolute error 8.881784197001252e-16 relative error 4.742656652170159e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.42605401097468154 Order of pole (three term test) 32.23831702437417 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5200000000000004 y[1] (closed_form) 1.8678191796776498 y[1] (numeric) 1.867819179677649 absolute error 6.661338147750939e-16 relative error 3.566372066540488e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.43120211362166944 Order of pole (three term test) 32.24688987138361 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5300000000000004 y[1] (closed_form) 1.8628070705147608 y[1] (numeric) 1.8628070705147597 absolute error 1.1102230246251565e-15 relative error 5.959946374470019e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.4361777411724933 Order of pole (three term test) 32.25556395906973 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5400000000000004 y[1] (closed_form) 1.857708681363824 y[1] (numeric) 1.857708681363823 absolute error 8.881784197001252e-16 relative error 4.7810425208761745e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.44097890344247404 Order of pole (three term test) 32.264335817913135 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5500000000000004 y[1] (closed_form) 1.8525245220595057 y[1] (numeric) 1.8525245220595048 absolute error 8.881784197001252e-16 relative error 4.794421931390745e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.44560368003071793 Order of pole (three term test) 32.27320193928721 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5600000000000004 y[1] (closed_form) 1.8472551110134159 y[1] (numeric) 1.8472551110134154 absolute error 4.440892098500626e-16 relative error 2.40404916030484e-14% Desired digits 12 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 0.45005022108825243 Order of pole (three term test) 32.28215877686164 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5700000000000004 y[1] (closed_form) 1.8419009751622686 y[1] (numeric) 1.841900975162268 absolute error 6.661338147750939e-16 relative error 3.616556067659439e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.45431674805794175 Order of pole (three term test) 32.29120274802083 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5800000000000004 y[1] (closed_form) 1.8364626499151866 y[1] (numeric) 1.8364626499151862 absolute error 4.440892098500626e-16 relative error 2.418177194458989e-14% Desired digits 12 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 0.45840155438588376 Order of pole (three term test) 32.30033023529687 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5900000000000004 y[1] (closed_form) 1.8309406791001632 y[1] (numeric) 1.8309406791001626 absolute error 6.661338147750939e-16 relative error 3.638205335535354e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 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) 32.30953758781656 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6000000000000004 y[1] (closed_form) 1.8253356149096782 y[1] (numeric) 1.8253356149096773 absolute error 8.881784197001252e-16 relative error 4.865836246470621e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.46601954298361303 Order of pole (three term test) 32.31882112276167 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6100000000000004 y[1] (closed_form) 1.8196480178454792 y[1] (numeric) 1.8196480178454786 absolute error 6.661338147750939e-16 relative error 3.6607838892041185e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.4695496781595338 Order of pole (three term test) 32.32817712684197 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6200000000000004 y[1] (closed_form) 1.8138784566625337 y[1] (numeric) 1.813878456662533 absolute error 6.661338147750939e-16 relative error 3.672428063348602e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.47289199972476953 Order of pole (three term test) 32.33760185778061 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6300000000000004 y[1] (closed_form) 1.8080275083121515 y[1] (numeric) 1.808027508312151 absolute error 4.440892098500626e-16 relative error 2.4562082590470837e-14% Desired digits 12 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 0.47604517079525777 Order of pole (three term test) 32.347091545810855 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6400000000000005 y[1] (closed_form) 1.8020957578842922 y[1] (numeric) 1.802095757884292 absolute error 2.220446049250313e-16 relative error 1.2321465380159237e-14% Desired digits 12 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 0.47900793014461257 Order of pole (three term test) 32.35664239518402 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6500000000000005 y[1] (closed_form) 1.7960837985490556 y[1] (numeric) 1.7960837985490554 absolute error 2.220446049250313e-16 relative error 1.2362708527542386e-14% Desired digits 12 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) 32.36625058568771 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6600000000000005 y[1] (closed_form) 1.7899922314973646 y[1] (numeric) 1.7899922314973646 absolute error 0.0 relative error 0.0% Desired digits 12 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 0.4843575500591329 Order of pole (three term test) 32.375912274173814 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6700000000000005 y[1] (closed_form) 1.783821665880849 y[1] (numeric) 1.7838216658808488 absolute error 2.220446049250313e-16 relative error 1.244769077380759e-14% Desired digits 12 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 0.4867422708476599 Order of pole (three term test) 32.38562359609577 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6800000000000005 y[1] (closed_form) 1.7775727187509276 y[1] (numeric) 1.7775727187509278 absolute error 2.220446049250313e-16 relative error 1.2491449862093888e-14% Desired digits 12 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 0.4889323012176581 Order of pole (three term test) 32.39538066705429 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6900000000000005 y[1] (closed_form) 1.7712460149971063 y[1] (numeric) 1.7712460149971068 absolute error 4.440892098500626e-16 relative error 2.5072136004257326e-14% Desired digits 12 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 0.4909267651861799 Order of pole (three term test) 32.40517958435108 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7000000000000005 y[1] (closed_form) 1.7648421872844882 y[1] (numeric) 1.7648421872844886 absolute error 4.440892098500626e-16 relative error 2.516311163965147e-14% Desired digits 12 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 0.4927248649942301 Order of pole (three term test) 32.41501642854988 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7100000000000005 y[1] (closed_form) 1.758361875990508 y[1] (numeric) 1.7583618759905084 absolute error 4.440892098500626e-16 relative error 2.525584840719442e-14% Desired digits 12 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 0.49432588142585987 Order of pole (three term test) 32.424887265044156 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7200000000000005 y[1] (closed_form) 1.7518057291408946 y[1] (numeric) 1.7518057291408953 absolute error 6.661338147750939e-16 relative error 3.8025552930562313e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.4957291740958433 Order of pole (three term test) 32.434788145630925 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7300000000000005 y[1] (closed_form) 1.7451744023448699 y[1] (numeric) 1.7451744023448705 absolute error 6.661338147750939e-16 relative error 3.817004271206683e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.4969341817058223 Order of pole (three term test) 32.44471511008996 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7400000000000005 y[1] (closed_form) 1.7384685587295876 y[1] (numeric) 1.7384685587295876 absolute error 0.0 relative error 0.0% Desired digits 12 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 0.4979404222688199 Order of pole (three term test) 32.45466418776784 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7500000000000006 y[1] (closed_form) 1.7316888688738206 y[1] (numeric) 1.7316888688738206 absolute error 0.0 relative error 0.0% Desired digits 12 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 0.4987474933020272 Order of pole (three term test) 32.46463139916615 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7600000000000006 y[1] (closed_form) 1.7248360107409049 y[1] (numeric) 1.7248360107409049 absolute error 0.0 relative error 0.0% Desired digits 12 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 0.4993550719877916 Order of pole (three term test) 32.474612757533215 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7700000000000006 y[1] (closed_form) 1.717910669610943 y[1] (numeric) 1.7179106696109432 absolute error 2.220446049250313e-16 relative error 1.2925270728734573e-14% Desired digits 12 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 0.49976291530273953 Order of pole (three term test) 32.48460427045877 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7800000000000006 y[1] (closed_form) 1.710913538012277 y[1] (numeric) 1.710913538012277 absolute error 0.0 relative error 0.0% Desired digits 12 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 0.4999708601149831 Order of pole (three term test) 32.49460194147087 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7900000000000006 y[1] (closed_form) 1.7038453156522357 y[1] (numeric) 1.703845315652236 absolute error 2.220446049250313e-16 relative error 1.3031969679714272e-14% Desired digits 12 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 0.49997882324936993 Order of pole (three term test) 32.504601771634405 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8000000000000006 y[1] (closed_form) 1.6967067093471648 y[1] (numeric) 1.696706709347165 absolute error 2.220446049250313e-16 relative error 1.3086799486427831e-14% Desired digits 12 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 0.49978680152075255 Order of pole (three term test) 32.51459976115064 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8100000000000006 y[1] (closed_form) 1.6894984329517466 y[1] (numeric) 1.6894984329517468 absolute error 2.220446049250313e-16 relative error 1.3142634559127353e-14% Desired digits 12 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 0.499394871735262 Order of pole (three term test) 32.524591910957085 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8200000000000006 y[1] (closed_form) 1.682221207287613 y[1] (numeric) 1.6822212072876137 absolute error 6.661338147750939e-16 relative error 3.959846730556664e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.49880319065958695 Order of pole (three term test) 32.53457422432703 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8300000000000006 y[1] (closed_form) 1.6748757600712665 y[1] (numeric) 1.6748757600712676 absolute error 1.1102230246251565e-15 relative error 6.62868883228638e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.49801199495826837 Order of pole (three term test) 32.54454270846823 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8400000000000006 y[1] (closed_form) 1.6674628258413078 y[1] (numeric) 1.6674628258413087 absolute error 8.881784197001252e-16 relative error 5.326526060645463e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.4970216010990379 Order of pole (three term test) 32.554493376119936 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8500000000000006 y[1] (closed_form) 1.6599831458849816 y[1] (numeric) 1.6599831458849832 absolute error 1.5543122344752192e-15 relative error 9.363421781289071e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.49583240522623423 Order of pole (three term test) 32.56442224714777 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8600000000000007 y[1] (closed_form) 1.6524374681640515 y[1] (numeric) 1.652437468164053 absolute error 1.5543122344752192e-15 relative error 9.40617883835656e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.4944448830023506 Order of pole (three term test) 32.57432535013568 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8700000000000007 y[1] (closed_form) 1.6448265472400005 y[1] (numeric) 1.6448265472400023 absolute error 1.7763568394002505e-15 relative error 1.0799660562269962e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.4928595894177766 Order of pole (three term test) 32.58419872397454 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8800000000000007 y[1] (closed_form) 1.6371511441985795 y[1] (numeric) 1.6371511441985818 absolute error 2.220446049250313e-15 relative error 1.356286532931734e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.49107715856880896 Order of pole (three term test) 32.59403841944644 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8900000000000007 y[1] (closed_form) 1.6294120265736964 y[1] (numeric) 1.6294120265736987 absolute error 2.220446049250313e-15 relative error 1.3627284032752808e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.4890983034040221 Order of pole (three term test) 32.60384050080439 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9000000000000007 y[1] (closed_form) 1.621609968270664 y[1] (numeric) 1.6216099682706662 absolute error 2.220446049250313e-15 relative error 1.369284903704845e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.4869238154390974 Order of pole (three term test) 32.61360104734654 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9100000000000007 y[1] (closed_form) 1.613745749488811 y[1] (numeric) 1.6137457494888132 absolute error 2.220446049250313e-15 relative error 1.375957798775729e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.4845545644402281 Order of pole (three term test) 32.62331615498442 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9200000000000007 y[1] (closed_form) 1.6058201566434622 y[1] (numeric) 1.605820156643465 absolute error 2.6645352591003757e-15 relative error 1.6592986755564672e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.4819914980762238 Order of pole (three term test) 32.632981937804495 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9300000000000007 y[1] (closed_form) 1.5978339822872978 y[1] (numeric) 1.5978339822873 absolute error 2.220446049250313e-15 relative error 1.3896600484561898e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.47923564153945686 Order of pole (three term test) 32.642594529622514 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9400000000000007 y[1] (closed_form) 1.5897880250310976 y[1] (numeric) 1.5897880250311003 absolute error 2.6645352591003757e-15 relative error 1.6760317835758354e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.47628809713579734 Order of pole (three term test) 32.65215008552992 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9500000000000007 y[1] (closed_form) 1.581683089463883 y[1] (numeric) 1.5816830894638854 absolute error 2.4424906541753444e-15 relative error 1.544235169766679e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.47315004384370696 Order of pole (three term test) 32.66164478343175 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9600000000000007 y[1] (closed_form) 1.573519986072456 y[1] (numeric) 1.5735199860724585 absolute error 2.4424906541753444e-15 relative error 1.5522463494549314e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.4698227368426619 Order of pole (three term test) 32.671074825575445 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9700000000000008 y[1] (closed_form) 1.5652995311603537 y[1] (numeric) 1.5652995311603566 absolute error 2.886579864025407e-15 relative error 1.8441070265226428e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.4663075070111 Order of pole (three term test) 32.680436440069876 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9800000000000008 y[1] (closed_form) 1.5570225467662167 y[1] (numeric) 1.5570225467662195 absolute error 2.886579864025407e-15 relative error 1.8539101248216032e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.46260576039408385 Order of pole (three term test) 32.68972588239408 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9900000000000008 y[1] (closed_form) 1.5486898605815869 y[1] (numeric) 1.54868986058159 absolute error 3.1086244689504383e-15 relative error 2.0072608132031303e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.45871897764090463 Order of pole (three term test) 32.69893943689496 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0000000000000007 y[1] (closed_form) 1.5403023058681393 y[1] (numeric) 1.540302305868142 absolute error 2.6645352591003757e-15 relative error 1.7298781212942486e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.45464871341284047 Order of pole (three term test) 32.70807341827358 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0099999999999996 y[1] (closed_form) 1.5318607213743558 y[1] (numeric) 1.5318607213743576 absolute error 1.7763568394002505e-15 relative error 1.1596072767023737e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.45039659576131386 Order of pole (three term test) 32.717124173059155 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0199999999999985 y[1] (closed_form) 1.5233659512516509 y[1] (numeric) 1.523365951251652 absolute error 1.1102230246251565e-15 relative error 7.287960084134469e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.4459643254766904 Order of pole (three term test) 32.72608808107046 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0299999999999974 y[1] (closed_form) 1.5148188449699576 y[1] (numeric) 1.5148188449699578 absolute error 2.220446049250313e-16 relative error 1.4658162305172205e-14% Desired digits 12 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 0.44135367540798803 Order of pole (three term test) 32.7349615568638 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0399999999999963 y[1] (closed_form) 1.5062202572327816 y[1] (numeric) 1.506220257232781 absolute error 6.661338147750939e-16 relative error 4.422552489095524e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.43656648975375995 Order of pole (three term test) 32.74374105116717 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0499999999999952 y[1] (closed_form) 1.4975710478917312 y[1] (numeric) 1.4975710478917297 absolute error 1.5543122344752192e-15 relative error 1.0378888111274371e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.4316046833244394 Order of pole (three term test) 32.752423052299925 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.059999999999994 y[1] (closed_form) 1.4888720818605328 y[1] (numeric) 1.4888720818605303 absolute error 2.4424906541753444e-15 relative error 1.6404973160106175e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.42647024077644125 Order of pole (three term test) 32.76100408757735 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.069999999999993 y[1] (closed_form) 1.4801242290285404 y[1] (numeric) 1.480124229028537 absolute error 3.3306690738754696e-15 relative error 2.2502631931520435e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.42116521581832655 Order of pole (three term test) 32.76948072469975 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0799999999999919 y[1] (closed_form) 1.4713283641737471 y[1] (numeric) 1.471328364173743 absolute error 4.218847493575595e-15 relative error 2.8673731821548685e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 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 0.4156917303893462 Order of pole (three term test) 32.7778495731253 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0899999999999908 y[1] (closed_form) 1.462485366875309 y[1] (numeric) 1.4624853668753037 absolute error 5.329070518200751e-15 relative error 3.6438453600302625e-13% Desired digits 12 Estimated correct digits 12 Correct digits 14 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 0.41005197381069236 Order of pole (three term test) 32.78610728542621 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0999999999999897 y[1] (closed_form) 1.4535961214255866 y[1] (numeric) 1.4535961214255801 absolute error 6.439293542825908e-15 relative error 4.429905561739319e-13% Desired digits 12 Estimated correct digits 12 Correct digits 14 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 0.4042482019098012 Order of pole (three term test) 32.79425055862766 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1099999999999886 y[1] (closed_form) 1.4446615167417172 y[1] (numeric) 1.4446615167417098 absolute error 7.327471962526033e-15 relative error 5.072102965026976e-13% Desired digits 12 Estimated correct digits 12 Correct digits 14 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 0.39828273611805015 Order of pole (three term test) 32.802276135528956 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1199999999999875 y[1] (closed_form) 1.4356824462767235 y[1] (numeric) 1.4356824462767153 absolute error 8.215650382226158e-15 relative error 5.7224704554496e-13% Desired digits 12 Estimated correct digits 12 Correct digits 14 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 0.3921579625422177 Order of pole (three term test) 32.81018080600633 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1299999999999863 y[1] (closed_form) 1.4266598079301698 y[1] (numeric) 1.4266598079301607 absolute error 9.103828801926284e-15 relative error 6.381219090439173e-13% Desired digits 12 Estimated correct digits 12 Correct digits 14 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 0.3858763310100716 Order of pole (three term test) 32.81796140829699 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1399999999999852 y[1] (closed_form) 1.4175945039583715 y[1] (numeric) 1.4175945039583615 absolute error 9.992007221626409e-15 relative error 7.048565152958458e-13% Desired digits 12 Estimated correct digits 12 Correct digits 14 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 0.3794403540904705 Order of pole (three term test) 32.82561483026376 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1499999999999841 y[1] (closed_form) 1.4084874408841719 y[1] (numeric) 1.4084874408841608 absolute error 1.1102230246251565e-14 relative error 7.882377878557574e-13% Desired digits 12 Estimated correct digits 12 Correct digits 14 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 0.3728526060883705 Order of pole (three term test) 32.8331380106399 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.159999999999983 y[1] (closed_form) 1.3993395294062887 y[1] (numeric) 1.3993395294062767 absolute error 1.199040866595169e-14 relative error 8.568619991060337e-13% Desired digits 12 Estimated correct digits 12 Correct digits 14 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 0.36611572201513737 Order of pole (three term test) 32.840527940253565 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.169999999999982 y[1] (closed_form) 1.3901516843082469 y[1] (numeric) 1.390151684308234 absolute error 1.2878587085651816e-14 relative error 9.264159610079044e-13% Desired digits 12 Estimated correct digits 12 Correct digits 14 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 0.35923239653457556 Order of pole (three term test) 32.84778166323144 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1799999999999808 y[1] (closed_form) 1.3809248243668995 y[1] (numeric) 1.3809248243668857 absolute error 1.3766765505351941e-14 relative error 9.969236023882379e-13% Desired digits 12 Estimated correct digits 12 Correct digits 14 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 0.3522053828851016 Order of pole (three term test) 32.85489627818105 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1899999999999797 y[1] (closed_form) 1.3716598722605517 y[1] (numeric) 1.3716598722605367 absolute error 1.509903313490213e-14 relative error 1.1007855110624694e-12% Desired digits 12 Estimated correct digits 12 Correct digits 14 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 0.3450374917784829 Order of pole (three term test) 32.86186893935127 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1999999999999786 y[1] (closed_form) 1.3623577544766934 y[1] (numeric) 1.3623577544766776 absolute error 1.5765166949677223e-14 relative error 1.1571972852118359e-12% Desired digits 12 Estimated correct digits 12 Correct digits 14 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 0.33773159027559096 Order of pole (three term test) 32.868696857770615 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2099999999999775 y[1] (closed_form) 1.3530194012193513 y[1] (numeric) 1.3530194012193344 absolute error 1.687538997430238e-14 relative error 1.2472393196353394e-12% Desired digits 12 Estimated correct digits 12 Correct digits 14 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 0.3302906006396171 Order of pole (three term test) 32.875377302362736 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2199999999999764 y[1] (closed_form) 1.3436457463160691 y[1] (numeric) 1.3436457463160512 absolute error 1.7985612998927536e-14 relative error 1.3385680748247414e-12% Desired digits 12 Estimated correct digits 12 Correct digits 14 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 0.3227174991672033 Order of pole (three term test) 32.88190760103887 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2299999999999753 y[1] (closed_form) 1.3342377271245258 y[1] (numeric) 1.3342377271245065 absolute error 1.9317880628477724e-14 relative error 1.4478589711378148e-12% Desired digits 12 Estimated correct digits 12 Correct digits 14 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 0.3150153149979654 Order of pole (three term test) 32.88828514176663 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2399999999999742 y[1] (closed_form) 1.3247962844388006 y[1] (numeric) 1.3247962844387804 absolute error 2.020605904817785e-14 relative error 1.5252200874595129e-12% Desired digits 12 Estimated correct digits 12 Correct digits 14 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 0.30718712890287625 Order of pole (three term test) 32.89450737361474 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2499999999999731 y[1] (closed_form) 1.315322362395294 y[1] (numeric) 1.3153223623952728 absolute error 2.1316282072803006e-14 relative error 1.6206127624854307e-12% Desired digits 12 Estimated correct digits 12 Correct digits 14 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 0.29923607205200004 Order of pole (three term test) 32.90057180777345 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.259999999999972 y[1] (closed_form) 1.305816908378316 y[1] (numeric) 1.3058169083782936 absolute error 2.2426505097428162e-14 relative error 1.7174310543489183e-12% Desired digits 12 Estimated correct digits 12 Correct digits 14 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 0.29116532476206347 Order of pole (three term test) 32.906476018549924 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.269999999999971 y[1] (closed_form) 1.2962808729253466 y[1] (numeric) 1.296280872925323 absolute error 2.353672812205332e-14 relative error 1.8157120585245887e-12% Desired digits 12 Estimated correct digits 12 Correct digits 14 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 0.2829781152243753 Order of pole (three term test) 32.9122176443386 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2799999999999698 y[1] (closed_form) 1.2867152096319845 y[1] (numeric) 1.28671520963196 absolute error 2.4424906541753444e-14 relative error 1.8982371824717336e-12% Desired digits 12 Estimated correct digits 12 Correct digits 14 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 0.27467771821358883 Order of pole (three term test) 32.91779438856569 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2899999999999687 y[1] (closed_form) 1.2771208750565877 y[1] (numeric) 1.2771208750565624 absolute error 2.531308496145357e-14 relative error 1.9820430043735665e-12% Desired digits 12 Estimated correct digits 12 Correct digits 14 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 0.2662674537778372 Order of pole (three term test) 32.92320402060787 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2999999999999676 y[1] (closed_form) 1.2674988286246185 y[1] (numeric) 1.2674988286245923 absolute error 2.6201263381153694e-14 relative error 2.0671627294192506e-12% Desired digits 12 Estimated correct digits 12 Correct digits 14 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 0.2577506859107598 Order of pole (three term test) 32.92844437668446 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.3099999999999665 y[1] (closed_form) 1.257850032532702 y[1] (numeric) 1.2578500325326747 absolute error 2.731148640577885e-14 relative error 2.1712831974720163e-12% Desired digits 12 Estimated correct digits 12 Correct digits 14 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 0.24913082120594834 Order of pole (three term test) 32.933513360722884 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.3199999999999654 y[1] (closed_form) 1.2481754516524064 y[1] (numeric) 1.2481754516523778 absolute error 2.864375403532904e-14 relative error 2.2948499746096427e-12% Desired digits 12 Estimated correct digits 12 Correct digits 14 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 0.24041130749435452 Order of pole (three term test) 32.938408945197125 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.3299999999999643 y[1] (closed_form) 1.2384760534337578 y[1] (numeric) 1.2384760534337278 absolute error 2.9976021664879227e-14 relative error 2.420395742151711e-12% Desired digits 12 Estimated correct digits 12 Correct digits 14 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 0.23159563246520415 Order of pole (three term test) 32.943129171938665 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.3399999999999632 y[1] (closed_form) 1.2287528078084953 y[1] (numeric) 1.228752807808464 absolute error 3.1308289294429414e-14 relative error 2.5479729605068705e-12% Desired digits 12 Estimated correct digits 12 Correct digits 14 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 0.22268732227096866 Order of pole (three term test) 32.94767215291973 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.3499999999999621 y[1] (closed_form) 1.2190066870930785 y[1] (numeric) 1.219006687093046 absolute error 3.241851231905457e-14 relative error 2.6594203840146137e-12% Desired digits 12 Estimated correct digits 12 Correct digits 14 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 0.21368994011694933 Order of pole (three term test) 32.952036071008514 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.359999999999961 y[1] (closed_form) 1.2092386658914576 y[1] (numeric) 1.209238665891424 absolute error 3.352873534367973e-14 relative error 2.77271445988391e-12% Desired digits 12 Estimated correct digits 12 Correct digits 14 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 0.20460708483604445 Order of pole (three term test) 32.95621918069597 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.36999999999996 y[1] (closed_form) 1.1994497209976123 y[1] (numeric) 1.1994497209975779 absolute error 3.441691376337985e-14 relative error 2.8693919520656898e-12% Desired digits 12 Estimated correct digits 12 Correct digits 14 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 0.19544238944926304 Order of pole (three term test) 32.96021980879398 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.3799999999999588 y[1] (closed_form) 1.1896408312978748 y[1] (numeric) 1.1896408312978395 absolute error 3.530509218307998e-14 relative error 2.9677101906936747e-12% Desired digits 12 Estimated correct digits 12 Correct digits 14 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 0.18619951971256596 Order of pole (three term test) 32.96403635510465 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.3899999999999577 y[1] (closed_form) 1.179812977673041 y[1] (numeric) 1.1798129776730049 absolute error 3.6193270602780103e-14 relative error 3.067712534758222e-12% Desired digits 12 Estimated correct digits 12 Correct digits 14 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 0.17688217265061107 Order of pole (three term test) 32.96766729306035 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.3999999999999566 y[1] (closed_form) 1.1699671429002838 y[1] (numeric) 1.1699671429002463 absolute error 3.752553823233029e-14 relative error 3.2074010334432607e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 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 0.1674940750779934 Order of pole (three term test) 32.97111117033432 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.4099999999999555 y[1] (closed_form) 1.160104311554875 y[1] (numeric) 1.1601043115548366 absolute error 3.8413716652030416e-14 relative error 3.3112295393976197e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 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 0.15803898210856912 Order of pole (three term test) 32.974366609421544 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.4199999999999544 y[1] (closed_form) 1.150225469911731 y[1] (numeric) 1.1502254699116912 absolute error 3.9745984281580604e-14 relative error 3.455495059123559e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 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 0.14852067565345975 Order of pole (three term test) 32.977432308189805 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.4299999999999533 y[1] (closed_form) 1.140331605846783 y[1] (numeric) 1.1403316058467423 absolute error 4.063416270128073e-14 relative error 3.563363717443118e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 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 0.1389429629083382 Order of pole (three term test) 32.98030704040046 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.4399999999999522 y[1] (closed_form) 1.130423708738193 y[1] (numeric) 1.130423708738151 absolute error 4.196643033083092e-14 relative error 3.712451358409219e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 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 0.1293096748306014 Order of pole (three term test) 32.98298965619897 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.449999999999951 y[1] (closed_form) 1.1205027693674152 y[1] (numeric) 1.1205027693673721 absolute error 4.3076653355456074e-14 relative error 3.844404006227953e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 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 0.11962466460703851 Order of pole (three term test) 32.985479082574784 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.45999999999995 y[1] (closed_form) 1.1105697798201193 y[1] (numeric) 1.1105697798200753 absolute error 4.39648317751562e-14 relative error 3.958763562094879e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 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 0.1098918061126072 Order of pole (three term test) 32.98777432379053 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.469999999999949 y[1] (closed_form) 1.1006257333869824 y[1] (numeric) 1.1006257333869376 absolute error 4.4853010194856324e-14 relative error 4.075228193768382e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 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 0.1001149923609353 Order of pole (three term test) 32.989874461780325 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.4799999999999478 y[1] (closed_form) 1.0906716244643617 y[1] (numeric) 1.0906716244643153 absolute error 4.6407322429331543e-14 relative error 4.254930759028648e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 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 0.09029813394716772 Order of pole (three term test) 32.991778656517 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.4899999999999467 y[1] (closed_form) 1.0807084484548537 y[1] (numeric) 1.0807084484548062 absolute error 4.75175454539567e-14 relative error 4.3968884967906986e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 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 0.08044515748378046 Order of pole (three term test) 32.99348614634801 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.4999999999999456 y[1] (closed_form) 1.0707372016677572 y[1] (numeric) 1.0707372016677088 absolute error 4.8405723873656825e-14 relative error 4.520784726472669e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 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 0.07056000402998741 Order of pole (three term test) 32.99499624830021 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 3 ) = sin ( x ) ; Iterations 1401 Total Elapsed Time 1 Seconds Elapsed Time(since restart) 1 Seconds Time to Timeout 2 Minutes 59.0 Seconds Percent Done 100.14285714285325%