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using DifferentialEquations, ArgParse
function buchstab_model(dω,ω,h,p,u)
dω[1] = ( h(p, u-1)[1] - ω[1] ) / u
end
function buchstabtab(up, res=1, prec=40)
setprecision(prec) do
buchstab_history(p, u) = 1/u
buchstab_initial = [1/BigFloat(2)]
buchstab_problem = DDEProblem(buchstab_model, buchstab_initial, buchstab_history,
(BigFloat(2), BigFloat(up)+3); constant_lags=[1])
alg = MethodOfSteps(Tsit5())
buchstab = solve(buchstab_problem, alg)
return [(x, buchstab(x)[1]) for x in (BigFloat(2):BigFloat(res):BigFloat(up))]
end
end
s = ArgParseSettings()
@add_arg_table s begin
"--resolution", "-r"
help = "Evaluate at points spaced by this resolution"
arg_type = BigFloat
default = 1/BigFloat(10)
"--precision", "-p"
help = "Use this much floating point precision"
arg_type = Int
default = 40
"bound"
help = "Evaluate up to bound"
arg_type = Int
required = true
end
args = parse_args(ARGS, s)
prec = args["precision"]
table = buchstabtab(args["bound"], args["resolution"], prec)
for (x,bx) in table
print(x, "\t", bx, "\n")
end
2.0 0.50
2.0999999999985 0.52157630634701
2.2000000000007 0.5374190833445
2.2999999999993 0.54885393980112
2.4000000000015 0.55686477484232
2.5 0.56218584807357
2.5999999999985 0.56538554056715
2.7000000000007 0.56689986002948
2.7999999999993 0.56706706796285
2.9000000000015 0.56615605923344
3.0 0.56438242347758
3.0999999999985 0.56266459268045
3.2000000000007 0.56163933379867
3.3000000000029 0.5610950057744
3.4000000000015 0.56086563559256
3.5 0.56083091827531
3.5999999999985 0.56091500129514
3.7000000000007 0.56105937735629
3.8000000000029 0.56121827356947
3.9000000000015 0.56135885112963
4.0 0.56145797496356
4.1000000000058 0.56150891681955
4.1999999999971 0.56152564479453
4.3000000000029 0.56152133876913
4.4000000000015 0.56150650212385
4.5 0.56148896174727
4.6000000000058 0.56147386802786
4.6999999999971 0.56146369486032
4.8000000000029 0.5614582396438
4.9000000000015 0.56145515950448
5.0 0.5614543076872
5.1000000000058 0.56145486287096
5.1999999999971 0.56145602209926
5.3000000000029 0.56145734204711
5.4000000000015 0.56145850755092
5.5 0.56145933161042
5.6000000000058 0.56145975538766
5.6999999999971 0.56145984820796
5.8000000000029 0.5614598069069
5.9000000000015 0.56145975164327
6.0 0.56145966531403
6.0999999999985 0.56145958617253
6.2000000000044 0.56145952622683
6.3000000000029 0.56145948360427
6.4000000000015 0.56145945614844
6.5 0.56145944142099
6.5999999999985 0.5614594366989
6.7000000000044 0.56145943897809
6.8000000000029 0.56145944497257
6.9000000000015 0.56145945111166
7.0 0.56145945486787
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