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## Loaded kelvin (2.0.2) -- Solutions to the Kelvin differential equationSetup a function to plot Kelvin solutions:
plot_kelvin_curves <- function(){
# Kelvin functions (order 0 by default)
num.pts <- 1e3
curve(expr=Kei,
from=0.001, to=5, n=num.pts,
ylim=c(-7,7), xlim=c(0,5),
yaxs="i",
xaxs="i",
main="Fundamental Kelvin functions",
ylab="Ke(x) or Be(x)", lwd=2)
curve(expr=Ker,from=0.001,to=5,n=num.pts,add=T,col='red', lwd=2)
# complementary Kelvin functions (order 0 by default)
curve(expr=Bei, from=0.001, to=5, n=num.pts, add=TRUE, lty=2, lwd=2)
curve(expr=Ber, from=0.001, to=5 ,n=num.pts, add=TRUE, col='red', lty=2, lwd=2)
legend(0.5, 5, c(expression(Kei[0]), expression(Ker[0])), col=c(1,2), lty=c(1,1), lwd=2)
legend(2.8, -3.8, c(expression(Bei[0]), expression(Ber[0])), col=c(1,2), lty=c(2,2), lwd=2)
xseq <- seq.int(0.001, 5, length.out=num.pts)
Knu <- Keir(xseq, nSeq=6, return.list=FALSE)
matplot(xseq, Re(Knu), type="l", xaxs="i", xlim=c(0,5), yaxs="i", ylim=c(-7,7),
lty=1, lwd=2, main="Fundamental and higher order Kelvin functions (Ker)")
legend(3.5, 7, 0:5, col=1:6, lty=1, lwd=2)
Bnu <- Beir(xseq, nSeq=6, return.list=FALSE)
matplot(xseq, Re(Bnu), type="l", xaxs="i", xlim=c(0,5), yaxs="i", ylim=c(-7,7),
lty=1, lwd=2, main="Fundamental and higher order complimentary Kelvin functions (Ber)")
legend(0.5, 7, 0:5, col=1:6, lty=1, lwd=2)
}
Compare these curves with ones given by Wolfram.
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.