# Kelvin curves

#### 2020-06-17

library(kelvin)
## Loaded kelvin (2.0.2) -- Solutions to the Kelvin differential equation

Setup 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)

# 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)
}
plot_kelvin_curves()

Compare these curves with ones given by Wolfram.