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library(kelvin)
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) 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) }
plot_kelvin_curves()
Compare these curves with ones given by Wolfram.
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