besselzero: Find First k Positive Zeros for the Bessel Functions

In CircularDDM: Circular Drift-Diffusion Model

Description

Find first k positive zeros of the Bessel function J(n,x) or Y(n,x) using Halley's method.

Usage

besselzero(nu, k, kind)

Arguments

nu	The order of the corresponding Bessel function.
k	an integer for first k positive zeros.
kind	0, 1, or 2. A switch selects besselI, besselJ or besselY

Value

a vector

References

besselzero.m

Examples

nu <- seq(0, 5, length.out=10)
output <- matrix(numeric(5*length(nu)), nrow=5)
  for(i in 1:length(nu)) {
    output[,i] <- besselzero(nu[i], 5, 1)
  }
output

output <- matrix(numeric(5*length(nu)), nrow=5)
for(i in 1:length(nu)) {
    output[,i] <- besselzero(nu[i], 5, 2)
}
output

Example output

          [,1]      [,2]      [,3]      [,4]      [,5]      [,6]      [,7]
[1,]  2.404826  3.220109  3.980805  4.709341  5.416212  6.107288  6.786227
[2,]  5.520078  6.365899  7.175043  7.957684  8.720066  9.466340 10.199428
[3,]  8.653728  9.508977 10.337270 11.144227 11.933772 12.708771 13.471390
[4,] 11.791534 12.651326 13.489892 14.310774 15.116639 15.909550 16.691145
[5,] 14.930918 15.793377 16.638351 17.468274 18.285067 19.090280 19.885183
          [,8]      [,9]     [,10]
[1,]  7.455489  8.116813  8.771484
[2,] 10.921475 11.634110 12.338604
[3,] 14.223313 14.965879 15.700174
[4,] 17.462746 18.225440 18.980134
[5,] 20.670833 21.448119 22.217800
          [,1]      [,2]      [,3]      [,4]     [,5]      [,6]      [,7]
[1,]  3.957678  4.793657  5.585297  6.347302  7.08779  7.811784  8.522642
[2,]  7.086051  7.937582  8.758002  9.554719 10.33263 11.095169 11.844850
[3,] 10.222345 11.080205 11.914307 12.729056 13.52766 14.312536 15.085562
[4,] 13.361097 14.222377 15.064479 15.890316 16.70213 17.501717 18.290500
[5,] 16.500922 17.364340 18.211693 19.045045 19.86606 20.676087 21.476268
          [,8]      [,9]    [,10]
[1,]  9.222733  9.913802 10.59718
[2,] 12.583577 13.312835 14.03380
[3,] 15.848227 16.601738 17.34709
[4,] 19.069662 19.840185 20.60290
[5,] 22.267549 23.050740 23.82654

CircularDDM documentation built on May 2, 2019, 2:07 a.m.