Numerical solution of the modified Bessel equation

Research output: Contribution to journalArticle

3 Citations (Scopus)
114 Downloads (Pure)

Abstract

A Green's-function-based solver for the modified Bessel equation has been developed with the primary motivation of solving the Poisson and biharmonic equations in cylindrical geometries. The method is implemented using a discrete Hankel transform and a Green's function based on the modified Bessel functions of the first and second kind. The computation of these Bessel functions has been implemented to avoid scaling problems due to their exponential and singular behaviour, allowing the method to be used for large-order problems, as would arise in solving the Poisson equation with a dense azimuthal grid. The method has been tested on monotonically decaying and oscillatory inputs, checking for errors due to interpolation and/or aliasing. The error has been found to reach machine precision and to have computational time linearly proportional to the number of nodes.
Original languageEnglish
Pages (from-to)1048-1062
Number of pages15
JournalIMA Journal of Numerical Analysis
Volume33
Issue number3
Early online date26 Oct 2012
DOIs
Publication statusPublished - Jul 2013

Keywords

  • modified Bessel function
  • Poisson equation
  • biharmonic equation

Fingerprint Dive into the research topics of 'Numerical solution of the modified Bessel equation'. Together they form a unique fingerprint.

  • Cite this