Numerical solution of the modified Bessel equation

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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
Issue number3
Early online date26 Oct 2012
Publication statusPublished - Jul 2013


  • modified Bessel function
  • Poisson equation
  • biharmonic equation


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