Carley, M., 2013. Numerical solution of the modified Bessel equation. IMA Journal of Numerical Analysis, 33 (3), pp. 1048-1062.
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.
|Item Type ||Articles|
|Uncontrolled Keywords||modified bessel function, poisson equation, biharmonic equation|
|Departments||Faculty of Engineering & Design > Mechanical Engineering|
|Research Centres||Aerospace Engineering Research Centre|
|Publisher Statement||imanum11_revision_2.pdf: This is a pre-copy-editing, author-produced PDF of an article accepted for publication in IMA Journal of Numerical Analysis following peer review. The definitive publisher-authenticated version Carley, M. 2013. Numerical solution of the modified Bessel equation. IMA Journal of Numerical Analysis, 33(3), pp.1048-1062 is available online at http://dx.doi.org/10.1093/imanum/drs031|
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