Abstract
This paper deals with the pseudospectral solution of differential equations with coordinate singularities such as those which describe situations in spherical or cylindrical geometries. We use the differential equation, together with a smoothness assumption on the solution, to construct "pole conditions." The pole conditions, which are straightforward and easily implemented, serve as numerical boundary conditions at the coordinate singularity. Standard pseudospectral methods, including fast transformation techniques, can then be applied to the singular problem. The method is illustrated using the eigenvalue problem of Bessel's equation and a Poisson equation on the unit disk. Numerical results show that spectral convergence is achieved.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
