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SOLUTIONS TO PSEUDODIFFERENTIAL EQUATIONS USING SPHERICAL RADIAL BASIS FUNCTIONS

Part of: Partial differential equations, boundary value problems

Published online by Cambridge University Press:  17 April 2009

T. D. PHAM  and
T. TRAN
T. D. PHAM
Affiliation:
School of Mathematics and Statistics, The University of New South Wales, Sydney 2052, Australia (email: t.d.pham@student.unsw.edu.au)
T. TRAN*
Affiliation:
School of Mathematics and Statistics, The University of New South Wales, Sydney 2052, Australia (email: thanh.tran@unsw.edu.au)
*
✉For correspondence; e-mail: thanh.tran@unsw.edu.au
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Abstract

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Spherical radial basis functions are used to define approximate solutions to pseudodifferential equations of negative order on the unit sphere. These equations arise from geodesy. The approximate solutions are found by the collocation method. A salient feature of our approach in this paper is a simple error analysis for the collocation method using the same argument as that for the Galerkin method.

Keywords

pseudodifferential equationsphereradial basis functioncollocation method

MSC classification

Secondary: 65N15: Error bounds 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 65N35: Spectral, collocation and related methods
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 79 , Issue 3 , June 2009 , pp. 473 - 485
Copyright
Copyright © Australian Mathematical Society 2009

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