The Method of Particular Solutions for Solving Axisymmetric Polyharmonic and Poly-Helmholtz Equations

Document Type

Article

Publication Date

12-1-2009

Department

Mathematics

School

Mathematics and Natural Sciences

Abstract

In this paper we derive analytical particular solutions for the axisymmetric polyharmonic and poly-Helmholtz partial differential operators using Chebyshev polynomials as basis functions. We further extend the proposed approach to the particular solutions of the product of Helmholtz-type operators. By using this formulation, we can approximate the particular solution when the forcing term of the differential equation is approximated by a truncated series of Chebyshev polynomials. These formulas were further implemented to solve inhomogeneous partial differential equations (PDEs) in which the homogeneous solutions were obtained by the method of fundamental solutions (MFS). Several numerical experiments were carried out to validate our newly derived particular solutions. Due to the exponential convergence of Chebyshev interpolation and the MFS, our numerical results are extremely accurate. (C) 2009 Elsevier Ltd. All rights reserved.

Publication Title

Engineering Analysis With Boundary Elements

Volume

33

Issue

12

First Page

1396

Last Page

1402

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