Title

Particular Solutions for Axisymmetric Helmholtz-Type Operators

Document Type

Article

Publication Date

11-1-2005

Department

Mathematics

Abstract

In this paper, we consider the solution of the axisymmetric heat equation with axisymmetric data in an axisymmetric domain in R-3. To solve this problem, we remove the time-dependence by various transform or time-stepping methods. This converts the problem to one of a sequence of modified inhomogeneous Helmholtz equations. Generalizing previous work, we consider solving these equations by boundary-type methods. In order to do this, one needs to subtract off a particular solution, so that one obtains a sequence of modified homogeneous Helmholtz equations. We do this by modifying the usual Dual Reciprocity Method (DRM) and approximating the right-hand sides by Fourier-polynomials or bivariate polynomials. This inevitably leads to analytical solving a sequence of ordinary differential equations (ODEs.) The analytic formulas and their precision are checked using MATHEMATICA. In fact, by using an infinite precision technique, the particular solutions can be obtained with infinite precision themselves. This work will form the basis for numerical algorithms for solving axisymmetric heat equation. (C) 2005 Elsevier Ltd. All rights reserved.

Publication Title

Engineering Analysis With Boundary Elements

Volume

29

Issue

11

First Page

1066

Last Page

1076