Mathematical Problems in Engineering

Mathematical Problems in Engineering / 2005 / Article

Open Access

Volume 2005 |Article ID 508091 | https://doi.org/10.1155/MPE.2005.583

Artur Maciąg, "Three-dimensional wave polynomials", Mathematical Problems in Engineering, vol. 2005, Article ID 508091, 16 pages, 2005. https://doi.org/10.1155/MPE.2005.583

Three-dimensional wave polynomials

Received16 Apr 2004
Revised14 Sep 2004

Abstract

We demonstrate a specific power series expansion technique to solve the three-dimensional homogeneous and inhomogeneous wave equations. As solving functions, so-called wave polynomials are used. The presented method is useful for a finite body of certain shape. Recurrent formulas to improve efficiency are obtained for the wave polynomials and their derivatives in a Cartesian, spherical, and cylindrical coordinate system. Formulas for a particular solution of the inhomogeneous wave equation are derived. The accuracy of the method is discussed and some typical examples are shown.

Copyright © 2005 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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