Mathematical Problems in Engineering
Volume 2005 (2005), Issue 5, Pages 583-598

Three-dimensional wave polynomials

Artur Maciąg

Department of Mathematics, Faculty of Management and Compuer Modelling, Kielce University of Technology, Kielce 25-314, Poland

Received 16 April 2004; Revised 14 September 2004

Copyright © 2005 Artur Maciąg. 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.


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.