Mathematical Problems in Engineering
Volume 2005 (2005), Issue 5, Pages 583-598
Three-dimensional wave polynomials
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.