Mathematical Problems in Engineering
Volume 2005 (2005), Issue 5, Pages 583-598
doi:10.1155/MPE.2005.583
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.