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
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.
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