Wave polynomials for solving different types of two-dimensional wave equations

Artur Maciąg; Jörg Wauer

Artur Maciąg Kielce University of Technology
Jörg Wauer Universität Karlsruhe

Abstract

The paper demonstrates a specific power series expansion technique used to obtain the approximate solution of the two-dimensional wave equation in some unusual cases. The solution for inhomogeneous wave equation, for more complicated shape geometry of the body, discrete boundary conditions and a membrane whose thickness is not constant is shown. As solving functions (Trefftz functions), so-called wave polynomials are used. Recurrent formulas for the particular solution are obtained. Some examples are included.

Keywords

wave equation, wave polynomials, Trefftz method, membrane vibrations,

References

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[3] P.C. Rosenbloom and D.V. Widder. Expansion in terms of heat polynomials and associated functions . Trans. Am. Math. Soc., 92: 220-266, 1956.
[4] H. Yano, S. Fukutani and A. Kieda. A boundary residual method with heat polynomials for solving unsteady heat conduction problems. Journal of the Franklin Institute, 316 (4): 291-298, 1983.
[5] S. Futakiewicz and L. Hożejowski. Heat polynomials method in the n-dimensional direct and inverse heat conduction problems. In: A.J. Nowak, C.A. Brebbia, R. Bielecki and M. Zerroukat, eds., Advanced Computational Method in Heat Transfer V, 103-112, Southampton UK and Boston USA: Computational Mechanics Publications 1998.

Wave polynomials for solving different types of two-dimensional wave equations

Abstract

Keywords

References

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