Three‐dimensional wave polynomials | Zendy

A. Maciąg | Zendy

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Three‐dimensional wave polynomials

Author(s) -

A. Maciąg

Publication year - 2005

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/mpe.2005.583

Subject(s) - cartesian coordinate system , mathematics , homogeneous , mathematical analysis , wave equation , power series , orthogonal polynomials , series (stratigraphy) , wave function , geometry , physics , quantum mechanics , paleontology , combinatorics , biology

We demonstrate a specific power series expansion technique tosolve the three-dimensional homogeneous andinhomogeneous wave equations. As solving functions, so-called wavepolynomials are used. The presented method is useful for a finitebody of certain shape. Recurrent formulas to improve efficiencyare obtained for the wave polynomials and their derivatives in aCartesian, spherical, and cylindrical coordinate system. Formulasfor a particular solution of the inhomogeneous wave equation arederived. The accuracy of the method is discussed and some typicalexamples are shown

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