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Zbl 1159.65084
Dehghan, Mehdi; Shokri, Ali
A meshless method for numerical solution of a linear hyperbolic equation with variable coefficients in two space dimensions. (English)
[J] Numer. Methods Partial Differ. Equations 25, No. 2, 494-506 (2009). ISSN 0749-159X; ISSN 1098-2426/e

Summary: A meshless method is proposed for the numerical solution of the two space dimensional linear hyperbolic equation subject to appropriate initial and Dirichlet boundary conditions. The new developed scheme uses collocation points and approximates the solution employing thin plate splines radial basis functions. Numerical results are obtained for various cases involving variable, singular and constant coefficients, and are compared with analytical solutions to confirm the good accuracy of the presented scheme.

MSC 2000:: *65M70 Spectral, collocation and related methods (IVP of PDE)
35L15 Second order hyperbolic equations, initial value problems

Keywords: collocation; radial basis functions; thin plate splines; two-dimensional linear hyperbolic equation; two-dimensional telegraph equation; meshless method; numerical results

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Zentralblatt MATH Berlin [Germany]