A meshless method for numerical solution of a linear hyperbolic equation with variable coefficients in two space dimensions. (English) Zbl 1159.65084

Dehghan, Mehdi; Shokri, Ali

Numer. Methods Partial Differ. Equations 25, No. 2, 494-506 (2009).

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:

65M70	Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35L15	Initial value problems for second-order hyperbolic equations

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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