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Application of the singular boundary method to the two-dimensional telegraph equation on arbitrary domains. (English) Zbl 1436.65096

Summary: The singular boundary method (SBM) is employed to solve the two-dimensional telegraph equation on arbitrary domains. The Houbolt finite difference method is used to discretize the time derivatives. The original equations are then split into a system of partial differential equations, which is solved using the method of particular solution, in combination with the singular boundary method to obtain the homogeneous solution. Finally, three numerical examples are studied to demonstrate the accuracy and efficiency of the proposed method.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65N38 Boundary element methods for boundary value problems involving PDEs
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
65N80 Fundamental solutions, Green’s function methods, etc. for boundary value problems involving PDEs
35Q60 PDEs in connection with optics and electromagnetic theory
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