A numerical algorithm for the solution of telegraph equations. (English) Zbl 1132.65087

El-Azab, M. S.; El-Gamel, Mohamed

Appl. Math. Comput. 190, No. 1, 757-764 (2007).

The paper describes a numerical approximation for the nonlinear telegraph equation, a second-order hyperbolic partial differential equation. The scheme uses Rothe’s method for time discretization, and a Galerkin method with scaling functions as test and trial functions for space discretization. Compactly supported Daubechies scaling functions are used. The corresponding connection coefficients are computed to evaluate the nonlinear terms in coefficient space and error estimates are given. Finally numerical results are presented in one space dimension using Daubechies scaling functions of order 6.

Reviewer: Kai Schneider (Marseille)

MSC:

65M20	Method of lines for initial value and initial-boundary value problems involving PDEs
65M60	Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65T60	Numerical methods for wavelets
35L70	Second-order nonlinear hyperbolic equations
65M15	Error bounds for initial value and initial-boundary value problems involving PDEs

Keywords:

wavelet; Rothe’s method; nonlinear telegraph equation; Galerkin method; Daubechies scaling functions; error estimates; numerical results

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