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

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.

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
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