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**Numerical solution of hyperbolic telegraph equation using the Chebyshev tau method.**
*(English)*
Zbl 1186.65136

The authors give a numerical scheme to solve the one-dimensional hyperbolic telegraph equation. The approach consists of reducing the problem to a set of algebraic equations by expanding the approximate solution in terms of shifted Chebyshev polynomials with unknown coefficients. The operational matrices of the integral and the derivative are given and these matrices together with the tau method are then utilized to evaluate the unknown coefficients of shifted Chebyshev polynomials.

Reviewer: Nicolae Pop (Baia Mare)

### MSC:

65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |

35L05 | Wave equation |

### Keywords:

Chebyshev polynomials; hyperbolic equation; operational matrix; tau method; telegraph equation
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\textit{A. Saadatmandi} and \textit{M. Dehghan}, Numer. Methods Partial Differ. Equations 26, No. 1, 239--252 (2010; Zbl 1186.65136)

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