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**Legendre multiwavelet Galerkin method for solving the hyperbolic telegraph equation.**
*(English)*
Zbl 1189.65231

Summary: Recently, it is found that telegraph equation is more suitable than ordinary diffusion equation in modeling reaction diffusion for such branches of sciences. In this article a numerical method for solving the one-dimensional hyperbolic telegraph equation is presented. The method is based upon Legendre multiwavelet approximations. The properties of Legendre multiwavelet are first presented. These properties together with the Galerkin method are then utilized to reduce the telegraph equation to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

### MSC:

65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |

35L15 | Initial value problems for second-order hyperbolic equations |

65T60 | Numerical methods for wavelets |

### Keywords:

Galerkin method; Legendre multiwavelet; second-order hyperbolic telegraph equation; numerical examples
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\textit{S. A. Yousefi}, Numer. Methods Partial Differ. Equations 26, No. 3, 535--543 (2010; Zbl 1189.65231)

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