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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:
65M60Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE)
35L15Second order hyperbolic equations, initial value problems
65T60Wavelets (numerical methods)