  The present article is devoted to developing the Legendre wavelet operational
matrix method (LWOMM) to find the numerical solution of two-dimensional
hyperbolic telegraph equations (HTE) with appropriate initial time boundary
space conditions. The Legendre wavelets series with unknown coefficients have
been used for approximating the solution in both of the spatial and temporal
variables. The basic idea for discretizing two-dimensional HTE is based on
differentiation and integration of operational matrices. By implementing LWOMM
on HTE, HTE is transformed into algebraic generalized Sylvester equation.
Numerical experiments are provided to illustrate the accuracy and efficiency of
the presented numerical scheme. Comparisons of numerical results associated
with the proposed method with some of the existing numerical methods confirm
that the method is easy, accurate and fast experimentally. Moreover, we have
investigated the convergence analysis of multidimensional Legendre wavelet
approximation. Finally, we have compared our result with the research article
of Mittal and Bhatia (see [1]).
