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\begin{document}

\title{Multi-dimensional Legendre wavelet matrix approach for hyperbolic
telegraph equation with dirichlet boundary condition}



\author[1]{Vijay Patel}%
\author[1]{Dhirendra Bahuguna}%
\affil[1]{Indian Institute of Technology Kanpur}%


\vspace{-1em}



  
  \date{May 04, 2024}


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\begin{abstract}
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 has 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.%
\end{abstract}%



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