Journal
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES INDIA SECTION A-PHYSICAL SCIENCES
Volume 92, Issue 4, Pages 605-623Publisher
NATL ACAD SCIENCES INDIA
DOI: 10.1007/s40010-022-00779-8
Keywords
Telegraph equation; Legendre wavelets; Operational matrices; Kronecker multiplications; Algebraic generalized Sylvester equation; BICGSTAB method
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Funding
- National Postdoctoral Fellowship from Science and Engineering Research Board, India [PDF/2019/001275]
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This paper presents the Legendre wavelet operational matrix method (LWOMM) for finding the numerical solution of two-dimensional hyperbolic telegraph equations (HTE), the proposed numerical scheme is accurate and efficient, validated through numerical experiments, convergence analysis of multidimensional Legendre wavelet approximation is investigated.
In this paper, we present the Legendre wavelet operational matrix method (LWOMM) to find the numerical solution of two-dimensional hyperbolic telegraph equations (HTE) with appropriate initial and boundary 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.
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