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Lagrange’s operational approach for the approximate solution of two-dimensional hyperbolic telegraph equation subject to Dirichlet boundary conditions

Author

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  • Devi, Vinita
  • Maurya, Rahul Kumar
  • Singh, Somveer
  • Singh, Vineet Kumar

Abstract

The key purpose of this study is to present two schemes based on Lagrange polynomials to deal with the numerical solution of second order two-dimensional telegraph equation (TDTE) with the Dirichlet boundary conditions. First, we convert the main equation into partial integro-differential equations (PIDEs) with the help of initial and boundary conditions. The operational matrices of differentiation and integration are then used to transform the PIDEs into algebraic generalized Sylvester equation. We compared the results obtained by the proposed schemes with Bernoulli matrix method and B-spline differential quadrature method which shows that the proposed schemes are accurate for small number of basis functions.

Suggested Citation

  • Devi, Vinita & Maurya, Rahul Kumar & Singh, Somveer & Singh, Vineet Kumar, 2020. "Lagrange’s operational approach for the approximate solution of two-dimensional hyperbolic telegraph equation subject to Dirichlet boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 367(C).
    • Handle: RePEc:eee:apmaco:v:367:y:2020:i:c:s009630031930709x
    DOI: 10.1016/j.amc.2019.124717
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    References listed on IDEAS

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    1. Orsingher, Enzo, 1985. "Hyperbolic equations arising in random models," Stochastic Processes and their Applications, Elsevier, vol. 21(1), pages 93-106, December.
    2. Dehghan, Mehdi & Shirilord, Akbar, 2019. "A generalized modified Hermitian and skew-Hermitian splitting (GMHSS) method for solving complex Sylvester matrix equation," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 632-651.
    3. Singh, Somveer & Patel, Vijay Kumar & Singh, Vineet Kumar & Tohidi, Emran, 2017. "Numerical solution of nonlinear weakly singular partial integro-differential equation via operational matrices," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 310-321.
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