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A shifted Jacobi collocation algorithm for wave type equations with non-local conservation conditions

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Central European Journal of Physics

Abstract

In this paper, we propose an efficient spectral collocation algorithm to solve numerically wave type equations subject to initial, boundary and non-local conservation conditions. The shifted Jacobi pseudospectral approximation is investigated for the discretization of the spatial variable of such equations. It possesses spectral accuracy in the spatial variable. The shifted Jacobi-Gauss-Lobatto (SJ-GL) quadrature rule is established for treating the non-local conservation conditions, and then the problem with its initial and non-local boundary conditions are reduced to a system of second-order ordinary differential equations in temporal variable. This system is solved by two-stage forth-order A-stable implicit RK scheme. Five numerical examples with comparisons are given. The computational results demonstrate that the proposed algorithm is more accurate than finite difference method, method of lines and spline collocation approach

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt

    Eid H. Doha

  2. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

    Ali H. Bhrawy

  3. Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt

    Ali H. Bhrawy & Mohammed A. Abdelkawy

Authors
  1. Eid H. Doha
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  2. Ali H. Bhrawy
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  3. Mohammed A. Abdelkawy
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Correspondence to Ali H. Bhrawy.

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Doha, E.H., Bhrawy, A.H. & Abdelkawy, M.A. A shifted Jacobi collocation algorithm for wave type equations with non-local conservation conditions. centr.eur.j.phys. 12, 637–653 (2014). https://doi.org/10.2478/s11534-014-0493-4

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  • DOI: https://doi.org/10.2478/s11534-014-0493-4

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