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Numerical solution of initial-boundary system of nonlinear hyperbolic equations

Author

Listed:
  • E. H. Doha

    (Cairo University)

  • A. H. Bhrawy

    (King Abdulaziz University
    Beni-Suef University)

  • M. A. Abdelkawy

    (Beni-Suef University)

  • R. M. Hafez

    (Modern Academy)

Abstract

In this article, we present a numerical approximation of the initial-boundary system of nonlinear hyperbolic equations based on spectral Jacobi-Gauss-Radau collocation (J-GR-C) method. A J-GR-C method in combination with the implicit Runge-Kutta scheme are employed to obtain a highly accurate approximation to the mentioned problem. J-GR-C method, based on Jacobi polynomials and Gauss-Radau quadrature integration, reduces solving the system of nonlinear hyperbolic equations to solve a system of nonlinear ordinary differential equations (SNODEs). In the examples given, numerical results by the J-GR-C method are compared with the exact solutions. In fact, by selecting relatively few J-GR-C points, we are able to get very accurate approximations. In this way, the results show that this method has a good accuracy and efficiency for solving coupled partial differential equations.

Suggested Citation

  • E. H. Doha & A. H. Bhrawy & M. A. Abdelkawy & R. M. Hafez, 2015. "Numerical solution of initial-boundary system of nonlinear hyperbolic equations," Indian Journal of Pure and Applied Mathematics, Springer, vol. 46(5), pages 647-668, October.
    • Handle: RePEc:spr:indpam:v:46:y:2015:i:5:d:10.1007_s13226-015-0152-5
    DOI: 10.1007/s13226-015-0152-5
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