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An Efficient Numerical Approach for Solving Nonlinear Coupled Hyperbolic Partial Differential Equations with Nonlocal Conditions

Author

Listed:
  • A. H. Bhrawy
  • M. A. Alghamdi
  • Eman S. Alaidarous

Abstract

One of the most important advantages of collocation method is the possibility of dealing with nonlinear partial differential equations (PDEs) as well as PDEs with variable coefficients. A numerical solution based on a Jacobi collocation method is extended to solve nonlinear coupled hyperbolic PDEs with variable coefficients subject to initial‐boundary nonlocal conservation conditions. This approach, based on Jacobi polynomials and Gauss‐Lobatto quadrature integration, reduces solving the nonlinear coupled hyperbolic PDEs with variable coefficients to a system of nonlinear ordinary differential equation which is far easier to solve. In fact, we deal with initial‐boundary coupled hyperbolic PDEs with variable coefficients as well as initial‐nonlocal conditions. Using triangular, soliton, and exponential‐triangular solutions as exact solutions, the obtained results show that the proposed numerical algorithm is efficient and very accurate.

Suggested Citation

  • A. H. Bhrawy & M. A. Alghamdi & Eman S. Alaidarous, 2014. "An Efficient Numerical Approach for Solving Nonlinear Coupled Hyperbolic Partial Differential Equations with Nonlocal Conditions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:295936
    DOI: 10.1155/2014/295936
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    References listed on IDEAS

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    1. D. Baleanu & A. H. Bhrawy & T. M. Taha, 2013. "Two Efficient Generalized Laguerre Spectral Algorithms for Fractional Initial Value Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. D. Baleanu & A. H. Bhrawy & T. M. Taha, 2013. "Two Efficient Generalized Laguerre Spectral Algorithms for Fractional Initial Value Problems," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-10, June.
    3. W. M. Abd-Elhameed & E. H. Doha & Y. H. Youssri, 2013. "New Wavelets Collocation Method for Solving Second-Order Multipoint Boundary Value Problems Using Chebyshev Polynomials of Third and Fourth Kinds," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, October.
    4. W. M. Abd-Elhameed & E. H. Doha & Y. H. Youssri, 2013. "New Wavelets Collocation Method for Solving Second‐Order Multipoint Boundary Value Problems Using Chebyshev Polynomials of Third and Fourth Kinds," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
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