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Approximate Solution of Fractional Nonlinear Partial Differential Equations by the Legendre Multiwavelet Galerkin Method

Author

Listed:
  • M. A. Mohamed
  • M. Sh. Torky

Abstract

The Legendre multiwavelet Galerkin method is adopted to give the approximate solution for the nonlinear fractional partial differential equations (NFPDEs). The Legendre multiwavelet properties are presented. The main characteristic of this approach is using these properties together with the Galerkin method to reduce the NFPDEs to the solution of nonlinear system of algebraic equations. We presented the numerical results and a comparison with the exact solution in the cases when we have an exact solution to demonstrate the applicability and efficiency of the method. The fractional derivative is described in the Caputo sense.

Suggested Citation

  • M. A. Mohamed & M. Sh. Torky, 2014. "Approximate Solution of Fractional Nonlinear Partial Differential Equations by the Legendre Multiwavelet Galerkin Method," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:192519
    DOI: 10.1155/2014/192519
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    References listed on IDEAS

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    1. Khaled A. Gepreel & Taher A. Nofal & Fawziah M. Alotaibi, 2013. "Numerical Solutions for the Time and Space Fractional Nonlinear Partial Differential Equations," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-12, November.
    2. Yanqin Liu, 2012. "Approximate Solutions of Fractional Nonlinear Equations Using Homotopy Perturbation Transformation Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    3. Khaled A. Gepreel & Taher A. Nofal & Fawziah M. Alotaibi, 2013. "Numerical Solutions for the Time and Space Fractional Nonlinear Partial Differential Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    4. Yanqin Liu, 2012. "Approximate Solutions of Fractional Nonlinear Equations Using Homotopy Perturbation Transformation Method," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-14, April.
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