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Second kind shifted Chebyshev polynomials for solving space fractional order diffusion equation

Author

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  • Sweilam, N.H.
  • Nagy, A.M.
  • El-Sayed, Adel A.

Abstract

In this paper, an efficient numerical method for solving space fractional order diffusion equation is presented. The numerical approach is based on shifted Chebyshev polynomials of the second kind where the fractional derivatives are expressed in terms of Caputo type. Space fractional order diffusion equation is reduced to a system of ordinary differential equations using the properties of shifted Chebyshev polynomials of the second kind together with Chebyshev collocation method. The finite difference method is used to solve this system of equations. Several numerical examples are provided to confirm the reliability and effectiveness of the proposed method.

Suggested Citation

  • Sweilam, N.H. & Nagy, A.M. & El-Sayed, Adel A., 2015. "Second kind shifted Chebyshev polynomials for solving space fractional order diffusion equation," Chaos, Solitons & Fractals, Elsevier, vol. 73(C), pages 141-147.
    • Handle: RePEc:eee:chsofr:v:73:y:2015:i:c:p:141-147
    DOI: 10.1016/j.chaos.2015.01.010
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    Cited by:

    1. Sweilam, Nasser H. & Abou Hasan, Muner M. & Baleanu, Dumitru, 2017. "New studies for general fractional financial models of awareness and trial advertising decisions," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 772-784.
    2. Nagy, A.M., 2017. "Numerical solution of time fractional nonlinear Klein–Gordon equation using Sinc–Chebyshev collocation method," Applied Mathematics and Computation, Elsevier, vol. 310(C), pages 139-148.
    3. Kheybari, Samad & Darvishi, Mohammad Taghi & Hashemi, Mir Sajjad, 2019. "Numerical simulation for the space-fractional diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 57-69.
    4. H. Çerdik Yaslan, 2021. "Numerical solution of the nonlinear conformable space–time fractional partial differential equations," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(2), pages 407-419, June.
    5. Agarwal, P. & El-Sayed, A.A., 2018. "Non-standard finite difference and Chebyshev collocation methods for solving fractional diffusion equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 500(C), pages 40-49.

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