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The third kind Chebyshev wavelets collocation method for solving the time-fractional convection diffusion equations with variable coefficients

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  • Zhou, Fengying
  • Xu, Xiaoyong

Abstract

In this paper, a numerical method based on the third kind Chebyshev wavelets is proposed for solving a class of time-fractional convection diffusion equations with variable coefficients. The third kind Chebyshev wavelets operational matrices of the integer order integration and the fractional order integration are derived respectively. They are utilized to reduce the problem to a system of linear algebraic equations by combining the collocation method. The uniform convergence analysis and error estimation for the third kind Chebyshev wavelets expansion are investigated. Illustrative examples are given and the numerical results are presented to demonstrate the efficiency and accuracy of the proposed method.

Suggested Citation

  • Zhou, Fengying & Xu, Xiaoyong, 2016. "The third kind Chebyshev wavelets collocation method for solving the time-fractional convection diffusion equations with variable coefficients," Applied Mathematics and Computation, Elsevier, vol. 280(C), pages 11-29.
    • Handle: RePEc:eee:apmaco:v:280:y:2016:i:c:p:11-29
    DOI: 10.1016/j.amc.2016.01.029
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    Cited by:

    1. Dehestani, H. & Ordokhani, Y. & Razzaghi, M., 2018. "Fractional-order Legendre–Laguerre functions and their applications in fractional partial differential equations," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 433-453.
    2. Prakash, Amit & Kumar, Manoj & Baleanu, Dumitru, 2018. "A new iterative technique for a fractional model of nonlinear Zakharov–Kuznetsov equations via Sumudu transform," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 30-40.
    3. Faheem, Mo & Khan, Arshad & Raza, Akmal, 2022. "A high resolution Hermite wavelet technique for solving space–time-fractional partial differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 588-609.
    4. Ahmed Gamal Atta & Waleed Mohamed Abd-Elhameed & Galal Mahrous Moatimid & Youssri Hassan Youssri, 2022. "A Fast Galerkin Approach for Solving the Fractional Rayleigh–Stokes Problem via Sixth-Kind Chebyshev Polynomials," Mathematics, MDPI, vol. 10(11), pages 1-16, May.
    5. Hassani, Hossein & Naraghirad, Eskandar, 2019. "A new computational method based on optimization scheme for solving variable-order time fractional Burgers’ equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 162(C), pages 1-17.
    6. Wu, Longyuan & Zhai, Shuying, 2020. "A new high order ADI numerical difference formula for time-fractional convection-diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 387(C).
    7. Sweilam, Nasser Hassan & El-Sayed, Adel Abd Elaziz & Boulaaras, Salah, 2021. "Fractional-order advection-dispersion problem solution via the spectral collocation method and the non-standard finite difference technique," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).

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