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Analysis of a Numerical Method for the Solution of Time Fractional Burgers Equation

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Abstract

Due to the nonlinearity and fractional order of equation, there are a few efficient numerical methods in the literature with stability and convergence analysis for the solution of nonlinear time fractional partial differential equations. The aim of this paper is to construct and analyze an efficient numerical method for the solution of time fractional Burgers equation. The proposed method is based on a finite difference scheme in time and the Chebyshev spectral collocation method in space. We discuss the stability and convergence of the proposed method and show that the method is unconditionally stable and convergent with order \({\mathcal {O}}(\tau ^2+N^{-s})\) where \(\tau \), N, and s are time step size, number of collocation points, and regularity of exact solution, respectively. The numerical results are reported in terms of accuracy, computational order, and CPU time to confirm the efficiency of proposed method. It is illustrated that the numerical results are in good agreement with the theoretical ones.

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematical Science, University of Kashan, Kashan, Iran

    Akbar Mohebbi

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  1. Akbar Mohebbi
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Mohebbi, A. Analysis of a Numerical Method for the Solution of Time Fractional Burgers Equation. Bull. Iran. Math. Soc. 44, 457–480 (2018). https://doi.org/10.1007/s41980-018-0031-z

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