Abstract
This paper develops a numerical method for approximating the space fractional diffusion equation in Caputo derivative sense. In this discretization process, firstly, the compact finite difference with convergence order \({\mathcal {O}}(\delta \tau ^{2})\) is used to obtain the semi-discrete in time derivative. Afterward, the spatial fractional derivative is discretized by using the Chebyshev collocation method of the third-kind. This collocation scheme is based on the operational matrix. In addition, time-discrete stability and convergence are theoretically proved in detail. We solve two examples by the proposed method and the obtained results are compared with other numerical methods. The numerical results show that our method is much more accurate than existing methods.
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Communicated by Agnieszka Malinowska.
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Safdari, H., Mesgarani, H., Javidi, M. et al. Convergence analysis of the space fractional-order diffusion equation based on the compact finite difference scheme. Comp. Appl. Math. 39, 62 (2020). https://doi.org/10.1007/s40314-020-1078-z
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DOI: https://doi.org/10.1007/s40314-020-1078-z
Keywords
- The space fractional-order diffusion equation
- The compact finite difference
- The Chebyshev collocation method
- Convergence
- Stability