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Numerical Algorithms
Erschienen in: Numerical Algorithms 3/2021

27.04.2020 | Original Paper

Numerical correction of finite difference solution for two-dimensional space-fractional diffusion equations with boundary singularity

verfasst von: Zhaopeng Hao, Wanrong Cao, Shengyue Li

Erschienen in: Numerical Algorithms | Ausgabe 3/2021

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Abstract

In this paper, an efficient algorithm is presented by adopting the extrapolation technique to improve the accuracy of finite difference schemes for two-dimensional space-fractional diffusion equations with non-smooth solution. The popular fractional centered difference scheme is revisited and the stability and error estimation of numerical solution are given in maximum norm. Based on the analysis of leading singularity of exact solution for the underlying problem, the extrapolation technique and numerical correction method are exploited to enhance the accuracy and convergence rate of the computation. Two numerical examples are provided to validate the theoretical prediction and efficiency of the algorithm. It is shown that, by using the proposed algorithm, both accuracy and convergence rate of numerical solutions can be significantly improved and the second-order accuracy can even be recovered for the equations with large fractional orders.
Vorheriger Artikel Convergence and dynamics of improved Chebyshev-Secant-type methods for non differentiable operators
Nächster Artikel Jacobi spectral approximation for boundary value problems of nonlinear fractional pantograph differential equations

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Metadaten
Titel
Numerical correction of finite difference solution for two-dimensional space-fractional diffusion equations with boundary singularity
verfasst von
Zhaopeng Hao
Wanrong Cao
Shengyue Li
Publikationsdatum
27.04.2020
Verlag
Springer US
Erschienen in
Numerical Algorithms / Ausgabe 3/2021
Print ISSN: 1017-1398
Elektronische ISSN: 1572-9265
DOI
https://doi.org/10.1007/s11075-020-00923-8

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