A Second-Order Accurate Numerical Approximation for a Two-Sided Space-Fractional Diffusion Equation

Taohua Liu, Xiucao Yin, Yinghao Chen and Muzhou Hou ()
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Taohua Liu: School of Science, Shaoyang University, Shaoyang 422000, China
Xiucao Yin: School of Science, Shaoyang University, Shaoyang 422000, China
Yinghao Chen: School of Mathematics and Statistics, Central South University, Changsha 410083, China
Muzhou Hou: School of Mathematics and Statistics, Central South University, Changsha 410083, China

Mathematics, 2023, vol. 11, issue 8, 1-15

Abstract: In this paper, we investigate a practical numerical method for solving a one-dimensional two-sided space-fractional diffusion equation with variable coefficients in a finite domain, which is based on the classical Crank-Nicolson (CN) method combined with Richardson extrapolation. Second-order exact numerical estimates in time and space are obtained. The unconditional stability and convergence of the method are tested. Two numerical examples are also presented and compared with the exact solution.

Keywords: variable coefficients; crank-nicolson method; stability and convergence; richardson extrapolation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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