Stability and convergence of 3-point WSGD schemes for two-sided space fractional advection-diffusion equations with variable coefficients
Stability and convergence of 3-point WSGD schemes for two-sided space fractional advection-diffusion equations with variable coefficients
复制标题
变系数两侧空间分数平流扩散方程3点WSGD格式的稳定性和收敛性
DOI：
10.1016/j.apnum.2021.05.007
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发表时间：
2021
影响因子：
2.8
通讯作者：
She Zihang
中科院分区：
文献类型：
--
作者：
Lin Fu-Rong;She Zihang
In this paper, we consider high order numerical methods for the solution of the initial-boundary value problem of two-sided space fractional advection-diffusion equations (SFADEs). We use the Crank-Nicolson (CN) technique to discretize the temporal derivative, and apply 3-point weighted and shifted Grünwald difference (WSGD) operators to discretize the fractional derivatives of order α∈(1, 2) and fractional derivatives of order β∈(0, 1), respectively. As a result, a new family of CN-WSGD schemes for SFADEs with temporally 2nd order and spatially jth order (j≥ 2) accuracy are obtained. We then analyse the stability and the convergence of the numerical schemes. The extrapolated WSGD (EWSGD) operators are also discussed. Numerical examples are implemented to verify the theoretical results.
