An Efficient Second-Order Convergent Scheme for One-Side Space Fractional Diffusion Equations with Variable Coefficients

• 作者: Hai-Wei Sun Michael KNg Pin Lyu Seakweng Vong Xue-lei Lin
• 来源期刊: 应用数学与计算数学学报(英文)
• 学科: 数学
• 关键词: One-side space fractional difusion equation Variable difusion coefcients Stability and convergence High-order fnite-diference scheme PRECONDITIONER
• 年，卷（期）: 2020,（2）
• 页码范围: 215-239
• 页数: 25页
• 分类号: O17

摘要

In this paper,a second-order fnite-diference scheme is investigated for time-dependent space fractional difusion equations with variable coefcients.In the presented scheme,the Crank-Nicolson temporal discretization and a second-order weighted-and-shifted Grünwald-Letnikov spatial discretization are employed.Theoretically,the unconditional stability and the second-order convergence in time and space of the proposed scheme are established under some conditions on the variable coefcients.Moreover,a Toeplitz preconditioner is proposed for linear systems arising from the proposed scheme.The condition number of the preconditioned matrix is proven to be bounded by a constant independent of the discretization step-sizes,so that the Krylov subspace solver for the preconditioned linear systems converges linearly.Numerical results are reported to show the convergence rate and the efciency of the proposed scheme.