A Second-Order Uniformly Stable Explicit Asymmetric Discretization Method for One-Dimensional Fractional Diffusion Equations. (28th May 2019)

• Record Type: Journal Article
• Authors: Zhu, Lin
• Other Names: Martínez Eulalia Academic Editor.
• Is Part Of: Complexity. Volume 2019(2019)
• Publication Date: 2019-05-28
• Subjects: Chaotic behavior in systems -- Periodicals; Complexity (Philosophy) -- Periodicals; 003
• DOI: 10.1155/2019/4238420
• Languages: English
• ISSNs: 1076-2787

Abstract

Abstract : Using the asymmetric discretization technique, an explicit finite difference scheme is constructed for one-dimensional spatial fractional diffusion equations (FDEs). The spatial fractional derivative is approximated by the weighted and shifted Grünwald difference operator. The scheme can be solved explicitly by calculating unknowns in the different nodal-point sequences at the odd time-step and the even time-step. The uniform stability is proven and the error between the discrete solution and analytical solution is theoretically estimated. Numerical examples are given to verify theoretical analysis.