High order difference schemes for a time fractional differential equation with Neumann boundary conditions

2013/11/22 by Seakweng Vong, Zhibo Wang, Vong, Seakweng +1
Mathematics · #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1311.5641

openalex publication_date 2013/11/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Based on our recent results, in this paper, a compact finite difference scheme is derived for a time fractional differential equation subject to the Neumann boundary conditions. The proposed scheme is second order accurate in time and fourth order accurate in space. In addition, a high order alternating direction implicit (ADI) scheme is also constructed for the two-dimensional case. Stability and convergence of the schemes are analyzed using their matrix forms.

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