Finite difference scheme with spatial fourth-order accuracy for a class of time fractional parabolic equations with variable coefficient

Advances in Difference Equations

Fanwei Meng¹  Qinghua Feng² 

[1] School of Mathematical Sciences, Qufu Normal University, Qufu, China;School of Science, Shandong University of Technology, Zibo, China

关键词: time fractional parabolic equation;    variable coefficient;    high-order difference scheme;    unconditional stability;   

DOI  :  10.1186/s13662-016-1035-8

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we establish a finite difference scheme for a class of time fractional parabolic equations with variable coefficient, where the time fractional derivative is defined in the sense of the Caputo derivative. The local truncating error, unique solvability, stability, and convergence for the present scheme are discussed by use of the Fourier analysis method, which shows that the present finite difference scheme is unconditionally stable and possesses spatial fourth-order accuracy. Theoretical analysis is supported by two numerical examples, and the maximum errors and the convergence order are checked.

【 授权许可】

CC BY