A high-order difference scheme for the fractional sub-diffusion equation. Issue 2 (1st February 2017)

• Record Type: Journal Article
• Authors: Hao, Zhao-peng; Lin, Guang; Sun, Zhi-zhong
• Is Part Of: International journal of computer mathematics. Volume 94:Issue 2(2017)
• Page Start: 405
• Page End: 426
• Publication Date: 2017-02-01
• Subjects: fractional derivative -- multi-term -- Lubich's operator -- difference scheme -- compact -- convergence; 35R11 -- 65M06 -- 65M12 -- 65M15; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2015.1109642
• Languages: English
• ISSNs: 0020-7160

Abstract

ABSTRACT: Based on the Lubich's high-order operators, a second-order temporal finite-difference method is considered for the fractional sub-diffusion equation. It has been proved that the finite-difference scheme is unconditionally stable and convergent in L 2 norm by the energy method in both one- and two-dimensional cases. The rate of convergence is order of two in temporal direction under the initial value satisfying some suitable conditions. Some numerical examples are given to confirm the theoretical results.