Fast and high-order difference schemes for the fourth-order fractional sub-diffusion equations with spatially variable coefficient under the first Dirichlet boundary conditions

Zhe Pu, Maohua Ran and Hong Luo

Mathematics and Computers in Simulation (MATCOM), 2021, vol. 187, issue C, 110-133

Abstract: In this paper, we focus on the numerical computation for a class of fourth-order fractional sub-diffusion equations with spatially variable coefficient under the first Dirichlet boundary conditions. Two finite difference schemes with second order accuracy are derived by applying L2−1σ formula and FL2−1σ formula respectively to approximate the time Caputo derivative. The main novelty is that a novel technique is introduced to deal with the first Dirichlet boundary conditions, which is compatible with the main equation with spatially variable coefficient. The solvability, unconditional stability and convergence of both schemes are proved by using the discrete energy method and mathematical induction. A difference scheme for such problem with two dimensions is also proposed and analyzed. Numerical results show that the suggested schemes have the almost same accuracy and the FL2−1σ scheme can reduce the storage and computational cost significantly.

Keywords: Variable coefficient; First Dirichlet boundary conditions; Caputo derivative; Fast calculation; Stability; Convergence (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475421000562
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:187:y:2021:i:c:p:110-133

DOI: 10.1016/j.matcom.2021.02.017

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().