L1 scheme on graded mesh for subdiffusion equation with nonlocal diffusion term

Sudhakar Chaudhary and Pari J. Kundaliya

Mathematics and Computers in Simulation (MATCOM), 2022, vol. 195, issue C, 119-137

Abstract: The solution of time fractional partial differential equations in general exhibit a weak singularity near the initial time. In this article we propose a method for solving time fractional diffusion equation with nonlocal diffusion term. The proposed method comprises L1 scheme on graded mesh, finite element method and Newton’s method. We discuss the well-posedness of the weak formulation at discrete level and derive a priori error estimates for fully-discrete formulation in L2(Ω) and H1(Ω) norms. Finally, some numerical experiments are conducted to validate the theoretical findings.

Keywords: Nonlocal problem; Initial singularity; L1 scheme; Graded mesh; Error estimate (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475422000064
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:195:y:2022:i:c:p:119-137

DOI: 10.1016/j.matcom.2022.01.006

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 ().