Fast ADI difference/compact difference schemes for the nonlocal evolution equation with weakly singular kernels in three dimensions

Leijie Qiao, Da Xu, Bo Tang and Jun Zhou

Mathematics and Computers in Simulation (MATCOM), 2022, vol. 194, issue C, 329-347

Abstract: We consider two kinds of efficient numerical methods to solve the three-dimensional evolution equation with weakly singular kernels. The proposed techniques are based on the finite difference/compact difference methods for the spatial discretization and an alternating direction implicit (ADI) algorithm for the time direction, combined with the second-order convolution quadrature (CQ) rule for the Riemann–Liouville (R-L) integral term and the classical L1 formula for the Caputo fractional derivative. The unconditional stability and convergence of the ADI finite difference scheme are proved rigorously. Numerical results are presented to support the theoretical analysis.

Keywords: Three-dimensional evolution equation; ADI difference/compact difference methods; Second-order convolution quadrature; Stability and convergence; Numerical simulation (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475421004390
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:194:y:2022:i:c:p:329-347

DOI: 10.1016/j.matcom.2021.12.005

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 ().