Besse relaxation difference scheme for a nonlinear integro-differential equation

Xinya Peng, Leiwei Li and Jia Zhang

PLOS ONE, 2025, vol. 20, issue 8, 1-23

Abstract: In this paper, Besse relaxation difference and compact difference scheme for a nonlinear integro-differential equation, which is crucial in modeling complex systems with memory and nonlocal effects, are proposed. A Besse relaxation difference scheme is developed by combining Besse relaxation time discretization with second-order spatial discretization, in which the Besse relaxation technique enhanced the accuracy and stability of dealing with nonlinear terms. To further improve spatial accuracy, a fourth-order compact finite difference approximation is used to construct the Besse relaxation compact difference scheme. To verify the effectiveness of the proposed Besse relaxation difference schemes, we have established the unconditional stability and optimal convergence of both methods in the discrete L2 norms. Numerical experiments demonstrate that these relaxation schemes attain the predicted convergence rates and high accuracy for smooth solutions, singular solutions, as well as featuring unbounded derivatives solutions.

Date: 2025
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0327515 (text/html)
https://journals.plos.org/plosone/article/file?id= ... 27515&type=printable (application/pdf)

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:plo:pone00:0327515

DOI: 10.1371/journal.pone.0327515

Access Statistics for this article

More articles in PLOS ONE from Public Library of Science
Bibliographic data for series maintained by plosone ().