Work

Besse relaxation difference scheme for a nonlinear integro-differential equation

Year: 2025

Type: article

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 [Formula: see text] 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.

Source: PLoS ONE

DOI: 10.1371/journal.pone.0327515

Authors: Xinya Peng, Leiwei Li, Jia Zhang

Institution: Central South University of Forestry and Technology

Language: English

Topic: Differential Equations and Numerical Methods

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,382

Funders: Department of Transportation of Hunan Province, Fundamental Research Funds for Central Universities of the Central South University