@article{Chen2025, 
author = {Jiwen Chen and Li-Bin Liu and Guangqing Long and Zaitang Huang},
title = {Convergence analysis of a second-order finite difference scheme on Shishkin-type meshes for a singularly perturbed Volterra integro-differential equation},
year = {2025},
journal = {Networks and Heterogeneous Media},
volume = {20},
number = {4},
pages = {1333-1345},
keywords = {Volterra integro-differential equation, singularly perturbed, Shishkin mesh, BDF2},
url = {https://www.sciopen.com/article/10.3934/nhm.2025057},
doi = {10.3934/nhm.2025057},
abstract = {In this paper, a novel second-order numerical method on a Shishkin mesh is constructed to solve a singularly perturbed Volterra integro-differential equation. The proposed numerical scheme employs a second-order backward differentiation formula (BDF2) for discretizing the first-order derivative term, while utilizing the trapezoidal rule to approximate the integral term. Specifically, at the grid transition point, a first-order finite difference approximation is implemented to handle the first-order derivative computation. Subsequently, comprehensive truncation error estimations and rigorous convergence analyses are systematically conducted. Finally, two numerical examples are performed to verify the theoretical findings.}
}