 Virtual element approximation and BDF2 time-discrete scheme for a partial integro-differential equation with a singular Abel's kernelMostafa Abbaszadeh, Mahmoud A. Zaky and Mehdi Dehghan Applied Mathematics and Computation, 2025, vol. 501, issue C Abstract: This work focuses on developing a virtual element framework for analyzing nonlinear partial integro-differential equations with singular Abel-type kernels. To address the singularity in the integral term, we propose two strategies: one based on linear interpolation over a uniform temporal mesh and another employing a graded mesh. Notably, while the uniform mesh fails to retain second-order temporal accuracy, the graded mesh successfully achieves it. For spatial discretization, we adopt the virtual element method and derive rigorous error estimates for the semi-discrete scheme. Nonlinear terms are approximated via a second-order temporal discretization. Following this, we establish a fully-discrete scheme. We rigorously establish the unconditional stability and convergence rates of the proposed method in separate theorems. Finally, we validate the theoretical results through numerical experiments on various domains. Keywords: Partial integro-differential equation; Abel's kernel; Virtual element approximation; Optimal error estimate; Convergence; Stability (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:501:y:2025:i:c:s009630032500178x DOI: 10.1016/j.amc.2025.129451 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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