Optimal superconvergence results for Volterra functional integral equations with proportional vanishing delays

Wanyuan Ming, Chengming Huang and Longbin Zhao

Applied Mathematics and Computation, 2018, vol. 320, issue C, 292-301

Abstract: In this paper, we develop a new technique to study the optimal convergence orders of collocation methods for Volterra functional integral equations with vanishing delays on quasi-geometric meshes. Basing on a perturbation analysis, we show that for m collocation points, the global convergence order of the collocation solution is only m. However, the collocation solution may exhibit superconvergence with order m+1 at the collocation points. In particular, the local convergence order may attain 2m−1 at the nodes, provided that the collocation is based on the m Radau II points. Finally, some numerical examples are performed to verify our theoretical results.

Keywords: Volterra functional integral equations; Vanishing delays; Collocation methods; Quasi-geometric meshes; Perturbation analysis (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:320:y:2018:i:c:p:292-301

DOI: 10.1016/j.amc.2017.09.045

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