 Collocation methods for Volterra functional integral equations with non-vanishing delaysWanyuan Ming and Chengming Huang Applied Mathematics and Computation, 2017, vol. 296, issue C, 198-214 Abstract: In this paper the existence, uniqueness, regularity properties, and in particular, the local representation of solutions for general Volterra functional integral equations with non-vanishing delays, are investigated. Based on the solution representation, we detailedly analyze the attainable (global and local) convergence order of (iterated) collocation solutions on θ-invariant meshes. It turns out that collocation at the m Gauss (-Legendre) points neither leads to the optimal global convergence order m+1, nor yields the local convergence order 2m on the whole interval, which is in sharp contrast to the case of the classical Volterra delay integral equations. However, if the collocation is based on the m Radau II points, the local superconvergence order 2m−1 will exhibit at all mesh points. Finally, some numerical experiments are performed to confirm our theoretical findings. Keywords: Volterra functional integral equations; Non-vanishing delays; Collocation methods; Optimal order of superconvergence; θ-invariant meshes (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:296:y:2017:i:c:p:198-214 DOI: 10.1016/j.amc.2016.10.021 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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