On Filon methods for a class of Volterra integral equations with highly oscillatory Bessel kernels

Chunhua Fang, Junjie Ma and Meiying Xiang

Applied Mathematics and Computation, 2015, vol. 268, issue C, 783-792

Abstract: This paper focuses on the convergence of a class of collocation methods for Volterra integral equations of the second kind with highly oscillatory Bessel functions. Compared to existing theoretical results, sharper frequency-related convergence rates of these methods are established by exploring the asymptotic expansions of solutions and solving error equations. Theoretical results in this paper show the direct Filon method and continuous linear collocation method share the same convergence rate. Both of them admit a better convergence rate compared to the piecewise constant collocation method in solving Volterra integral equations with highly oscillatory Bessel kernels. These results are verified by numerical experiments.

Keywords: Volterra integral equation; Collocation method; Highly oscillatory integral; Convergence; Filon method (search for similar items in EconPapers)
Date: 2015
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300315008929
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:268:y:2015:i:c:p:783-792

DOI: 10.1016/j.amc.2015.06.111

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().