Multistep collocation method for Fredholm integral equations of the second kind

Min Wang

Applied Mathematics and Computation, 2022, vol. 420, issue C

Abstract: In this paper a Multistep Collocation (MC) method for the second kind Fredholm integral equations (FIEs) is proposed and analyzed. The multistep collocation method is applied to FIE with smooth kernels under uniform mesh and weakly singular kernels |s−t|−α(0<α<1) using a graded mesh then the same convergence rate as collocation method but with a lower degree of freedom is obtained. Moreover, in order to avoid the round-off errors caused by graded mesh, a Hybrid Multistep Collocation (HMC) method by combining multistep collocation and hybrid collocation method is proposed. The HMC method converges faster with lower degrees of freedom and more efficiently captures the weakly singular properties by nonpolynomial interpolation at the first subinterval. The L∞-norm convergence results are analysed and proved. Numerical examples are presented to demonstrate the efficiency of the proposed methods.

Keywords: Fredholm integral equations; Multistep collocation; Hybrid multistep collocation; Weakly singular kernels; Fast algorithm (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S009630032100953X
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:420:y:2022:i:c:s009630032100953x

DOI: 10.1016/j.amc.2021.126870

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 ().