 Solving the third-kind Volterra integral equation via the boundary value technique: Lagrange polynomial versus fractional interpolationHao Chen and Junjie Ma Applied Mathematics and Computation, 2022, vol. 414, issue C Abstract: The solution to the third-kind Volterra integral equation (VIE3) usually has unbounded derivatives near the original point t=0, which brings difficulties to numerical computation. In this paper, we analyze two kinds of modified multistep collocation methods for VIE3: collocation boundary value method with the fractional interpolation (FCBVM) and that with Lagrange interpolation (CBVMG). The former is developed based on the non-polynomial interpolation which is particularly feasible for approximating functions in the form of tη with the real number η≥0. The latter is devised by using classical polynomial interpolation. The application of the boundary value technique enables both approaches to efficiently solve long-time integration problems. Moreover, we investigate the convergence properties of these two kinds of algorithms by Grönwall’s inequality. Keywords: Fractional interpolation; Graded mesh; Collocation boundary value technique; Weakly singular; The third-kind Volterra integral equation (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:414:y:2022:i:c:s0096300321007694 DOI: 10.1016/j.amc.2021.126685 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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