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Solving the third-kind Volterra integral equation via the boundary value technique: Lagrange polynomial versus fractional interpolation

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  • Chen, Hao
  • Ma, Junjie

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.

Suggested Citation

  • Chen, Hao & Ma, Junjie, 2022. "Solving the third-kind Volterra integral equation via the boundary value technique: Lagrange polynomial versus fractional interpolation," Applied Mathematics and Computation, Elsevier, vol. 414(C).
    • Handle: RePEc:eee:apmaco:v:414:y:2022:i:c:s0096300321007694
    DOI: 10.1016/j.amc.2021.126685
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    Cited by:

    1. Guo, Yuling & Xu, Xiaoyu & Wang, Zicheng & Wang, Zhongqing, 2024. "An hp-version Legendre collocation method for the third-kind VIEs with nonlinear vanishing delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 338-350.

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