Fall 2020 Smoothing transformation and collocation methods for third-kind linear Volterra integral equations
Xiaoli Xu, Yu Xiao, Hui Ming Song
J. Integral Equations Applications 32(3): 361-375 (Fall 2020). DOI: 10.1216/jie.2020.32.361


In 2016, Sonia et al. first considered the convergence order for the third-kind linear Volterra integral equations (VIEs) based on the assumption that solutions are smooth. For the third-kind linear VIEs with nonsmooth solutions, we construct high-order numerical algorithms and discuss the convergence order. By introducing a new suitable independent variable, we obtain a transformed equation with a smooth exact solution. Then the solvability of the transformed equation is investigated on the basis of piecewise polynomial collocation methods. Meanwhile, the convergence order of the collocation solution is given. Furthermore, based on the inverse transformation, we get the convergence order of the original equation. Numerical simulations are finally presented to demonstrate the effectiveness of the theoretical results.


Download Citation

Xiaoli Xu. Yu Xiao. Hui Ming Song. "Smoothing transformation and collocation methods for third-kind linear Volterra integral equations." J. Integral Equations Applications 32 (3) 361 - 375, Fall 2020. https://doi.org/10.1216/jie.2020.32.361


Received: 13 May 2019; Revised: 30 June 2019; Accepted: 25 July 2019; Published: Fall 2020
First available in Project Euclid: 17 September 2020

zbMATH: 07283062
MathSciNet: MR4150705
Digital Object Identifier: 10.1216/jie.2020.32.361

Primary: 45A05 , 45D05

Keywords: convergence order , piecewise polynomial collocation methods , Smoothing transformation , solvability , third-kind linear VIEs

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium


This article is only available to subscribers.
It is not available for individual sale.

Vol.32 • No. 3 • Fall 2020
Back to Top