A new strategy for the numerical solution of nonlinear Volterra integral equations with vanishing delays

Zhang Xiao-yong

Applied Mathematics and Computation, 2020, vol. 365, issue C

Abstract: The aim of this paper is to develop a high-order algorithm for nonlinear Volterra integral equations with vanishing variable delays. The algorithm is a non-trivial extension of the single-step methods. This method is based on the variational form, so the algorithm is relatively simple. This scheme enjoys high order accuracy and can be implemented in a stable and efficient manner. We prove the existence and uniqueness of the numerical solution, and derive error estimates of the algorithm. Numerical results show a good agreement with the theoretical analysis.

Keywords: Nonlinear Volterra integral equation; Pseudo-spectral method; Convergence (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:365:y:2020:i:c:s0096300319306009

DOI: 10.1016/j.amc.2019.124608

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