Journal
APPLIED MATHEMATICS AND COMPUTATION
Volume 365, Issue -, Pages -Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.amc.2019.124608
Keywords
Nonlinear Volterra integral equation; Pseudo-spectral method; Convergence
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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. (C) 2019 Elsevier Inc. All rights reserved.
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