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

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  • Xiao-yong, Zhang

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.

Suggested Citation

  • Xiao-yong, Zhang, 2020. "A new strategy for the numerical solution of nonlinear Volterra integral equations with vanishing delays," Applied Mathematics and Computation, Elsevier, vol. 365(C).
    • Handle: RePEc:eee:apmaco:v:365:y:2020:i:c:s0096300319306009
    DOI: 10.1016/j.amc.2019.124608
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    Cited by:

    1. Vijai Kumar Pathak & Lakshmi Narayan Mishra, 2022. "Application of Fixed Point Theorem to Solvability for Non-Linear Fractional Hadamard Functional Integral Equations," Mathematics, MDPI, vol. 10(14), pages 1-16, July.

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