On the second-order neutral Volterra integro-differential equation and its numerical solution

Ilhame Amirali, Burcu Fedakar and Gabil M. Amiraliyev

Applied Mathematics and Computation, 2024, vol. 476, issue C

Abstract: In this paper, we consider an initial-value problem for a second-order neutral Volterra integro-differential equation. First, we give the stability inequality indicating the stability of the problem with respect to the right-side and initial conditions. Further, we develop a finite difference method that uses for differential part second difference derivative, for the integral part appropriate composite trapezoidal and midpoint rectangle rules followed by second-order accurate difference quantities at intermediate points. Error estimate for the approximate solution is established, which shows the second-order accuracy. Finally, the numerical experiments are presented confirming the accuracy of the proposed scheme.

Keywords: Neutal Volterra integro-differential equation; Stability bound; Difference scheme; Error analysis (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:476:y:2024:i:c:s0096300324002339

DOI: 10.1016/j.amc.2024.128765

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