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Öğe On the second-order neutral Volterra integro-differential equation and its numerical solution(Elsevier Science Inc, 2024) Amirali, Ilhame; Fedakar, Burcu; Amiraliyev, Gabil M.In this paper, we consider an initial-value problem for a second-order neutral Volterra integrodifferential 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.Öğe Second-order numerical method for a neutral Volterra integro-differential equation(Elsevier, 2025) Amirali, Ilhame; Fedakar, Burcu; Amiraliyev, Gabil M.This paper is dedicated to obtaining an approximate solution for a neutral second-order Volterra integro-differential equation. Our method is the second-order accurate finite difference scheme on a uniform mesh. The error analysis is carried out and numerical results are given to support the proposed approach.Öğe Stability analysis of neutral Volterra integro-differential equation(Ankara Üniversitesi, 2024) Fedakar, Burcu; Amirali, İlhameThe study establishes the stability bounds of the second-order neutral Volterra integro-differential equation concerning both the right-side and initial conditions. The examples are given to show the applicability of the method and confirm the predicted theoretical analysis.
