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Öğe Numerical solutions for second-order neutral volterra integro-differential equations: Stability analysis and finite difference method(Elsevier, 2025) Fedakar, Burcu; Amirali, Ilhame; Durmaz, Muhammet Enes; Amiraliyev, Gabil M.This work deals with the initial-value problem for a second-order neutral Volterra integrodifferential equation. First, we give the stability inequality indicating 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. In support of theoretical results, numerical results are performed by employing the proposed numerical technique.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 A second-order finite difference method for fourth-order neutral Volterra integro-differential equation(Springer, 2025) Amirali, Ilhame; Fedakar, Burcu; Dag, Damla; Amiraliyev, Gabil M.This paper's objective is to introduce a numerical method for solving a neutral Volterra integro-differential equation that involves fourth- and second-order derivatives. First, the stability properties of exact solution are analyzed. To solve this problem numerically, on the uniform mesh, the finite difference method, including the composite trapezoidal rule for the integral part of the equation, is used. The method has been demonstrated to be second-order convergent in the discrete maximum norm. In order to verify the efficiency of the suggested method, two numerical examples are given.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 and numerical solution of fourth-order neutral Volterra integro-differential equation(Elsevier, 2026) Fedakar, Burcu; Amirali, Ilhame; Amiraliyev, Gabil M.In this paper, we study an initial-value problem for a fourth-order neutral Volterra integrodifferential equation. First, the properties of the exact solution are analysed. Next, the problem is solved numerically using the finite difference method containing the composite trapezoidal rule for the integral part of the equation. Error estimate for the approximate solution is carried out and second-order convergence is attained. In support of the idea, numerical examples are given.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.
