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Öğe Finite Difference Method for Advanced Volterra Integro-Differential Equation with Delay(Pleiades Publishing Ltd, 2025) Acar, H.; Amirali, I.; Durmaz, M. E.; Amiraliyev, G. M.The aim of this paper is to introduce a numerical method for advanced Volterra delay integro-differential equation with initial condition. A finite difference scheme on a uniform mesh using the trapezoidal formula is developed to numerically solve this problem. Additionally, demonstrated that this approach yields second-order convergence in the discrete maximum norm. The proposed method is validated through the presentation of numerical results.Öğe First-order numerical method for the singularly perturbed nonlinear Fredholm integro-differential equation with integral boundary condition(Institute of Physics, 2023) Amirali, I.; Durmaz, M.E.; Acar, H.; Amiraliyev, G.M.In this work, we consider first-order singularly perturbed quasilinear Fredholm integro-differential equation with integral boundary condition. Building a numerical strategy with uniform ?-parameter convergence is our goal. With the use of exponential basis functions, quadrature interpolation rules and the method of integral identities, a fitted difference scheme is constructed and examined. The weight and remainder term are both expressed in integral form. It is shown that the method exhibits uniform first-order convergence of the perturbation parameter. Error estimates for the approximation solution are established and a numerical example is given to validate the theoretical findings. © Published under licence by IOP Publishing Ltd.Öğe A Monotone Type Second-Order Numerical Method for Volterra-Fredholm Integro-Differential Equation(Pleiades Publishing Ltd, 2025) Amirali, I.; Fedakar, B.; Amiraliyev, G. M.The aim of this study is to present a monotone type second-order numerical method for solving Volterra-Fredholm integro-differential equation. To solve numerically this problem we construct a finite difference scheme on a uniform mesh using composite trapezoidal rule. Also, numerical results are given to support the proposed approach.Öğe A second order accurate method for a parameterized singularly perturbed problem with integral boundary condition(Elsevier B.V., 2022) Kudu, M.; Amirali, I.; Amiraliyev, G. M.In this paper, we consider a class of parameterized singularly perturbed problems with integral boundary condition. A finite difference scheme of hybrid type with an appropriate Shishkin mesh is suggested to solve the problem. We prove that the method is of almost second order convergent in the discrete maximum norm. Numerical results are presented, which illustrate the theoretical results. © 2021 Elsevier B.V.
