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    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.
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    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.