Yazar "Amiraliyev, Gabil M." seçeneğine göre listele

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    Analysis of Difference Approximations to Delay Pseudo-Parabolic Equations
    (Springer, 2016) Amiraliyev, Gabil M.; Kudu, Mustafa; Amirali, İlhame
    This work deals with the one-dimensional initial-boundary Sobolev or pseudo-parabolic problem with delay. For solving this problem numerically, we construct fourth-order difference-differential scheme and obtain the error estimate for its solution. Further, for the time variable, we use the appropriate Runge-Kutta method for the realization of our differential-difference problem. Numerical results supporting the theory are presented.
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    Convergence analysis of fitted numerical method for a singularly perturbed nonlinear Volterra integro-differential equation with delay
    (Elsevier Science Bv, 2019) Yapman, Ömer; Amiraliyev, Gabil M.; Amirali, İlhame
    In this paper, the initial value problem for a quasilinear singularly perturbed delay Volterra integro-differential equation was considered. By the method of integral identities with the use of exponential basis functions and interpolating quadrature rules with the weight and remainder term in integral form, a fitted difference scheme is constructed and analysed. It is shown that the method displays first order uniform convergence in perturbation parameter. Some numerical results are given to confirm the theoretical analysis. (C) 2019 Elsevier B.V. All rights reserved.
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    An efficient numerical method for a singularly perturbed Fredholm integro-differential equation with integral boundary condition
    (Springer Heidelberg, 2023) Durmaz, Muhammet Enes; Amirali, Ilhame; Amiraliyev, Gabil M.
    In this paper, a linear singularly perturbed Fredholm integro-differential initial value problem with integral condition is being considered. On a Shishkin-type mesh, a fitted finite difference approach is applied using a composite trapezoidal rule in both; in the integral part of equation and in the initial condition. The proposed technique acquires a uniform second-order convergence in respect to perturbation parameter. Further provided the numerical results to support the theoretical estimates.
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    A finite-difference method for a singularly perturbed delay integro-differential equation
    (Elsevier Science Bv, 2016) Kudu, Mustafa; Amirali, İlhame; Amiraliyev, Gabil M.
    We consider the singularly perturbed initial value problem for a linear first order Volterra integro-differential equation with delay. Our purpose is to construct and analyse a numerical method with uniform convergence in the perturbation parameter. The numerical solution of this problem is discretized using implicit difference rules for differential part and the composite numerical quadrature rules for integral part. On a layer adapted mesh error estimations for the approximate solution are established. Numerical examples supporting the theory are presented. (C) 2016 Elsevier B.V. All rights reserved.
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    A Fitted Second-Order Difference Method for a Parameterized Problem with Integral Boundary Condition Exhibiting Initial Layer
    (Springer Basel Ag, 2021) Kudu, Mustafa; Amirali, Ilhame; Amiraliyev, Gabil M.
    In this paper, the homogeneous type fitted difference scheme for solving singularly perturbed problem depending on a parameter with integral boundary condition is proposed. We prove that the method is O(N(-2)lnN) uniform convergent on Shishkin meshes. Numerical results are also presented.
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    High-order finite difference technique for delay pseudo-parabolic equations
    (Elsevier Science Bv, 2017) Amiraliyev, Gabil M.; Çimen, Erkan; Amirali, İlhame; Çakır, Musa
    One dimensional initial boundary delay pseudo-parabolic problem is being considered. To solve this problem numerically, we construct higher order difference method for approximation to the considered problem and obtain the error estimate for its solution. Based on the method of energy estimate the fully discrete scheme is shown to be convergent of order four in space and of order two in time. Numerical example is presented. (C) 2017 Elsevier B.V. All rights reserved.
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    Numerical solution of linear pseudo-parabolic equation with time delay using three layer difference method
    (Elsevier, 2024) Amirali, Ilhame; Amiraliyev, Gabil M.
    In this paper, we consider the one-dimensional initial-boundary problem for a pseudoparabolic equation with a time delay in the second spatial derivative. To solve this problem numerically, we construct a higher-order difference method and obtain the error estimate for its solution. Based on the method of energy estimates the fully discrete scheme is shown to be convergent of order four in space and of order two in time. Given numerical results illustrate the convergence and effectiveness of the numerical method. & COPY; 2023 Elsevier B.V. All rights reserved.
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    Numerical solution of singularly perturbed Fredholm integro-differential equations by homogeneous second order difference method
    (Elsevier, 2022) Durmaz, Muhammet Enes; Çakır, Musa; Amirali, Ilhame; Amiraliyev, Gabil M.
    This work presents a computational approximate to solve singularly perturbed Fredholm integro-differential equation with the reduced second type Fredholm equation. This problem is discretized by a finite difference approximate, which generates second-order uniformly convergent numerical approximations to the solution. Parameter-uniform approximations are generated using Shishkin type meshes. The performance of the numerical scheme is tested which supports the effectiveness of the technique. (c) 2022 Elsevier B.V. All rights reserved.
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    A numerical technique for solving nonlinear singularly perturbed Fredholm integro-differential equations
    (Elsevier, 2024) Panda, Abhilipsa; Mohapatra, Jugal; Amirali, Ilhame; Durmaz, Muhammet Enes; Amiraliyev, Gabil M.
    This study deals with two numerical schemes for solving a class of singularly perturbed nonlinear Fredholm integro-differential equations. The nonlinear terms are linearized using the quasi -linearization technique. On the layer adapted Shishkin mesh, the numerical solution is initially calculated using the finite difference scheme for the differential part and quadrature rule for the integral part. The method proves to be first -order convergent in the discrete maximum norm. Then, using a post -processing technique we significantly enhance the accuracy from first order to second order. Further, a hybrid scheme on the nonuniform mesh is also constructed and analyzed whose solution converges uniformly, independent of the perturbation parameter and directly gives second order accuracy. Parameter uniform error estimates are demonstrated and the theoretical results are validated through some numerical tests.
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    Numerical treatment of a quasilinear initial value problem with boundary layer
    (Taylor & Francis Ltd, 2016) Çakır, Musa; Çimen, Erkan; Amirali, İlhame; Amiraliyev, Gabil M.
    The paper deals with the singularly perturbed quasilinear initial value problem exhibiting initial layer. First the nature of solution of differential problem before presenting method for its numerical solution is discussed. The numerical solution of the problem is performed with the use of a finite-fitted difference scheme on an appropriate piecewise uniform mesh (Shishkin-type mesh). An error analysis shows that the method is first-order convergent except for a logarithmic factor, in the discrete maximum norm, independently of the perturbation parameter. Finally, numerical results supporting the theory are presented.
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    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.
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    A RESENT SURVEY ON NUMERICAL METHODS FOR SOLVING SINGULARLY PERTURBED PROBLEMS
    (Baku State Univ, Inst Applied Mathematics, 2018) Amirali, İlhame; Amiraliyev, Gabil M.
    …
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    A second-order numerical approximation of a singularly perturbed nonlinear Fredholm integro-differential equation
    (Elsevier, 2023) Durmaz, Muhammet Enes; Amirali, Ilhame; Mohapatra, Jugal; Amiraliyev, Gabil M.
    We consider a singularly perturbed problem for a nonlinear first-order Fredholm integrodifferential equation. Our aim is to build and analyze a numerical approach with uniform convergence in the epsilon-parameter. The numerical solution of problem is discretized utilizing interpolation quadrature formulas for the differential part and the composite rectangular rule for the integral part. Error estimations for the approximate solution are established. In support of the idea, numerical examples are provided.(c) 2023 IMACS. Published by Elsevier B.V. All rights reserved.
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    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.
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    Stability inequalities for the delay pseudo-parabolic equations
    (Academic Publications Ltd., 2019) Amirali, İlhame; Çatı, Seda; Amiraliyev, Gabil M.
    This paper deals with the initial-boundary value problem for linear pseudo-parabolic equation. Using the method of energy estimates the stability bounds obtained for the considered problem. Illustrative example is also presented. © 2019 Academic Publications.
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    Three layer difference method for linear pseudo-parabolic equation with delay
    (Elsevier, 2022) Amirali, Ilhame; Amiraliyev, Gabil M.
    This paper deals with the study a finite-difference approximation of the one dimensional initial-boundary value problem for a pseudo-parabolic equation containing time delay in second derivative. We propose three layer difference scheme and obtain the error estimates for its solution. Based on the method of energy estimates the fully discrete scheme is shown to be convergent of order four in space and order two in time. Numerical results are presented to illustrate the theoretical findings. (C) 2021 Elsevier B.V. All rights reserved.
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    UNIFORM NUMERICAL APPROXIMATION FOR PARAMETER DEPENDENT SINGULARLY PERTURBED PROBLEM WITH INTEGRAL BOUNDARY CONDITION
    (Univ Miskolc Inst Math, 2018) Kudu, Mustafa; Amirali, İlhame; Amiraliyev, Gabil M.
    In this paper, a parameter-uniform numerical method for a parameterized singularly perturbed ordinary differential equation containing integral boundary condition is studied. Asymptotic estimates on the solution and its derivatives are derived. A numerical algorithm based on upwind finite difference operator and an appropriate piecewise uniform mesh is constructed. Parameter-uniform error estimate for the numerical solution is established. Numerical results are presented, which illustrate the theoretical results.