Yazar "Amirali, İlhame" 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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    ANALYSIS OF HIGHER ORDER DIFFERENCE METHOD FOR A PSEUDO-PARABOLIC EQUATION WITH DELAY
    (Univ Miskolc Inst Math, 2019) Amirali, İlhame
    In this paper, the author considers the one dimensional initial-boundary problem for a pseudo-parabolic equation with time delay in second spatial derivative. To solve this problem numerically, the author constructs 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. Some numerical examples illustrate the convergence and effectiveness of the numerical method.
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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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    Convergence analysis of the numerical method for a singularly perturbed periodical boundary value problem
    (Journal Mathematics & Computer Science-Jmcs, 2016) Çakır, Musa; Amirali, İlhame; Kudu, Mustafa; Amiraliyev, Gabli M.
    This work deals with the singularly perturbed periodical boundary value problem for a quasilinear second-order differential equation. The numerical method is constructed on piecewise uniform Shishkin type mesh, which gives first-order uniform convergence in the discrete maximum norm. Numerical results supporting the theory are presented. (C) 2016 All rights reserved.
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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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    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 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.
  • Küçük Resim Yok
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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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  • Küçük Resim Yok
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    Stability analysis of neutral Volterra integro-differential equation
    (Ankara Üniversitesi, 2024) Fedakar, Burcu; Amirali, İlhame
    The 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.
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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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    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.