Yazar "Kudu, Mustafa" 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 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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    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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    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.