Browsing by Author "Amiraliyev, GM"

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The Convergence of a Finite Difference Method on Layer-Adapted Mesh for a Singularly Perturbed System
(Elsevier Science inc, 2005) Amiraliyev, GM
This paper is concerned with the numerical solution for singular perturbation system of two coupled ordinary differential equations with first and second orders and with initial and boundary conditions, respectively. Finite difference scheme on a special non-uniform mesh, whose solution converges pointwise independently of the singular perturbation parameter is constructed and analyzed. Numerical results supporting the theory are presented. (C) 2004 Elsevier Inc. All rights reserved.
A Finite Difference Method for the Singularly Perturbed Problem With Nonlocal Boundary Condition
(Elsevier Science inc, 2005) Cakir, M; Amiraliyev, GM
The purpose of this paper is to present a finite difference method for numerical solutions of singularly perturbed boundary value problem for second order ordinary differential equation with nonlocal boundary condition. By the method of integral identities with the use exponential basis functions and interpolating quadrature rules with the weight and remainder term in integral form an exponentially fitted difference scheme on an uniform mesh is developed which is shown to be original F-uniformly first order accurate in the discrete maximum norm for original problem. Numerical results are presented, which illustrate the theoretical results. (C) 2004 Elsevier Inc. All rights reserved.
A Note on a Parameterized Singular Perturbation Problem
(Elsevier Science Bv, 2005) Amiraliyev, GM; Duru, H
We consider a uniform finite difference method on Shishkin mesh for a quasilinear first-order singularly perturbed boundary value problem (BVP) depending on a parameter. We prove that the method is first-order convergent except for a logarithmic factor, in the discrete maximum norm, independently of the perturbation parameter. Numerical experiments support these theoretical results. (c) 2004 Elsevier B.V All rights reserved.
Numerical Solution of the Singularly Perturbed Problem With Nonlocal Boundary Condition
(Shanghai Univ, 2002) Amiraliyev, GM; Çakir, M
Singularly perturbed boundary value problem with nonlocal conditions is examined. The appopriate solution exhibits boundary layer behavior for small positive values of the perturbative parameter. An exponentially fitted finite difference scheme on a non-equidistant mesh is constructed for solving this problem. The uniform convergence analysis in small parameter is given. Numerical example is provided, too.
A Uniformly Convergent Difference Method for the Periodical Boundary Value Problem
(Pergamon-elsevier Science Ltd, 2003) Amiraliyev, GM; Duru, H
The periodical boundary value problem for linear second-order ordinary differential equation with small parameter by the first and second derivatives is considered. By the method of integral identities with the use of exponential basis functions and interpolating quadrature rules with weight and remainder term in integral form, an exponentially fitted difference scheme is constructed in a uniform mesh which gives first-order uniform convergence in the discrete maximum norm. Numerical experiments support these theoretical results. (C) 2003 Elsevier Ltd. All rights reserved.
A Uniformly Convergent Finite Difference Method for a Singularly Perturbed Initial Value Problem
(Shanghai Univ, 1999) Amiraliyev, GM; Duru, H
Initial value problem for linear second order ordinary differential equation with small parameter by the first and second derivatives is considered. An exponentially fitted difference scheme with constant fitting factors is developed in a uniform mesh, which gives first-order uniform convergence in the sense of discrete maximum norm. Numerical results are also presented.