Browsing by Author "Duru, H"

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Difference Schemes for the Singularly Perturbed Sobolev Periodic Boundary Problem
(Elsevier Science inc, 2004) Duru, H
A finite-difference method is suggested and analyzed for evolution equations of Sobolev type in a single space variable and with boundary layers. The convergence and error estimates for an exponentially fitted difference scheme in an equidistant mesh are obtained. The numerical methods discussed here are extremely robust; in the sense that they have good convergence properties not only for small values of the perturbation parameter, but also for moderate and large values. (C) 2003 Elsevier Inc. All rights reserved.
The Hardy-Littlewood Inequality for (Β, Γ)-Distance Riesz Potentials
(Elsevier Science inc, 2004) Çinar, I; Duru, H
The generalized with respect to (beta, gamma)-distance Riesz potential defined on Sobolev space W-p(l)(R-n) is constructed and for this potential the theorem of Hardy-Littlewood-Sobolev type has been established. (C) 2003 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.
On Continuity Properties of Potentials Depending on Λ-Distance
(Elsevier Science inc, 2003) Cinar, I; Duru, H
This study establishes the theorem on continuity of generalized Riesz potentials with non-isotrop kernels depending on lambda-distance. (C) 2002 Elsevier Science Inc. All rights reserved.
Some Specialties of the Solutions of the Differential Equations in Banach Space
(Elsevier Science inc, 2004) Duru, H; Gulle, A
In this paper we investigate the existence and uniqueness of solution of differential equation in Banach space under condition (1.2). The theorems which we proved had been investigated at first in the papers [Canada, Math. Bull. 2(1) (1959); Canada, Math. Bull. 1(1) (1958); Y.D. Mamedov, The Convergence of Iterations for Differential Equations in Banach Spaces, in: Convergent Methods of Ordinary Differential Equations, Naukova Dumka, Kiev, 1964 (Russian)] by other methods for special case. (C) 2003 Elsevier Inc. All rights reserved.
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.