Amirali, Ilhame; Durmaz, Muhammet Enes; Amiraliyev, Gabil M.

In this paper, we propose a finite difference technique for approximating solutions of first-order Volterra delay integro-differential equation. The presented numerical method acquires a second-order convergence in discrete maximum norm. The derived results are numerically validated in test problems to support the theoretical analysis.

Amiraliyev, Gabil M.; Durmaz, Muhammet Enes; Kudu, Mustafa

The boundary-value problem for a second order singularly perturbed Fredholm integro-differential equation was considered in this paper. For the numerical solution of this problem, we use an exponentially fitted difference scheme on a uniform mesh which is succeeded by the method of integral identities with the use of exponential basis functions and interpolating quadrature rules with the weight and remainder terms in integral form. Also, the method is first order convergent in the discrete maximum norm. Numerical example shows that recommended method has a good approximation characteristic.

Kızıltuğ, Sezai; Önder, Mehmet; Yaylı, Yusuf

In this study, we define a new type of associated curves in the Euclidean 3-space such as normal-direction curve and normal-donor curve. We obtain characterizations for these curves. Moreover, we give applications of normal-direction curves to some special curves such as helix, slant helix, plane curve or normal-direction (ND)-normal curves in E3. And, we show that slant helices and rectifying curves can be constructed by using normal-direction curves.

Amiraliyev, Gabil M.; Yapman, Ömer

In this paper, we analyze the convergence of the fitted mesh method applied to singularly perturbed Volterra delay-integro-differential equation. Our mesh comprises a special nonuniform mesh on the first subinterval and uniform mesh on another part. Error estimates are obtained using difference analogue of Gronwall's inequality with delay. A numerical test that confirms the theoretical results is presented.

Alagoz, Osman; Gunduz, Birol; Akbulut, Sezgin

In this work, we consider an iterative method given by Karaca and Yildirim [6] to approximate fixed point of continuous mappings defined on an arbitrary interval. Then, we give a necessary and sufficient condition for convergence theorem. We also compare the rate of convergence between the other iteration methods. Finally, we provide a numerical example which supports our theoretical results. Our findings improve corresponding results in the contemporary literature.

Kudu, Mustafa; Amirali, Ilhame; 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.

Yağmur, Nihat; Orhan, Halit

Let be the sequence of partial sums of generalized and normalized Struve functions and F: = v+(d+2)/2≠0,-1,12.... The purpose of the present paper is to determine lower bounds for where Λ[fv,d,c] is the Alexander transform of fv,d,c.

Kiziltuğ, S.; Önder, M.

General definition of associated curves of a Frenet curve is given in a three dimensional compact Lie group G. The principal normal direction curve and principal normal donor curve are introduced and some characterizations for these curves are obtained in G. Later, the relationships between a principal normal direction curve and some special curves such as helix, slant helix or curve with a special torsion are obtained.

Gunduz, Birol; Akbulut, Sezgin

In this paper, we study strong convergence of an iteration process for a finite family of asymptotically quasi-nonexpansive mappings in convex metric spaces. We prove some strong convergence theorems for this iterative algorithm. Our results improve and extend the corresponding results of Kettapun et al.

Gunduz, Birol; Akbulut, Sezgin

In this paper, we prove some strong and δ-convergence theorems for two finite families of nonexpansive maps on a hyperbolic space. Our iterative scheme is independent and simpler than the Ishikawa type iteration process. Our results refine and generalize several recent and comparable results in uniformly convex Banach spaces as well as CAT(0) spaces.