Browsing by Author "Cakir, M."

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Explicit Finite Difference Methods for the Delay Pseudoparabolic Equations
(Hindawi Publishing Corporation, 2014) Amirali, I.; Amiraliyev, G. M.; Cakir, M.; Cimen, E.
Finite difference technique is applied to numerical solution of the initial-boundary value problem for the semilinear delay Sobolev or pseudoparabolic equation. By the method of integral identities two-level difference scheme is constructed. For the time integration the implicit rule is being used. Based on the method of energy estimates the fully discrete scheme is shown to be absolutely stable and convergent of order two in space and of order one in time. The error estimates are obtained in the discrete norm. Some numerical results confirming the expected behavior of the method are shown.
An Innovative Technique for Solving Singularly Perturbed Problems With Integral Boundary Conditions on the Non-Uniform Mesh
(Prof. Dr. Mehmet Zeki Sarıkaya, 2025) Temel, Z.; Cakir, M.
We investigate an innovative numerical method for solving linear singularly perturbed problems with integral boundary conditions. Firstly, proving a uniformly convergent numerical method for solving the singularly perturbed problem is the main goal of this problem. Secondly, a piecewise equidistant mesh is used to generate the finite difference scheme. Next, the difference technique’s stability and convergence analysis are covered. Lastly, two test instances’ numerical results are shown. © 2025, Prof. Dr. Mehmet Zeki SARIKAYA. All rights reserved.
A Novel Numerical Approach for Fredholm Integro-Differential Equations
(Pleiades Publishing inc, 2022) Cakir, H. G.; Cakir, F.; Cakir, M.
We examine the numerical solution of a second-order linear Fredholm integro-differential equation (FIDE) by a finite difference method. The discretization of the problem is obtained by a finite difference method on a uniform mesh. We construct the method using the integral identity method with basis functions and dealing with the integral terms by interpolating quadrature rules with remainder terms. We further employ the factorization method to establish the algorithm. We demonstrate the error estimates and the convergence of the method. The numerical results are enclosed to verify the order of accuracy.
A Novel Numerical Approach for Solving Convection-Diffusion Problem With Boundary Layer Behavior
(Gazi Universitesi, 2020) Cakir, M.; Masiha, R.Y.; Arslan, D.
This study deals with a new approach method for solving singularly perturbed boundary value problem of convection-diffusion type. Firstly, bounds on the solution and its derivative of solution to be used later in the article are obtained. This robust method is constructed with fitted difference scheme on a uniform mesh. It is proved that the presented method is first-order convergent with respect to the perturbation parameter ε in the discrete maximum norm. Two examples are given to illustrate the efficiency of the method. The numerical results are presented in tables and figures. © 2020, Gazi University Eti Mahallesi. All rights reserved.
A Novel Uniform Numerical Approach To Solve a Singularly Perturbed Volterra Integro-Differential Equation
(Pleiades Publishing inc, 2023) Cakir, M.; Cimen, E.
In this paper, the initial value problem for the second order singularly perturbed Volterra integro-differential equation is considered. To solve this problem, a finite difference scheme is constructed, which based on the method of integral identities using interpolating quadrature rules with remainder terms in integral form. As a result of the error analysis, it is proved that the method is first-order convergent uniformly with respect to the perturbation parameter in the discrete maximum norm. Numerical experiments supporting the theoretical results are also presented.
Numerical Simulation for Singularly Perturbed Problem With Two Nonlocal Boundary Conditions
(Association of Mathematicians (MATDER), 2022) Arslan, D.; Cakir, M.
In this paper, numerical solution for singularly perturbed problem with nonlocal boundary conditions is obtained. Finite difference method is used to discretize this problem on the Bakhvalov-Shishkin mesh. The some properties of exact solution are analyzed. The error is obtained first-order in the discrete maximum norm. Finally, an example is solved to show the advantages of the finite difference method. © MatDer.
Numerical Solution of a Singularly Perturbed Three-Point Boundary Value Problem
(Taylor & Francis Ltd, 2007) Cakir, M.; Amiraliyev, G. M.
We consider a uniform finite difference method on an S-mesh (Shishkin type mesh) for a singularly perturbed semilinear one-dimensional convection-diffusion three-point boundary value problem with zeroth-order reduced equation. We show that the method is first-order convergent in the discrete maximum norm, independently of the perturbation parameter except for a logarithmic factor. An effective iterative algorithm for solving the non-linear difference problem and some numerical results are presented.
Synthesis, Characterization, Antioxidant Properties and Dft Calculation of Some New Pyrimidine Derivatives
(Taylor and Francis Ltd., 2019) Akbas, E.; Ergan, E.; Sahin, E.; Ekin, S.; Cakir, M.; Karakus, Y.
In this study, 5-benzoyl-4-(4-(methylthio)phenyl)-6-phenyl-1,2,3,4-tetrahydro-2-thioxo (1), oxo (2) and imino (3) pyrimidine derivatives were prepared via Multicomponent Cyclocondensation Reactions (MCRs). The compounds thiazolo[3,2-a]pyrimidin-3(5H)-one (4) and thiazin-4(6H)-one (5) were obtained via the reaction of compound 1 with bromoacetic acid and 3-bromopropionic acid, respectively. Structures were determined by using FT-IR, 1H/13C NMR and elemental analyses. Also the compounds 4 and 5 were analyzed by X-ray single crystal analysis. All compounds were investigated as corrosion inhibitors using density functional theory (DFT) at the level of B3LYP/6-31G (d, p). According to the calculations, the compound 3 appears to be a good inhibitor for corrosion. On the other hand, total antioxidant properties were measured in vitro by DPPH•, ABTS•+ test, hemolysis of phenylhydrazine erythrocytes and metal chelating effect. The results were compared with standard antioxidants such as trolox and α-tocopherol. These data revealed that compounds 1, 2 and 5 are more active with respect to 3 and 4 in scavenging the radicals. © 2018, © 2018 Taylor & Francis Group, LLC.