Ersoy Özdek, Demet
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Özdek, D. Ersoy
Ozdek, Demet Ersoy
Özdek, Demet
Ozdek, Demet
Ozdek, D
Ersoy Ozdek, Demet
Ozdek, D. Ersoy
Ozdek, Demet Ersoy
Özdek, Demet
Ozdek, Demet
Ozdek, D
Ersoy Ozdek, Demet
Ozdek, D. Ersoy
Job Title
Email Address
demet.ersoy@ieu.edu.tr
Main Affiliation
02.02. Mathematics
Status
Current Staff
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ORCID ID
Scopus Author ID
Turkish CoHE Profile ID
Google Scholar ID
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Sustainable Development Goals
SDG data is not available
Documents
9
Citations
53
h-index
4
Documents
9
Citations
44
Scholarly Output
10
Articles
10
Views / Downloads
26/37
Supervised MSc Theses
0
Supervised PhD Theses
0
WoS Citation Count
38
Scopus Citation Count
47
WoS h-index
3
Scopus h-index
4
Patents
0
Projects
0
WoS Citations per Publication
3.80
Scopus Citations per Publication
4.70
Open Access Source
3
Supervised Theses
0
| Journal | Count |
|---|---|
| Cmc-Computers Materıals & Contınua | 1 |
| Gazi Mühendislik Bilimleri Dergisi | 1 |
| Internatıonal Journal of Computatıonal Methods | 1 |
| Internatıonal Journal of Computer Mathematıcs | 1 |
| Journal of Applied Mathematics and Computing | 1 |
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10 results
Scholarly Output Search Results
Now showing 1 - 10 of 10
Article Chebyshev Polynomial Solution for the Sir Model of Covid 19(2023) Özdek, DemetIn this study, we deal with solving numerically initial value problem of a mathematical model of COVID-19 pandemic in Turkey. This model is a SIR model consisting of a nonlinear system of differential equations. In order to solve these equations, a collocation approach based on the Chebyshev polynomials is used. Chebyshev polynomials are orthonormal polynomials and the orthonormality reduces the computation cost of the method as an advantage. Another advantage is that the present method does not require any discretization of the domain. So the method is easy to implement. The main idea of the method is to convert the model to a system of nonlinear algebraic equations. For this we write the approximate solution of the system and its first derivative as the truncated series of Chebyshev polynomials with unknown coefficients in matrix forms and then utilizing the collocation points, the SIR model is converted to a system of the nonlinear equations. The obtained system is solved for the unknown coefficients of the assumed Chebyshev polynomial solution by MATLAB, and so the approximate solution is obtained. In order to check the robustness of the method, residual error of the solution is reviewed. The results show that the method is efficient and accurate.Article Citation - WoS: 1Citation - Scopus: 1Investigating the Impact of the Parameters on the Model of HIV Infection Including a Cure Rate and Latently Infected Cells(Springer Heidelberg, 2025) Özdek, DemetThe main purpose of this study is to explore the impact of problem parameters on three different models of Human Immunodeficiency Virus (HIV) infection. The first model is the most widely studied HIV infection model, involving three groups: uninfected T cells (T), infected T cells (I), and free virus particles (V). The second model includes an additional parameter that accounts for the effect of the cure rate. The third model extends the first by dividing infected cells into two subgroups—latently and actively infected T cells—and thus includes four nonlinear differential equations. These nonlinear systems are solved using the Lucas wavelet method, which offers significant advantages, such as ease of implementation in symbolic computation and effective numerical results. We solve the models for several parameter values and discuss the impact of these parameters on the course of HIV infection in detail. Due to the absence of an analytical solution, we examine the accuracy through residual error calculation and compare our results with other numerical results available in the literature, presenting them in the form of tables and figures. © The Author(s) under exclusive licence to Korean Society for Informatics and Computational Applied Mathematics 2025.Article Citation - WoS: 11Citation - Scopus: 14Legendre Wavelet Solution of High Order Nonlinear Ordinary Delay Differential Equations(Scientific Technical Research Council Turkey-Tubitak, 2019) Gumgum, Sevin; Ersoy Ozdek, Demet; Ozaltun, GokceThe purpose of this paper is to illustrate the use of the Legendre wavelet method in the solution of high-order nonlinear ordinary differential equations with variable and proportional delays. The main advantage of using Legendre polynomials lies in the orthonormality property, which enables a decrease in the computational cost and runtime. The method is applied to five differential equations up to sixth order, and the results are compared with the exact solutions and other numerical solutions when available. The accuracy of the method is presented in terms of absolute errors. The numerical results demonstrate that the method is accurate, effectual and simple to apply.Article Citation - WoS: 6Citation - Scopus: 7Laguerre Wavelet Solution of Bratu and Duffing Equations(Turkic World Mathematical Soc, 2021) Ozdek, D. ErsoyThe aim of this study is to solve the Bratu and Duffing equations by using the Laguerre wavelet method. The solution of these nonlinear equations is approximated by Laguerre wavelets which are defined by well known Laguerre polynomials. One of the advantages of the proposed method is that it does not require the approximation of the nonlinear term like other numerical methods. The application of the method converts the nonlinear differential equation to a system of algebraic equations. The method is tested on four examples and the solutions are compared with the analytical and other numerical solutions and it is observed that the proposed method has a better accuracy.Article Citation - WoS: 3Citation - Scopus: 4Computing the Green's Function of the Initial Boundary Value Problem for the Wave Equation in a Radially Layered Cylinder(World Scientific Publ Co Pte Ltd, 2015) Yakhno, V.; Ersoy Özdek, DemetIn this paper, a method for construction of the time-dependent approximate Green's function for the initial boundary value problem in a radially multilayered cylinder is suggested. This method is based on determination of the eigenvalues and the orthogonal set of the eigenfunctions; regularization of the Dirac delta function in the form of the Fourier series with a finite number of terms; expansion of the unknown Green's function in the form of Fourier series with unknown coefficients and computation of a finite number of unknown Fourier coefficients. Computational experiment confirms the robustness of the method for the approximate computation of the Dirac delta function and Green's function.Article Gegenbauer Parameter Effect on Gegenbauer Wavelet Solutions of Lane-Emden Equations(2024) Özdek, DemetIn this study, we aim to solve Lane-Emden equations numerically by the Gegenbauer wavelet method. This method is mainly based on orthonormal Gegenbauer polynomials and takes advantage of orthonormality which reduces the computational cost. As a further advantage, Gegenbauer polynomials are associated with a real parameter allowing them to be defined as Legendre polynomials or Chebyshev polynomials for some values. Although this provides an opportunity to be able to analyze the problem under consideration from a wide point of view, the effect of the Gegenbauer parameter on the solution of Lane-Emden equations has not been studied so far. This study demonstrates the robustness of the Gegenbauer wavelet method on three problems of Lane-Emden equations considering different values of this parameter.Article Citation - WoS: 3Citation - Scopus: 3Computation of the Green's Function for the Transverse Vibration of a Composite Circular Membrane(Springer, 2014) Yakhno, V. G.; Ersoy Özdek, DemetA new analytical method is suggested for the approximate computation of the time-dependent Green's function for the equations of the transverse vibration of a composite circular membrane with piecewise constant varying density and tension. The method is based on the derivation of eigenvalues and eigenfunctions for an ordinary differential equation with piecewise constant coefficients and an approximate computation of the Green's function in the form of the Fourier series with a finite number of terms relative to the orthogonal set of the derived eigenfunctions. A computational experiment confirms the robustness of the method.Article Citation - WoS: 11Citation - Scopus: 15Legendre Wavelet Solution of Neutral Differential Equations With Proportional Delays(Springer Heidelberg, 2019) Gumgum, Sevin; Ersoy Özdek, Demet; Özaltun, Gökçe; Bildik, NecdetThe aim of this paper is to solve neutral differential equations with proportional delays by using Legendre wavelet method. Using orthonormal polynomials is the main advantage of this method since it enables a decrease in the computational cost and runtime. Some examples are displayed to illustrate the efficiency and accuracy of the proposed method. Numerical results are compared with various numerical methods in literature and show that the present method is very effectual in solving neutral differential equations with proportional delays.Article Citation - WoS: 2Citation - Scopus: 2The Time-Dependent Green's Function of the Transverse Vibration of a Composite Rectangular Membrane(Tech Science Press, 2013) Yakhno, V. G.; Ersoy Özdek, DemetA new method for the approximate computation of the time-dependent Green's function for the equations of the transverse vibration of a multi stepped membrane is suggested. This method is based on generalization of the Fourier series expansion method and consists of the following steps. The first step is finding eigenvalues and an orthogonal set of eigenfunctions corresponding to an ordinary differential operator with boundary and matching conditions. The second step is a regularization (approximation) of the Dirac delta function in the form of the Fourier series with a finite number of terms, using the orthogonal set of eigenfunctions. The third step is an approximate computation of the Green's function in the form of the Fourier series with a finite number of terms relative to the orthogonal set of eigenfunctions. The computational experiment confirms the robustness of the method.Article Citation - WoS: 1Citation - Scopus: 1Computing Green's Function of the Initial-Boundary Value Problem for the Wave Equation in a Layered Cylinder(Taylor & Francis Ltd, 2014) Yakhno, V.; Ersoy Özdek, DemetA new analytical method for the approximate computation of the time-dependent Green's function for the initial-boundary value problem of the three-dimensional wave equation on multi-layered bounded cylinder is suggested in this paper. The method is based on the derivation of eigenvalues and eigenfunctions for an ordinary differential equation with piecewise constant coefficients, and an approximate computation of Green's function in the form of the Fourier series with a finite number of terms relative to the orthogonal set of the derived eigenfunctions. The computational experiment confirms the robustness of the method.
