Özaltun, Gökçe
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özaltun, Gökçe
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gokce.ozaltun@ieu.edu.tr
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02.02. Mathematics
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Former Staff
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1NO POVERTY
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2ZERO HUNGER
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3GOOD HEALTH AND WELL-BEING
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4QUALITY EDUCATION
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5GENDER EQUALITY
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6CLEAN WATER AND SANITATION
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9INDUSTRY, INNOVATION AND INFRASTRUCTURE
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11SUSTAINABLE CITIES AND COMMUNITIES
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12RESPONSIBLE CONSUMPTION AND PRODUCTION
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13CLIMATE ACTION
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14LIFE BELOW WATER
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5
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49
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4
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Scholarly Output
6
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6
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14/25
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WoS Citation Count
44
Scopus Citation Count
57
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WoS Citations per Publication
7.33
Scopus Citations per Publication
9.50
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2
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0
| Journal | Count |
|---|---|
| Hacettepe Journal of Mathematics and Statistics | 1 |
| International Journal of Biomathematics | 1 |
| Journal of Applıed Mathematıcs And Computıng | 1 |
| Journal of Computatıonal And Applıed Mathematıcs | 1 |
| Mathematics and Computers in Simulation | 1 |
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6 results
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Now showing 1 - 6 of 6
Article Citation - WoS: 6Citation - Scopus: 8Numerical Solutions of the Hiv Infection Model of Cd4(+) Cells by Laguerre Wavelets(Elsevier, 2023) Beler, Ayse; Özaltun, Gökçe; Gümgüm, Sevin; Özaltun Şimşek, GökçeIn this study, we analyze the numerical solutions of the Human Immunodeficiency Virus (HIV) infection on helper T cells by using the Laguerre wavelet method. Our goal is to find accurate approximate results of the models that measure the number of helper infected and uninfected T cells as well as the number of free virus particles at a given time. We present two different models which are governed by three first order nonlinear differential equations with different parameters. We include an error analysis in order to compare the results with other methods available in the literature, and observe that the Laguerre wavelet method gives highly accurate results, is very easy to implement, hence efficient, in the solution of the type of problems indicated.(c) 2023 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.Article Citation - Scopus: 1Gegenbauer Wavelet Solutions of the Sir and Sitr Systems of the Covid-19 Disease(World Scientific Publ Co Pte Ltd, 2024) Simsek, Gokce ozaltun; Beler, Ayse; Gumgum, SevinThis study aimed to investigate the influence of various parameters on the solutions of the susceptible-infected-recovered (SIR) and susceptible-treated-infectious-recovering (SITR) models to describe the spread of COVID-19. To achieve this, we employ the Gegenbauer wavelet technique to convert the system of nonlinear differential equations into a system of nonlinear algebraic equations. This approach has the advantage of not requiring the linearization of the nonlinear expressions, which significantly reduces truncation errors commonly associated with other methods. We conduct a thorough comparison of the absolute and residual errors generated by this technique against those produced by other numerical methods, finding that our results demonstrate a high level of accuracy. Additionally, the Gegenbauer wavelet technique is not only efficient but also straightforward to implement, contributing to a lower CPU time requirement. Overall, this study highlights the effectiveness of the Gegenbauer wavelet technique in accurately modeling the dynamics of COVID-19 transmission while offering practical computational advantages.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: 10Citation - Scopus: 11Gegenbauer Wavelet Solutions of Fractional Integro-Differential Equations(Elsevier, 2023) Ozaltun, Gokce; Konuralp, Ali; Gumgum, SevinThe aim of this study is to use Gegenbauer wavelets in the solution of fractional integrodifferential equations. The method is applied to several problems with different values of resolution parameter and the degree of the truncated polynomial. The results are compared with those obtained from other numerical methods. We observe that the current method is very effective and gives accurate results. One of the reasons for that is it enables us to improve accuracy by increasing resolution parameter, while keeping the degree of polynomial fixed. Another reason is nonlinear terms do not require linearization. Hence the method can be directly implemented and results in the system of algebraic equations which solved by Wolfram Mathematica. It can be asserted that this is the first application of the Gegenbauer wavelet method to the aforementioned types of problems. (C) 2022 Elsevier B.V. All rights reserved.Article Citation - WoS: 6Citation - Scopus: 8Numerical Solutions of Troesch and Duffing Equations by Taylor Wavelets(Hacettepe University, 2023) Özaltun, Gökçe; Gümgüm, Sevin; Şimşek, Gökçe ÖzaltunThe aim of this study is to obtain accurate numerical results for the Troesch and Duffing equations by using Taylor wavelets. Important features of the method include easy imple-mentation and simple calculation. The effectiveness and accuracy of the applied method is illustrated by solving these problems for several variables. One of the important vari-able is the resolution parameter which enables to use low degree polynomials and decrease the computational cost. Results show that the proposed method yields highly accurate solutions by using quite low degree polynomials. © 2023, Hacettepe University. All rights reserved.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, Necdet; Özdek, Demet ErsoyThe 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.
