Gümgüm, Sevin

Gümgüm, Sevin

Profile URL

https://hdl.handle.net/20.500.14365/6675

Name Variants

Turhan, Sevin Gümgüm
Gumgum, S.
Gümgüm, S.
Gumgum, Sevin

Email Address

sevin.gumgum@ieu.edu.tr

Main Affiliation

02.02. Mathematics

Status

Current Staff

Sustainable Development Goals

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Competency Cloud

Scholarly Output Search Results

Now showing 1 - 10 of 18

Citation - WoS: 15
Citation - Scopus: 17
Drbem Solution of Mixed Convection Flow of Nanofluids in Enclosures With Moving Walls
(Elsevier Science Bv, 2014) Gümgüm, Sevin; Tezer-Sezgin, M.
This paper presents the results of a numerical study on unsteady mixed convection flow of nanofluids in lid-driven enclosures filled with aluminum oxide and copper-water based nanofluids. The governing equations are solved by the Dual Reciprocity Boundary Element Method (DRBEM), and the time derivatives are discretized using the implicit central difference scheme. All the convective terms and the vorticity boundary conditions are evaluated in terms of the DRBEM coordinate matrix. Linear boundary elements and quadratic radial basis functions are used for the discretization of the boundary and approximation of inhomogeneity, respectively. Solutions are obtained for several values of volume fraction (phi), the Richardson number (Ri), heat source length (B), and the Reynolds number (Re). It is disclosed that the average Nusselt number increases with the increase in volume fraction, and decreases with an increase in both the Richardson number and heat source length. (C) 2013 Elsevier B.V. All rights reserved.
Lucas Polynomial Approach for Second Order Nonlinear Differential Equations
(2020) Gümgüm, Sevin; Kürkçü, Ömür Kıvanç; Sezer, Mehmet; Bayku S Sava Saner Il, Nurcan
This paper presents the Lucas polynomial solution of second-order nonlinearordinary differential equations with mixed conditions. Lucas matrix method is based oncollocation points together with truncated Lucas series. The main advantage of the methodis that it has a simple structure to deal with the nonlinear algebraic system obtained frommatrix relations. The method is applied to four problems. In the first two problems, exactsolutions are obtained. The last two problems, Bratu and Duffing equations are solvednumerically; the results are compared with the exact solutions and some other numericalsolutions. It is observed that the application of the method results in either the exact oraccurate numerical solutions.
Citation - WoS: 22
Citation - Scopus: 25
Drbem Solution of Natural Convection Flow of Nanofluids With a Heat Source
(Elsevier Sci Ltd, 2010) Gümgüm, Sevin; Tezer-Sezgin, M.
This paper presents the dual reciprocity boundary element method (DRBEM) solution of the unsteady natural convective flow of nanofluids in enclosures with a heat source. The implicit Euler scheme is used for time integration. All the convective terms are evaluated in terms of DRBEM coordinate matrix. The vorticity boundary conditions are obtained from the Taylor series expansion of stream function equation. The results report that the average Nusselt number increases with the increase in both volume fraction and Rayleigh number. It is also observed that an increase in heater length reduces the heat transfer. The average Nusselt number of aluminum oxide-water based nanofluid is found to be smaller than that of copper-water based nanofluid. Results are given in terms of streamlines, isotherms, vorticity contours, velocity profiles and tables containing average Nusselt number for several values of Rayleigh number, heater length, volume fraction, and number of iterations together with CPU times. (C) 2010 Elsevier Ltd. All rights reserved.
Citation - WoS: 6
Citation - Scopus: 8
Numerical Solutions of the Hiv Infection Model of Cd4(+) Cells by Laguerre Wavelets
(Elsevier, 2023) Beler, Ayse; Özaltun, Gökçe; Gümgüm, Sevin; Özaltun Şimşek, Gökçe
In 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.
Citation - WoS: 4
Citation - Scopus: 5
Drbem Formulation for Transient Stokes Flow With Slip Boundary Condition
(Elsevier Sci Ltd, 2017) Gümgüm, Sevin; Wrobel, Luiz C.
In this study, the effect of linear and nonlinear slip boundary conditions on the flow of a slow viscous fluid is investigated numerically. The boundary integral representation of the transient Stokes equations is given in primitive variables form. The fundamental solution to the steady Stokes equations is employed in the boundary element method (BEM) formulation. The time derivative is taken to the boundary with the dual reciprocity method and approximated by the finite difference method (FDM) until a steady-state is achieved. It is assumed that the fluid is capable of slip, with the slip velocity expressed as a function of shear rate at the wall. In the numerical tests, the fluid is initially assumed to be stationary; at each time step, the velocity boundary conditions along the walls are updated as the shear forces vary with time.
Citation - WoS: 46
Citation - Scopus: 57
Taylor Wavelet Solution of Linear and Nonlinear Lane-Emden Equations
(Elsevier, 2020) Gumgum, Sevin
This study aims to use the Taylor wavelet method to solve linear and nonlinear Lane-Emden equations. An advantage of the method is the orthonormality property of the polynomials which reduce the computational cost. Another advantage is that the nonlinear terms do not need to be approximated. The application of the method reduces the differential equations to a system of algebraic equations. Six differential equations that model different physical problems with initial and boundary conditions are solved to illustrate the efficiency and accuracy of the Taylor wavelet method. The results obtained from the method are compared with other numerical results and exact solutions and presented in terms of absolute error tables and graphics. We observe from these results that the method is highly accurate and capable of obtaining the exact solution when it is in the form of a polynomial. (C) 2020 IMACS. Published by Elsevier B.V. All rights reserved.
Citation - WoS: 15
Citation - Scopus: 18
Drbem Solution of the Natural Convective Flow of Micropolar Fluids
(Taylor & Francis Inc, 2010) Gümgüm, Sevin; Tezer-Sezgin, M.
The main purpose of this article is to present the use of the dual reciprocity boundary element method (DRBEM) in the analysis of the unsteady natural convective flow of micropolar fluids in a differentially heated rectangular cavity. The finite-difference method (FDM) is used for time discretization. All the convective terms and vorticity boundary condition are evaluated in terms of DRBEM coordinate matrix. Solutions are obtained for several values of microstructure parameter (k), Rayleigh number (Ra), and aspect ratio (A). Prandtl number values are taken as 0.71 and 7.0. The heat transfer rate (average Nusselt number) of micropolar fluids is found to be smaller than that of Newtonian fluid. Numerical results at steady-state are given in terms of streamlines, isotherms, vorticity contours, and velocity profiles, as well as a table containing Nusselt number values for several Ra and k.
Citation - Scopus: 1
Gegenbauer 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, Sevin
This 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.
Citation - WoS: 11
Lucas Polynomial Solution for Neutral Differential Equations With Proportional Delays
(Turkic World Mathematical Soc, 2020) Gümgüm, Sevin; Savasaneril, N. Baykus; Kurkcu, O. K.; Sezer, M.
This paper proposes a combined operational matrix approach based on Lucas and Taylor polynomials for the solution of neutral type differential equations with proportional delays. The advantage of the proposed method is the ease of its application. The method facilitates the solution of the given problem by reducing it to a matrix equation. Illustrative examples are validated by means of absolute errors. Residual error estimation is presented to improve the solutions. Presented in graphs and tables the results are compared with the existing methods in literature.
Citation - WoS: 11
Citation - Scopus: 15
Legendre Wavelet Solution of Neutral Differential Equations With Proportional Delays
(Springer Heidelberg, 2019) Gumgum, Sevin; Ersoy Özdek, Demet; Özaltun, Gökçe; Bildik, Necdet; Özdek, Demet Ersoy
The 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.