Mathematics / Matematik

Permanent URI for this collectionhttps://hdl.handle.net/11147/8

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Author: search.filters.author.Tanoğlu, Gamze

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  • Book
    Endüstriyel Matematik
    (01. Izmir Institute of Technology, 2024) Tanoğlu, Gamze; Yurt, Canberk
    Üniversitelerin öğrencilere meslek kazandırma misyonu dijital yüzyılda yeni nesil üniversiteler tanımı ile birlikte değişerek farklı bir misyona doğru evrilmiştir. Değişen bu misyon üniversitenin ürettiği bilimi toplumun diğer paydaşları ile paylaşarak toplumu dönüştürmek biçimde ifade edilebilir. İzmir Yüksek Teknoloji Enstitüsü, çocukları ve gençleri toplumun en değerli paydaşları görerek onların dönüşümüne ve gelişimine katkı sunmayı üniversitenin eğitim modeli olarak benimsemiştir. Bu atölye çalışması ile lise öğrencilerinin matematik müfredatında gördüğü konuları pekiştirerek öğrenmesi benimsenmiştir. Ayrıca, öğrencilerin bilgisayar yardımı ile özellikle de algoritma mantığı kullanarak ele alınan konuları deneyimleyerek öğrenmesini hedeflemektedir. Böylece bu çalıma ile ezberden uzak kalıcı öğrenme modeli sunulmuş olup matematiğin soyut yapısından somut yapısına bir köprü oluşturulması amaçlanmaktadır. Umuyorum bu atölye çalışması öğrencilere matematiğin günlük hayatta nerelerde kullanıldığı konusunda fikir vererek eğlenceli bir bilim olduğu konusunda da bir vizyon sunar.
  • Article
    Citation - WoS: 9
    Citation - Scopus: 8
    A Numerical Method Based on Legendre Wavelet and Quasilinearization Technique for Fractional Lane-Emden Type Equations
    (Springer, 2023) İdiz, Fatih; Tanoğlu, Gamze; Aghazadeh, Nasser
    In this research, we study the numerical solution of fractional Lane-Emden type equations, which emerge mainly in astrophysics applications. We propose a numerical approach making use of Legendre wavelets and the quasilinearization technique. The nonlinear term in fractional Lane-Emden type equations is iteratively linearized using the quasilinearization technique. The linearized equations are then solved using the Legendre wavelet collocation method. The proposed method is quite effective to overcome the singularity in fractional Lane-Emden type equations. Convergence and error analysis of the proposed method are given. We solve some test problems to compare the effectiveness of the proposed method with some other numerical methods in the literature.
  • Article
    Citation - WoS: 4
    Citation - Scopus: 4
    A New Numerical Algorithm Based on Quintic B-Spline and Adaptive Time Integrator for Cou- Pled Burger's Equation
    (Tabriz University, 2023) Çiçek, Yeşim; Gücüyenen Kaymak, Nurcan; Bahar, Ersin; Gürarslan, Gürhan; Tanoğlu, Gamze
    In this article, the coupled Burger's equation which is one of the known systems of the nonlinear parabolic partial differential equations is studied. The method presented here is based on a combination of the quintic B-spline and a high order time integration scheme known as adaptive Runge-Kutta method. First of all, the application of the new algorithm on the coupled Burger's equation is presented. Then, the convergence of the algorithm is studied in a theorem. Finally, to test the efficiency of the new method, coupled Burger's equations in literature are studied. We observed that the presented method has better accuracy and efficiency compared to the other methods in the literature. © 2023 University of Tabriz. All Rights Reserved.
  • Book
    Endüstriyel matematik
    (Izmir Institute of Technology, 2022) Tanoğlu, Gamze; Plattürk, Sabahat Defne; Yurt, Canberk; Kara, Utku
    Üniversitelerin öğrencilere meslek kazandırma misyonu dijital yüzyılda yeni nesil üniversiteler tanımı ile birlikte değişerek farklı bir misyona doğru evrilmiştir. Değişen bu misyon üniversitenin ürettiği bilimi toplumun diğer paydaşları ile paylaşarak toplumu dönüştürmek biçimde ifade edilebilir. İzmir Yüksek Teknoloji Enstitüsü, çocukları ve gençleri toplumum en değerli paydaşları görerek onların dönüşümüne ve gelişimine katkı sunmayı üniversitenin eğitim modeli olarak benimsemiştir. Bu atölye çalışması ile lise öğrencilerinin matematik müfredatında gördüğü konuları pekiştirerek öğrenmesi benimsenmiştir. Ayrıca, öğrencilerin bilgisayar yardımı ile özellikle de algoritma mantığı kullanarak ele alınan konuları deneyimleyerek öğrenmesini hedeflemektedir. Böylece bu çalışma ile ezberden uzak kalıcı öğrenme modeli sunulmuş olup matematiğin soyut yapısından somut yapısına bir köprü oluşturulması amaçlanmaktadır. Umuyorum bu atölye çalışması öğrencilere matematiğin günlük hayatta nerelerde kullanıldığını konusunda fikir vererek eğlenceli bir bilim olduğu konusunda da bir vizyon sunar.
  • Article
    Citation - WoS: 9
    Citation - Scopus: 8
    Taylor Wavelets Collocation Technique for Solving Fractional Nonlinear Singular Pdes
    (Springer, 2022) Aghazadeh, Nasser; Mohammadi, Amir; Tanoğlu, Gamze
    A novel technique has been introduced to solve the Emden-Fowler equations. It has been derived from the Taylor wavelets collocation method. The proposed scheme has been successfully implemented in order to solve the singular equations. The singular problem converts to a system of algebraic equations that can be solved numerically. Moreover, the technique is very effective to remove the strong singularity point at x = 0. The numerical experiments have been checked out with the exact and approximate solutions that have been achieved by others including the Adomian decomposition method (Wazwaz in Appl Math Comput 166:638-651, 2005), Modified Homotopy Perturbation Method (Singh et al. J Math Chem 54(4):918-931, 2016). Also, the error analysis of the technique has been considered.
  • Article
    A Reliable and Fast Mesh-Free Solver for the Telegraph Equation
    (Springer, 2022) İmamoğlu Karabaş, Neslişah; Korkut, Sıla Övgü; Gürarslan, Gürhan; Tanoğlu, Gamze
    In the presented study, the hyperbolic telegraph equation is taken as the focus point. To solve such an equation, an accurate, reliable, and efficient method has been proposed. The developed method is mainly based on the combination of a kind of mesh-free method and an adaptive method. Multiquadric radial basis function mesh-free method is considered on spatial domain and the adaptive fifth-order Runge–Kutta method is used on time domain. The validity and the performance of the proposed method have been checked on several test problems. The approximate solutions are compared with the exact solution, it is shown that the proposed method has more preferable to the other methods in the literature.
  • Article
    Citation - WoS: 1
    Citation - Scopus: 1
    Fatigue Life Prediction and Optimization of Gfrp Composites Based on Failure Tensor Polynomial in Fatigue Model With Exponential Fitting Approach
    (SAGE Publications, 2022) Güneş, Mehmet Deniz; İmamoğlu Karabaş, Neslişah; Deveci, Hamza Arda; Tanoğlu, Gamze; Tanoğlu, Metin
    In this study, a new fatigue life prediction and optimization strategy utilizing the Failure Tensor Polynomial in Fatigue (FTPF) model with exponential fitting and numerical bisection method for fiber reinforced polymer composites has been proposed. Within the experimental stage, glass/epoxy composite laminates with (Formula presented.), (Formula presented.), and (Formula presented.) lay-up configurations were fabricated, quasi-static and fatigue mechanical behavior of GFRP composites was characterized to be used in the FTPF model. The prediction capability of the FTPF model was tested based on the experimental data obtained for multidirectional laminates of various composite materials. Fatigue life prediction results of the glass/epoxy laminates were found to be better as compared to those for the linear fitting predictions. The results also indicated that the approach with exponential fitting provides better fatigue life predictions as compared to those obtained by linear fitting, especially for glass/epoxy laminates. Moreover, an optimization study using the proposed methodology for fatigue life advancement of the glass/epoxy laminates was performed by a powerful hybrid algorithm, PSA/GPSA. So, two optimization scenarios including various loading configurations were considered. The optimization results exhibited that the optimized stacking sequences having maximized fatigue life can be obtained in various loading cases. It was also revealed that the tension-compression loading and the loadings involving shear loads are critical for fatigue, and further improvement in fatigue life may be achieved by designing only symmetric lay-ups instead of symmetric-balanced and diversification of fiber angles to be used in the optimization.
  • Article
    The Application of a Finite Difference Method To a Dynamical Interface Problem
    (Acad. Publications, 2003) Tanoğlu, Gamze; Ağıroğlu, İzzet Onur
    A multiple-order-parameter model for Cu-Au system on a face cubic centered lattice was recently developed in the presence of anisotropy. In that model, three order parameters (non-conserved) and one concentration order parameter (conserved), which has been taken as a constant, were considered. Later on, the model has been extended, so that, concentration has been taken as a variable. It has been seen that two models were in a good agreement near critical temperature since the non-conserved order parameter behaves like a constant near critical temperature in both models.
  • Article
    Citation - WoS: 10
    Citation - Scopus: 12
    An Efficient Approach for Solving Nonlinear Multidimensional Schrodinger Equations
    (Elsevier, 2021) İmamoğlu Karabaş, Neslişah; Korkut, Sıla Övgü; Tanoğlu, Gamze; Aziz, Imran; Siraj-ul-Islam
    An efficient numerical method is proposed for the solution of the nonlinear cubic Schrodinger equation. The proposed method is based on the Frechet derivative and the meshless method with radial basis functions. An important characteristic of the method is that it can be extended from one-dimensional problems to multi-dimensional ones easily. By using the Frechet derivative and Newton-Raphson technique, the nonlinear equation is converted into a set of linear algebraic equations which are solved iteratively. Numerical examples reveal that the proposed method is efficient and reliable with respect to the accuracy and stability.
  • Conference Object
    The Hirota Method for Reaction-Diffusion Equations With Three Distinct Roots
    (American Institute of Physics, 2004) Tanoğlu, Gamze; Pashaev, Oktay
    The Hirota Method, with modified background is applied to construct exact analytical solutions of nonlinear reaction-diffusion equations of two types. The first equation has only nonlinear reaction part, while the second one has in addition the nonlinear transport term. For both cases, the reaction part has the form of the third order polynomial with three distinct roots. We found analytic one-soliton solutions and the relationships between three simple roots and the wave speed of the soliton. For the first case, if one of the roots is the mean value of other two roots, the soliton is static.We show that the restriction on three distinct roots to obtain moving soliton is removed in the second case by, adding nonlinear transport term to the first equation.