Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7148
Browse
8 results
Search Results
Article Citation - WoS: 4Citation - Scopus: 4A 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, GamzeIn 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.Article Citation - WoS: 9Citation - Scopus: 8Taylor Wavelets Collocation Technique for Solving Fractional Nonlinear Singular Pdes(Springer, 2022) Aghazadeh, Nasser; Mohammadi, Amir; Tanoğlu, GamzeA 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, GamzeIn 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: 1Citation - Scopus: 1Fatigue 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, MetinIn 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 An Operator Splitting Approximation Combined With the Supg Method for Transport Equations With Nonlinear Reaction Term(Tech Science Press, 2012) Baysal, Onur; Tanoğlu, GamzeIn this work, an operator splitting method is proposed in order to obtain a stable numerical solution for transport equation with non-linear reaction term. We split the transport equation into a reaction part and an advection diffusion part. The former one which becomes a nonlinear ordinary differential equation can be approximated by the simple higher order integrator or solved exactly. The later one is approximated by the Streamline-Upwind Petrov-Galerkin (SUPG) method combined with the generalized Euler time integration (q-method). Numerical results that illustrate the good performance of this method are reported.Article Citation - WoS: 5Citation - Scopus: 5Convergence Analysis and Numerical Solution of the Benjamin-Bona Equation by Lie-Trotter Splitting(TUBITAK, 2018) Zürnacı, Fatma; Gücüyenen Kaymak, Nurcan; Seydaoğlu, Muaz; Tanoğlu, GamzeIn this paper, an operator splitting method is used to analyze nonlinear Benjamin-Bona-Mahony-type equations. We split the equation into an unbounded linear part and a bounded nonlinear part and then Lie-Trotter splitting is applied to the equation. The local error bounds are obtained by using the approach based on the differential theory of operators in a Banach space and the quadrature error estimates via Lie commutator bounds. The global error estimate is obtained via Lady Windermere's fan argument. Finally, to confirm the expected convergence order, numerical examples are studied.Article Citation - WoS: 2Citation - Scopus: 2The Convergence of a New Symmetric Iterative Splitting Method for Non-Autonomous Systems(Taylor and Francis Ltd., 2012) Tanoğlu, Gamze; Korkut, SılaThe iterative splitting methods have been extensively applied to solve complicated systems of differential equations. In this process, we split the complex problem into several sub-problems, each of which can be solved sequentially. In this paper, we construct a new symmetric iterative splitting scheme based on the Magnus expansion for solving non-autonomous problems. We also study its convergence properties by using the concepts of stability, consistency, and order. Several numerical examples are illustrated to confirm the theoretical results by comparing frequently used methods. © 2012 Copyright Taylor and Francis Group, LLC.Article Citation - WoS: 13Citation - Scopus: 15Analysis of a Corner Layer Problem in Anisotropic Interfaces(Southwest Missouri State University, 2006) Alikakos, N. D.; Bates, P. W.; Cahn, J. W.; Fife, P. C.; Fusco, G.; Tanoğlu, GamzeWe investigate a model of anisotropic diffuse interfaces in ordered FCC crystals introduced recently by Braun et al and Tanoglu et al [3, 18, 19], focusing on parametric conditions which give extreme anisotropy. For a reduced model, we prove existence and stability of plane wave solutions connecting the disordered FCC state with the ordered Cu3Au state described by solutions to a system of three equations. These plane wave solutions correspond to planar interfaces. Different orientations of the planes in relation to the crystal axes give rise to different surface energies. Guided by previous work based on numerics and formal asymptotics, we reduce this problem in the six dimensional phase space of the system to a two dimensional phase space by taking advantage of the symmetries of the crystal and restricting attention to solutions with corresponding symmetries. For this reduced problem a standing wave solution is constructed that corresponds to a transition that, in the extreme anisotropy limit, is continuous but not differentiable. We also investigate the stability of the constructed solution by studying the eigenvalue problem for the linearized equation. We find that although the transition is stable, there is a growing number 0(1/ε), of critical eigenvalues, where 1/ε ≫ 1 is a measure of the anisotropy. Specifically we obtain a discrete spectrum with eigenvalues λn = ε2/3 μn with μn ∼ Cn2/3, as n → +∞. The scaling characteristics of the critical spectrum suggest a previously unknown microstructural instability.