Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7148
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Article On Smoothers for Multigrid of the Second Kind(John Wiley and Sons Inc., 2019) Aksoylu, Burak; Kaya, AdemWe study smoothers for the multigrid method of the second kind arising from Fredholm integral equations. Our model problems use nonlocal governing operators that enforce local boundary conditions. For discretization, we utilize the Nystrom method with the trapezoidal rule. We find the eigenvalues of matrices associated to periodic, antiperiodic, and Dirichlet problems in terms of the nonlocality parameter and mesh size. Knowing explicitly the spectrum of the matrices enables us to analyze the behavior of smoothers. Although spectral analyses exist for finding effective smoothers for 1D elliptic model problems, to the best of our knowledge, a guiding spectral analysis is not available for smoothers of a multigrid of the second kind. We fill this gap in the literature. The Picard iteration has been the default smoother for a multigrid of the second kind. Jacobi-like methods have not been considered as viable options. We propose two strategies. The first one focuses on the most oscillatory mode and aims to damp it effectively. For this choice, we show that weighted-Jacobi relaxation is equivalent to the Picard iteration. The second strategy focuses on the set of oscillatory modes and aims to damp them as quickly as possible, simultaneously. Although the Picard iteration is an effective smoother for model nonlocal problems under consideration, we show that it is possible to find better than ones using the second strategy. We also shed some light on internal mechanism of the Picard iteration and provide an example where the Picard iteration cannot be used as a smoother.Article Citation - WoS: 7Citation - Scopus: 10A Boundary Integral Equation for the Transmission Eigenvalue Problem for Maxwell Equation(John Wiley and Sons Inc., 2018) Cakoni, Fioralba; Ivanyshyn Yaman, Olha; Kress, Rainer; Le Louër, FrédériqueWe propose a new integral equation formulation to characterize and compute transmission eigenvalues in electromagnetic scattering. As opposed to the approach that was recently developed by Cakoni, Haddar and Meng (2015) which relies on a two-by-two system of boundary integral equations, our analysis is based on only one integral equation in terms of the electric-to-magnetic boundary trace operator that results in a simplification of the theory and in a considerable reduction of computational costs. We establish Fredholm properties of the integral operators and their analytic dependence on the wave number. Further, we use the numerical algorithm for analytic nonlinear eigenvalue problems that was recently proposed by Beyn (2012) for the numerical computation of the transmission eigenvalues via this new integral equation.Article Citation - WoS: 2Citation - Scopus: 3Bubble-Based Stabilized Finite Element Methods for Time-Dependent Convection–diffusion–reaction Problems(John Wiley and Sons Inc., 2016) Şendur, Ali; Neslitürk, Ali İhsanIn this paper, we propose a numerical algorithm for time-dependent convection–diffusion–reaction problems and compare its performance with the well-known numerical methods in the literature. Time discretization is performed by using fractional-step θ-scheme, while an economical form of the residual-free bubble method is used for the space discretization. We compare the proposed algorithm with the classical stabilized finite element methods over several benchmark problems for a wide range of problem configurations. The effect of the order in the sequence of discretization (in time and in space) to the quality of the approximation is also investigated. Numerical experiments show the improvement through the proposed algorithm over the classical methods in either cases.Article Citation - WoS: 22Citation - Scopus: 26Exact Solutions for Fractional Ddes Via Auxiliary Equation Method Coupled With the Fractional Complex Transform(John Wiley and Sons Inc., 2016) Aslan, İsmailDynamical behavior of many nonlinear systems can be described by fractional-order equations. This study is devoted to fractional differential–difference equations of rational type. Our focus is on the construction of exact solutions by means of the (G'/G)-expansion method coupled with the so-called fractional complex transform. The solution procedure is elucidated through two generalized time-fractional differential–difference equations of rational type. As a result, three types of discrete solutions emerged: hyperbolic, trigonometric, and rational. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.Article Citation - WoS: 21Citation - Scopus: 21An Analytic Approach To a Class of Fractional Differential-Difference Equations of Rational Type Via Symbolic Computation(John Wiley and Sons Inc., 2015) Aslan, İsmailFractional derivatives are powerful tools in solving the problems of science and engineering. In this paper, an analytical algorithm for solving fractional differential-difference equations in the sense of Jumarie's modified Riemann-Liouville derivative has been described and demonstrated. The algorithm has been tested against time-fractional differentialdifference equations of rational type via symbolic computation. Three examples are given to elucidate the solution procedure. Our analyses lead to closed form exact solutions in terms of hyperbolic, trigonometric, and rational functions, which might be subject to some adequate physical interpretations in the future. Copyright © 2013 JohnWiley & Sons, Ltd.Article Citation - WoS: 4Citation - Scopus: 4Dayside Episodic Ion Outflow From Martian Magnetic Cusps And/Or Magnetosheath Boundary Motion Associated With Plasma Oscillations(John Wiley and Sons Inc., 2014) Duru, Firdevs; Gurnett, D. A.; Morgan, D. D.; Lundin, R.; Duru, İsmail Hakkı; Winningham, J. D.; Frahm, R. A.The radar sounder on the Mars Express Spacecraft is able to make measurements of electron densities in the Martian ionosphere from both local electron plasma oscillations and remote soundings. A study of thousands of orbits shows that in some cases the electron plasma oscillations disappear and reappear abruptly near the upper boundary of the dayside ionosphere. In some cases, the Analyzer of Space Plasmas and Energetic Atoms (ASPERA-3) data show clear evidence of upwardly accelerated ionospheric ions, on interconnected magnetic field lines. In other cases, ASPERA-3 data show that when the plasma oscillations disappear, the spacecraft is in the magnetosheath and when they return, the ionospheric plasma reappears. These intermittent appearances of plasma suggest the multiple crossings of the magnetosheath boundary. The motion of the boundary or plasma clouds and ionospheric streamers (a relatively narrow strip of plasma attached to the ionosphere) can cause these multiple crossings.Article Citation - WoS: 17Citation - Scopus: 25The First Integral Method for Constructing Exact and Explicit Solutions To Nonlinear Evolution Equations(John Wiley and Sons Inc., 2012) Aslan, İsmailProblems that are modeled by nonlinear evolution equations occur in many areas of applied sciences. In the present study, we deal with the negative order KdV equation and the generalized Zakharov system and derive some further results using the so-called first integral method. By means of the established first integrals, some exact traveling wave solutions are obtained in a concise manner.Article Citation - WoS: 16Citation - Scopus: 15Constructing Rational and Multi-Wave Solutions To Higher Order Nees Via the Exp-Function Method(John Wiley and Sons Inc., 2011) Aslan, İsmailIn this paper, we present an application of some known generalizations of the Exp-function method to the fifth-order Burgers and to the seventh-order Korteweg de Vries equations for the first time. The two examples show that the Exp-function method can be an effective alternative tool for explicitly constructing rational and multi-wave solutions with arbitrary parameters to higher order nonlinear evolution equations. Being straightforward and concise, as pointed out previously, this procedure does not require the bilinear representation of the equation considered.Article Citation - WoS: 13Citation - Scopus: 14On a 2+1-Dimensional Whitham-Broer System: a Resonant Nls Connection(John Wiley and Sons Inc., 2011) Rogers, Colin; Pashaev, OktayIt is established that the Whitham-Broer-Kaup shallow water system and the "resonant" nonlinear Schrödinger equation are equivalent. A symmetric integrable 2+1-dimensional version of the Whitham-Broer-Kaup system is constructed which, in turn, is equivalent to a recently introduced resonant Davey-Stewartson I system incorporating a Madelung-Bohm type quantum potential. A bilinear representation is adopted and resonant solitonic interaction in this new 2+1-dimensional Kaup-Broer system is exhibited.Article Citation - WoS: 9Citation - Scopus: 10Application of the Exp-Function Method To Nonlinear Lattice Differential Equations for Multi-Wave and Rational Solutions(John Wiley and Sons Inc., 2011) Aslan, İsmailIn this paper, we extend the basic Exp-function method to nonlinear lattice differential equations for constructing multi-wave and rational solutions for the first time. We consider a differential-difference analogue of the Korteweg-de Vries equation to elucidate the solution procedure. Our approach is direct and unifying in the sense that the bilinear formalism of the equation studied becomes redundant.