Aydın, Ayhan

Profile Picture
Name Variants
Aydın,A.
Aydin, Ayhan
A.,Aydın
A., Ayhan
Aydın, Ayhan
Aydin,Ayhan
Ayhan Aydın
A., Aydın
Aydin A.
A.,Aydin
Ayhan, Aydin
Aydın A.
AYDIN A.
A.,Ayhan
A., Aydin
Aydin,A.
Ayhan, Aydın
Job Title
Profesör Doktor
Email Address
ayhan.aydin@atilim.edu.tr
ORCID ID
0000-0002-0837-9364
Scopus Author ID
Turkish CoHE Profile ID
Google Scholar ID
WoS Researcher ID
AAL-5690-2020
Scholarly Output

24

Articles

20

Citation Count

138

Supervised Theses

3

Filters

Reset filters

Settings

Scholarly Output Search Results

Now showing 1 - 10 of 24
  • Thumbnail Image
    Article
    Citation Count: 9
    Conservative finite difference schemes for the chiral nonlinear Schrodinger equation
    (Springer international Publishing Ag, 2015) Aydın, Ayhan; Al-Basyouni, Khalil S.; Aydin, Ayhan; Mathematics
    In this paper, we derive three finite difference schemes for the chiral nonlinear Schrodinger equation (CNLS). The CNLS equation has two kinds of progressive wave solutions: bright and dark soliton. The proposed methods are implicit, unconditionally stable and of second order in space and time directions. The exact solutions and the conserved quantities are used to assess the efficiency of these methods. Numerical simulations of single bright and dark solitons are given. The interactions of two bright solitons are also displayed.
  • Thumbnail Image
    Article
    Operator Splitting of the KdV-Burgers Type Equation with Fast and Slow Dynamics
    (2015) Aydın, Ayhan; Karasözen, Bülent; Mathematics
    The Korteweg de Vries-Burgers (KdV-Burgers) type equation arising from the discretiza tion of the viscous Burgers equation with fast dispersion and slow diffusion is solved using operator splitting. The dispersive and diffusive parts are discretized in space by second order conservative finite differences. The resulting system of ordinary differential equations are composed using the time reversible Strang splitting. The numerical results reveal that the periodicity of the solutions and the invariants of the KdV-Burgers equation are well preserved.
  • Thumbnail Image
    Article
    Citation Count: 0
    New Conservative Schemes for Zakharov Equation
    (Association of Mathematicians (MATDER), 2023) Aydın, Ayhan; Sabawe,B.A.K.; Mathematics
    New first-order and second-order energy preserving schemes are proposed for the Zakharov system. The methods are fully implicit and semi-explicit. It has been found that the first order method is also massconserving. Concrete schemes have been applied to simulate the soliton evolution of the Zakharov system. Numerical results show that the proposed methods capture the remarkable features of the Zakharov equation. We have obtained that the semi-explicit methods are more efficient than the fully implicit methods. Numerical results also demonstrate that the new energy-preserving schemes accurately simulate the soliton evolution of the Zakharov system. © MatDer.
  • Thumbnail Image
    Article
    Citation Count: 12
    Multi-symplectic integration of coupled non-linear Schrodinger system with soliton solutions
    (Taylor & Francis Ltd, 2009) Aydın, Ayhan; Karasoezen, Buelent; Mathematics
    Systems of coupled non-linear Schrodinger equations with soliton solutions are integrated using the six-point scheme which is equivalent to the multi-symplectic Preissman scheme. The numerical dispersion relations are studied for the linearized equation. Numerical results for elastic and inelastic soliton collisions are presented. Numerical experiments confirm the excellent conservation of energy, momentum and norm in long-term computations and their relations to the qualitative behaviour of the soliton solutions.
  • Thumbnail Image
    Article
    Citation Count: 40
    Symplectic and multi-symplectic methods for coupled nonlinear Schrodinger equations with periodic solutions
    (Elsevier, 2007) Aydın, Ayhan; Karasoezen, B.; Mathematics
    We consider for the integration of coupled nonlinear Schrodinger equations with periodic plane wave solutions a splitting method from the class of symplectic integrators and the multi-symplectic six-point scheme which is equivalent to the Preissman scheme. The numerical experiments show that both methods preserve very well the mass, energy and momentum in long-time evolution. The local errors in the energy are computed according to the discretizations in time and space for both methods. Due to its local nature, the multi-symplectic six-point scheme preserves the local invariants more accurately than the symplectic splitting method, but the global errors for conservation laws are almost the same. (C) 2007 Elsevier B.V. All rights reserved.
  • Thumbnail Image
    Article
    Citation Count: 0
    A convergent two-level linear scheme for the generalized Rosenau–KdV–RLW equation
    (Tubitak Scientific & Technological Research Council Turkey, 2019) Aydın, Ayhan; Aydın, Ayhan; Mathematics
    A new convergent two-level finite difference scheme is proposed for the numerical solution of initial valueproblem of the generalized Rosenau–KdV–RLW equation. The new scheme is second-order, linear, conservative, andunconditionally stable. It contains one free parameter. The impact of the parameter to error of the numerical solutionis studied. The prior estimate of the finite difference solution is obtained. The existence, uniqueness, and convergence ofthe scheme are proved by the discrete energy method. Accuracy and reliability of the scheme are tested by simulating thesolitary wave graph of the equation. Wave generation subject to initial Gaussian condition has been studied numerically.Different wave generations are observed depending on the dispersion coefficients and the nonlinear advection term.Numerical experiments indicate that the present scheme is conservative, efficient, and of high accuracy, and well simulatesthe solitary waves for a long time.
  • Thumbnail Image
    Article
    Multi-symplectic integration of coupled non-linear Schrödinger system with soliton solutions
    (International Journal of Computer Mathematics, 2009) Aydın, Ayhan; Karasözen, Bülent; Mathematics
    Systems of coupled non-linear Schrödinger equations with soliton solutions are integrated using the six-point scheme which is equivalent to the multi-symplectic Preissman scheme. The numerical dispersion relations are studied for the linearized equation. Numerical results for elastic and inelastic soliton collisions are presented. Numerical experiments confirm the excellent conservation of energy, momentum and norm in long-term computations and their relations to the qualitative behaviour of the soliton solutions.
  • Thumbnail Image
    Article
    LIE-POISSON INTEGRATORS FOR A RIGID SATELLITE ON A CIRCULAR ORBIT
    (2011) Aydın, Ayhan; Mathematics
    In the last two decades, many structure preserving numerical methods like Poisson integrators have been investigated in numerical studies. Since the structure matrices are different in many Poisson systems, no integrator is known yet to preserve the Poisson structure of any Poisson system. In the present paper, we propose Lie– Poisson integrators for Lie–Poisson systems whose structure matrix is different from the ones studied before. In particular, explicit Lie-Poisson integrators for the equations of rotational motion of a rigid body (the satellite) on a circular orbit around a fixed gravitational center have been constructed based on the splitting. The splitted parts have been composed by a first, a second and a third order compositions. It has been shown that the proposed schemes preserve the quadratic invariants of the equation. Numerical results reveal the preservation of the energy and agree with the theoretical treatment that the invariants lie on the sphere in long–term with different orders of accuracy.
  • Thumbnail Image
    Article
    Citation Count: 0
    Exact and nonstandard finite difference schemes for the Burgers equation B(2, 2)
    (Tubitak Scientific & Technological Research Council Turkey, 2021) Aydın, Ayhan; Köroğlu, Canan; Aydın, Ayhan; Mathematics
    In this paper, we consider the Burgers equation B(2, 2) . Exact and nonstandard finite difference schemes(NSFD) for the Burgers equation B(2, 2) are designed. First, two exact finite difference schemes for the Burgers equationB(2, 2) are proposed using traveling wave solution. Then, two NSFD schemes are represented for this equation. Thesetwo NSFD schemes are compared with a standard finite difference (SFD) scheme. Numerical results show that the NSFDschemes are accurate and efficient in the numerical simulation of the kink-wave solution of the B(2, 2) equation. We seethat although the SFD scheme yields numerical instability for large step sizes, NSFD schemes provide reliable results forlong time integration. Local truncation errors show that the NSFD schemes are consistent with the B(2, 2) equation.
  • Thumbnail Image
    Article
    Citation Count: 3
    Inverse spectral problem for finite Jacobi matrices with zero diagonal
    (Taylor & Francis Ltd, 2015) Aydın, Ayhan; Guseinov, Gusein Sh.; Hüseyin, Hüseyin Şirin; Mathematics
    In this study, the necessary and sufficient conditions for solvability of an inverse spectral problem about eigenvalues and normalizing numbers for finite-order real Jacobi matrices with zero diagonal elements are established. Anexplicit procedure of reconstruction of the matrix from the spectral data consisting of the eigenvalues and normalizing numbers is given. Numerical examples and error analysis are provided to demonstrate the solution technique of the inverse problem. The results obtained are used to justify the solving procedure of the finite Langmuir lattice by the method of inverse spectral problem.