Ayhan Aydın

Scholarly Output Search Results

Now showing 1 - 5 of 5

Citation - WoS: 24
Citation - Scopus: 24
Symplectic and multisymplectic Lobatto methods for the "good" Boussinesq equation
(Amer inst Physics, 2008) Aydin, A.; Karasoezen, B.
In this paper, we construct second order symplectic and multisymplectic integrators for the "good" Boussineq equation using the two-stage Lobatto IIIA-IIIB partitioned Runge-Kutta method, which yield an explicit scheme and is equivalent to the classical central difference approximation to the second order spatial derivative. Numerical dispersion properties and the stability of both integrators are investigated. Numerical results for different solitary wave solutions confirm the excellent long time behavior of symplectic and multisymplectic integrators by preservink local and global energy and momentum. (C) 2008 American Institute of Physics.
Citation - WoS: 23
Citation - Scopus: 25
Multisymplectic Integration of n-coupled Nonlinear Schrodinger Equation With Destabilized Periodic Wave Solutions
(Pergamon-elsevier Science Ltd, 2009) Aydin, Ayhan
N-coupled nonlinear Schrodinger equation (N-CNLS) is shown to be in multisymplectic form. 3-CNLS equation is studied for analytical and numerical purposes. A new six-point scheme which is equivalent to the multisymplectic Preissman scheme is derived for 3-CNLS equation. A new periodic wave solution is obtained and its stability analysis is discussed. 3-CNLS equation is integrated for destabilized periodic solutions both for integrable and non-integrable cases by multisymplectic six-point scheme. Different kinds of evolutions are observed for different parameters and coefficients of the system. Numerical results show that, the multisymplectic six-point scheme has excellent local and global conservation properties in long-time computation. (C) 2008 Elsevier Ltd. All rights reserved.
Citation - WoS: 17
Citation - Scopus: 16
Multisymplectic Box Schemes for the Complex Modified Korteweg-De Vries Equation
(Amer inst Physics, 2010) Aydin, A.; Karasozen, B.
In this paper, two multisymplectic integrators, an eight-point Preissman box scheme and a narrow box scheme, are considered for numerical integration of the complex modified Korteweg-de Vries equation. Energy and momentum preservation of both schemes and their dispersive properties are investigated. The performance of both methods is demonstrated through numerical tests on several solitary wave solutions. (C) 2010 American Institute of Physics. [doi:10.1063/1.3456068]
Citation - WoS: 4
Citation - Scopus: 5
An Unconventional Finite Difference Scheme for Modified Korteweg-De Vries Equation
(Hindawi Ltd, 2017) Koroglu, Canan; Aydin, Ayhan
A numerical solution of the modified Korteweg-de Vries (MKdV) equation is presented by using a nonstandard finite difference (NSFD) scheme with theta method which includes the implicit Euler and a Crank-Nicolson type discretization. Local truncation error of the NSFD scheme and linear stability analysis are discussed. To test the accuracy and efficiency of the method, some numerical examples are given. The numerical results of NSFD scheme are compared with the exact solution and a standard finite difference scheme. The numerical results illustrate that the NSFD scheme is a robust numerical tool for the numerical integration of the MKdV equation.
Citation - WoS: 12
Citation - Scopus: 12
Conservative Finite Difference Schemes for the Chiral Nonlinear Schrodinger Equation
(Springer international Publishing Ag, 2015) Ismail, Mohammad S.; Al-Basyouni, Khalil S.; Aydin, Ayhan
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.

Journal	Count
Turkish Journal of Mathematics	2
Journal of Mathematical Physics	2
Applied Mathematics and Computation	1
Boundary Value Problems	1
Chaos, Solitons & Fractals	1

Aydın, Ayhan

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