Aydın, Ayhan
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Aydın,A.
Aydin, Ayhan
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Aydın, Ayhan
Aydin,Ayhan
Ayhan Aydın
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Aydin A.
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Ayhan, Aydin
Aydın A.
AYDIN A.
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Aydin,A.
Ayhan, Aydın
Aydin, Ayhan
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Aydın, Ayhan
Aydin,Ayhan
Ayhan Aydın
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Aydin A.
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Ayhan, Aydin
Aydın A.
AYDIN A.
A.,Ayhan
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Aydin,A.
Ayhan, Aydın
Job Title
Profesör Doktor
Email Address
ayhan.aydin@atilim.edu.tr
ORCID ID
Scopus Author ID
Turkish CoHE Profile ID
Google Scholar ID
WoS Researcher ID
Scholarly Output
27
Articles
21
Citation Count
138
Supervised Theses
3
25 results
Scholarly Output Search Results
Now showing 1 - 10 of 25
Article An Unconventional Splitting for Korteweg de Vries–Burgers Equation(EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2015) Aydın, Ayhan; MathematicsNumerical solutions of the Korteweg de Vries–Burgers (KdVB) equation based on splitting is studied. We put a real parameter into a KdVB equation and split the equation into two parts. The real parameter that is inserted into the KdVB equation enables us to play with the splitted parts. The real parameter enables to write the each splitted equation as close to the Korteweg de Vries (KdV) equation as we wish and as far from the Burgers equation as we wish or vice a versa. Then we solve the splitted parts numerically and compose the solutions to obtained the integrator for the KdVB equation. Finally we present some numerical experiments for the solution of the KdV, Burger’s and KdVB equations. The numerical experiments shows that the new splitting gives feasible and valid results.Article Citation Count: 9Conservative finite difference schemes for the chiral nonlinear Schrodinger equation(Springer international Publishing Ag, 2015) Ismail, Mohammad S.; Al-Basyouni, Khalil S.; Aydin, Ayhan; MathematicsIn 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.Article Operator Splitting of the KdV-Burgers Type Equation with Fast and Slow Dynamics(2015) Aydın, Ayhan; Karasözen, Bülent; MathematicsThe 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.Article Citation Count: 0New Conservative Schemes for Zakharov Equation(Association of Mathematicians (MATDER), 2023) Aydin,A.; Sabawe,B.A.K.; MathematicsNew 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.Article Lobatto IIIA–IIIB discretization of the strongly coupled nonlinear Schrödinger equation(Journal of Computational and Applied Mathematics, 2009) Aydın, Ayhan; Karasözen, Bülent; MathematicsIn this paper, we construct a second order semi-explicit multi-symplectic integrator for the strongly coupled nonlinear Schrödinger equation based on the two-stage Lobatto IIIA–IIIB partitioned Runge–Kutta method. Numerical results for different solitary wave solutions including elastic and inelastic collisions, fusion of two solitons and with periodic solutions confirm the excellent long time behavior of the multi-symplectic integrator by preserving global energy, momentum and mass.Article Citation Count: 0Exact and nonstandard finite difference schemes for the Burgers equation B(2, 2)(Tubitak Scientific & Technological Research Council Turkey, 2021) Köroğlu, Canan; Aydın, Ayhan; MathematicsIn 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.Article Citation Count: 3Inverse spectral problem for finite Jacobi matrices with zero diagonal(Taylor & Francis Ltd, 2015) Aydin, Ayhan; Guseinov, Gusein Sh.; MathematicsIn 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.Article Symplectic and multi-symplectic methods for coupled nonlinear Schrödinger equations with periodic solutions(Computer Physics Communications, 2007) Aydın, Ayhan; Karasözen, Bülent; MathematicsWe consider for the integration of coupled nonlinear Schrödinger 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.Article Citation Count: 4An Unconventional Finite Difference Scheme for Modified Korteweg-de Vries Equation(Hindawi Ltd, 2017) Koroglu, Canan; Aydin, Ayhan; MathematicsA 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.Article Citation Count: 7A nonstandard numerical method for the modified KdV equation(indian Acad Sciences, 2017) Aydin, Ayhan; Koroglu, Canan; MathematicsA linearly implicit nonstandard finite difference method is presented for the numerical solution of modified Korteweg-de Vries equation. Local truncation error of the scheme is discussed. Numerical examples are presented to test the efficiency and accuracy of the scheme.
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