Browsing by Author "Aydin, A."

Now showing 1 - 7 of 7

Citation - WoS: 9
Lobatto IIIA-IIIB discretization of the strongly coupled nonlinear Schrodinger equation
(Elsevier Science Bv, 2011) Aydin, A.; Karasozen, B.; 01. Atılım University
In this paper, we construct a second order semi-explicit multi-symplectic integrator for the strongly coupled nonlinear Schrodinger 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. (C) 2010 Elsevier B.V. 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.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
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: 1
Multisymplectic Schemes for the Complex Modified Korteweg-De Vries Equation
(Amer inst Physics, 2008) Aydin, A.; Karasoezen, B.; 01. Atılım University
In this paper, the multisymplectic formulation of the CMKdV(complex modified Korteweg-de Vries equation) is derived. Based on the multisymplectic formulation, the eight-point multisymplectic Preissman scheme and a linear-nonlinear multisymplectic splitting scheme are developed. Both methods are compared numerically with respect to the conservation of local and global quantities of the CMKdV equation.
Citation - WoS: 1
Operator Splitting of the Kdv-Burgers Type Equation With Fast and Slow Dynamics
(Amer inst Physics, 2010) Aydin, A.; Karasozen, B.; 01. Atılım University
The Korteweg de Vries-Burgers (KdV-Burgers) type equation arising from the discretization 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.
Citation - WoS: 39
Citation - Scopus: 44
Symplectic and Multi-Symplectic Methods for Coupled Nonlinear Schrodinger Equations With Periodic Solutions
(Elsevier, 2007) Aydin, A.; Karasoezen, B.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
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.
Citation - WoS: 24
Citation - Scopus: 24
Symplectic and multisymplectic Lobatto methods for the "good" Boussinesq equation
(Amer inst Physics, 2008) Aydin, A.; Karasoezen, B.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
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: 6
An Unconventional Splitting for Korteweg de Vries-Burgers Equation
(European Journal Pure & Applied Mathematics, 2015) Aydin, A.; 01. Atılım University
Numerical 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.