Browsing by Author "Karasoezen, B."

Now showing 1 - 3 of 3

Citation Count: 1
Multisymplectic Schemes for the Complex Modified Korteweg-De Vries Equation
(Amer inst Physics, 2008) Aydin, A.; Karasoezen, B.
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 Count: 40
Symplectic and Multi-Symplectic Methods for Coupled Nonlinear Schrodinger Equations With Periodic Solutions
(Elsevier, 2007) Aydin, A.; 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.
Citation Count: 23
Symplectic and multisymplectic Lobatto methods for the "good" Boussinesq equation
(Amer inst Physics, 2008) Aydın, Ayhan; Karasoezen, B.; Mathematics
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.