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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: 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]