Runge-Kutta methods for Hamiltonian systems in non-standard symplectic two-form

Date

1998-01-01

Author

Karasözen, Bülent

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Runge-Kutta methods are applied to Hamiltonian systems on Poisson manifolds with a nonstandard symplectic two-form. It has been shown that the Gauss Legendre Runge-Kutta (GLRK) methods and combination of the partitioned Runge-Rutta methods of Lobatto IIIA and IIIb type are symplectic up to the second order in terms of the step size. Numerical results on Lotka-Volterra and Kermack-McKendrick epidemic disease model reveals that the application of the symplectic Runge-Kutta methods preserves the integral invariants of the underlying system for long-time computations.

Subject Keywords

Hamiltonian equations, Poisson manifolds, Symplectic two-forms, Symplectic Runge-Kutta methods, Lotka-Volterra equations, Epidemic models

URI

https://hdl.handle.net/11511/32122

Journal

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS

DOI

https://doi.org/10.1080/00207169808804629

Collections

Graduate School of Applied Mathematics, Article

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Citation Formats

B. Karasözen, “Runge-Kutta methods for Hamiltonian systems in non-standard symplectic two-form,” INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, pp. 113–122, 1998, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/32122.