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

1998-01-01
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.
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS

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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.