Diagonally Implicit Symplectic Runge-Kutta Methods with High Algebraic and Dispersion Order

Abstract EN

The numerical integration of Hamiltonian systems with oscillating solutions is considered in this paper.

A diagonally implicit symplectic nine-stages Runge-Kutta method with algebraic order 6 and dispersion order 8 is presented.

Numerical experiments with some Hamiltonian oscillatory problems are presented to show the proposed method is as competitive as the existing same type Runge-Kutta methods.