Diagonal implicit symplectic ERKN methods for solving oscillatory Hamiltonian systems
For researchers solving oscillatory Hamiltonian systems, this provides new symplectic integrators with improved stability and accuracy.
The paper constructs diagonal implicit symplectic ERKN methods for oscillatory Hamiltonian systems and demonstrates their remarkable numerical behavior through three experiments.
This paper studies diagonal implicit symplectic extended Runge--Kutta--Nyström (ERKN) methods for solving the oscillatory Hamiltonian system $H(q,p)=\dfrac{1}{2}p^{T}p+\dfrac{1}{2}q^{T}Mq+U(q)$. Based on symplectic conditions and order conditions, we construct some diagonal implicit symplectic ERKN methods. The stability of the obtained methods is discussed. Three numerical experiments are carried out and the numerical results demonstrate the remarkable numerical behavior of the new diagonal implicit symplectic methods when applied to the oscillatory Hamiltonian system.