Symplectic All-at-Once Method for Hamiltonian Systems

Abstract

The all-at-once technique has attracted many researchers’ interest in recent years. In this paper, we combine this technique with a classical symplectic and symmetric method for solving Hamiltonian systems. The solutions at all time steps are obtained at one-shot. In order to reduce the computational cost of solving the all-at-once system, a fast algorithm is designed. Numerical experiments of Hamiltonian systems with degrees of freedom n≤3 are provided to show that our method is more efficient than the classical symplectic method.