A Note on Construction of Higher-Order Symplectic Schemes from Lower-Order One via Formal Energies

Abstract

In this paper, we will prove by the help of formal energies only that one can improve the order of any symplectic scheme by modifying the Hamiltonian symbol $H$, and show through examples that this action exactly and directly simplifies Feng's way of construction of higher-order symplectic schemes by using higher-order terms of generating functions.