A survey on symplectic and multi-symplectic algorithms

We simply review symplectic and multi-symplectic algorithms in the paper. These algorithms have many superiorities to general non-symplectic algorithms, such as: they have long time behavior; they can preserve the symplectic geometry structure of the Hamiltonian system exactly; and they can simulate original physical phenomena well. Some commonly used methods to construct symplectic and multi-symplectic schemes are simply surveyed. Numerical examples are also enumerated to illustrate their performances.