3-Order Symplectic Runge-Kutta Method Based on Radau-Right Quadrature Formula

To preserve the symplecticity property of the solution flow, it is natural to search for symplectic numerical methods for Hamiltonian systems. The most important class of symplectic methods is symplectic Runge-Kutta method. Symplectic Euler method and midpoint rule are the two most widely-used symplectic Runge-Kutta methods. But the orders of the two well-known methods are not ideal. With the help of order conditions and symplecticity condition, we will propose a symplectic Runge-Kutta method based on Radau-right quadrature formula in this paper. This method is of order 3, which is higher than the well-known symplectic methods.