Application of a Fourth-Order Optimal Gradient Symplectic Integrator

Symplectic integrators are suitable for an autonomous Hamiltonian system which can be split into two integrable parts of kinetic and potential energies. Compared with several of existed fourth-order symplectic integrators, the fourth-order optimal gradient symplectic integrator is better in the aspect of precision of relative energy computation, so it is used as a basic numerical tool in a two-dimensional nonlinear oscillator. Based on high accuracy value of position and velocity provided by the fourth-order optimal gradient symplectic integrator, Poincare sections and the Fast Lyapunov Indicator (FLI) are used to describe the transition from regular motion to chaos of the model.