Abstract
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.
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