Symplectic Effect for the Numerical Solution of Conservative Systems

The focus of this paper is to use those numerical tools for conservative systems that provides an approximation flow for the Hamiltonian system, which defines a worldwide physical systems including planetary motion, simple Pendulum and several models. It has been observed that the symplectic scheme is found very effective for astronomical many body systems. We are particularly interested in those numerical schemes that possess the qualitative behavior of such systems and symplecticity of the flow. In this paper, we investigate the Hamiltonian systems for its symplecticity and G-symplecticity numerically and show explicitly how these techniques be effective for the preservation of energy. Since we have applied this scheme for the planetary body motion and found that the results are very much effective and the energy preserves during the motion of the planetary bodies. Since the aim of this paper is to investigate the energy preservation adopted by the symplectic methods.