MGPS: Midpoint-Series Group Preserving Scheme for Discretizing Nonlinear Dynamics

Abstract

In this article, we propose a new computational method for initial value problems in ordinary differential equations. The algorithm combines the merits of the group preserving scheme (GPS), which has the ability of avoiding possible spurious solutions utilizing the inherent symmetry group, the cone structure of the nonlinear dynamical system, and the classic midpoint rule. The error and stability analysis are included to demonstrate the convergence properties of the presented method. From the numerical experimental results we obtained, the algorithm can be said to be computationally effective and possesses better simulation ability generally. Meanwhile, it works well with the periodic Hamiltonian system.

Keywords

• hybrid systems
• ODEs
• group preserving scheme
• midpoint rule
• symmetry group
• MGPS