Iterative Implicit Methods for Solving Nonlinear Dynamical Systems: Application of the Levitron

摘要

In this paper we apply modified implicit methods for nonlinear dynamical systems related to constrained and non-separable Hamiltonian problems. The application of well-known standard Runge-Kutta integrator methods based on splitting schemes failed, while the energy conservation is no longer guaranteed. We propose a novel class of iterative implicit method that resolves the nonlinearity and achieve an asymptotic sym-plectic behavior. In comparison to explicit symplectic methods we achieve more accurate results for 5-10 iterations for only double computational time.