Iterative Implicit Methods for Solving Nonlinear Dynamical Systems: Application of the Levitron
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 symplectic behavior. In comparison to explicit symplectic methods we achieve more accurate results for 5–10 iterations for only double computational time.
KeywordsSemi-implicit integrators Levitron problem Iterative Euler method Crank-Nicolson methods Symplectic splitting Long time computations
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