Enhancing energy conserving methods
This paper is concerned with numerical methods for solving Hamiltonian problems which are energy-conserving. Since some implicit symplectic methods such as the Gauss Runge-Kutta methods suffer form instability due to resonance a new method based on the implicit midpoint rule is constructed. In this formulation, the potential energy function in the Hamiltonian system is split into two -- the strong part is then solved by an energy conserving method and the weak part by an explicit symplectic method such as \textit{L. Verlet}'s method [Computer `experiments' on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules, Phys. Rev. 159, 98-103 (1967)]. The demonstration of the stability of this approach is done numerically.
scientific article; zbMATH DE number 881188
scientific article