On the nonlinear stability of symplectic integrators
The paper deals mainly with the problem of achieving stability for symplectic numerical integrators by the mean of studying the topological equivalence of the level sets of the original Hamiltonian and those of the modified Hamiltonian associated to the numerical integrators. Using Morse theory, the authors gives criteria to detemine topological stability for integrators (in particular, there are results for Runge-Kutta and splitting methods). For non-degenerate Hamiltonians, `nonlinear stability' for integrators is defined and a simple (once given the modified Hamiltonian) analytical criterion for stability is stated. The criterion is used on Runge-Kutta and splitting algorithms for mechanical systems in one and two degree of freedom.
scientific article; zbMATH DE number 2081531