Periodic solutions of autonomous systems under discretization
- Bobylev, Nikolai A.
- Kloeden, Peter E.
2010 Mathematics Subject Classification
- 47H11 47H30
- autonomous ordinary differential equation, periodic solution, non-zero topological index, Hausdorff metric
The existence of a sequence of periodic trajectories of a general one-step numerical scheme corresponding to a null sequence of constant time-steps is established under the assumption that the autonomous ordinary differential equation has an isolated periodic solution with non-zero topological index. The convergence of the linearly interpolated numerical curve to the original invariant curve with respect to the Hausdorff metric is also shown.
- Numer. Funct. Anal. Optim., 18 (1997), no. 7 & 8, pp. 659-665