Suppression of the wrapping effect by Taylor model-based verified integrators: long-term stabilization by preconditioning. (English) Zbl 1133.65045
Summary: The verified integration of ranges of initial conditions through ordinary differential equations faces two major challenges, namely, the precise representation of the flow over the short term, and the avoidance of unfavorable buildup of errors in the long term. The Taylor model approach is very well suited to overcome the problems of short term flow representation.
In this paper we discuss a method based on preconditioning that stabilizes the long-term evolution of the flow. Examples of the performance of the method and comparisons to other approaches are given.
In this paper we discuss a method based on preconditioning that stabilizes the long-term evolution of the flow. Examples of the performance of the method and comparisons to other approaches are given.
MSC:
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 65G40 | General methods in interval analysis |
| 65G20 | Algorithms with automatic result verification |
| 34A30 | Linear ordinary differential equations and systems |
| 34A34 | Nonlinear ordinary differential equations and systems |
