The power of the method of backward error analysis and the method of modified equations can be demonstrated in the context of geometric integrators.
It is just one of a series of results on the long-time behaviour of geometric integrators.
This example, which is hardly atypical, raises important questions regarding the basis for relying on symplecticness as a key criterion for molecular dynamics integrators.
However, as we will see below, for some classes, namely symplectic and volume-preserving polynomial vector fields, we can construct explicit polynomial integrators by splitting.
For autonomous systems, it will thus generally be preferable to use a standard variational integrator, and not to enforce exact energy conservation.
We want integrators that preserve the foliation automatically.
Improved grower/integrator relations would enhance the poultry industry.
The order of this approximation is related to the order of the resulting integrator.
