Discretization methods for ordinary differential equations based on the use of matrix exponentials have been known for decades. This set of ideas has come off age and acquired greater urgency recently, within the context of geometric integration and discretization methods on manifolds based on the use of Lie-group actions.
No takes yet. Share an insight, caveat, or question.
Elena Celledoni (2001) studied this question.
Synapse has enriched one closely related paper. Consider it for comparative context: