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We consider high-order splitting schemes for large-scale differential Riccatiequations. Such equations arise in many different areas and are especiallyimportant within the field of optimal control. In the large-scale case, it iscritical to employ structural properties of the matrix-valued solution, or thecomputational cost and storage requirements become infeasible. Our maincontribution is therefore to formulate these high-order splitting schemes in aefficient way by utilizing a low-rank factorization. Previous results indicatedthat this was impossible for methods of order higher than 2, but our newapproach overcomes these difficulties. In addition, we demonstrate that theproposed methods contain natural embedded error estimates. These may be usede.g. for time step adaptivity, and our numerical experiments in this directionshow promising results.

Adaptive high-order splitting schemes for large-scale differential Riccati equations