Exponential integrators for large-scale stiff Riccati differential equations

Riccati differential equations arise in many different areas and are particularly important within the field of control theory. In this paper we consider numerical integration for large-scale systems of stiff Riccati differential equations. We show how to apply exponential Rosenbrock-type integrators to get approximate solutions. Two typical exponential integration schemes are considered. The implementation issues are addressed and some low-rank approximations are exploited based on high quality numerical algebra codes. Numerical comparisons demonstrate that the exponential integrators can obtain high accuracy and efficiency for solving large-scale systems of stiff Riccati differential equations. (C) 2020 Elsevier B.V. All rights reserved.

Automated summary

This paper discusses numerical integration for large-scale systems of stiff Riccati differential equations using exponential Rosenbrock-type integrators, addressing implementation issues and utilizing low-rank approximations based on high quality numerical algebra codes. Numerical comparisons demonstrate the high accuracy and efficiency of exponential integrators for solving large-scale systems of stiff Riccati differential equations.