# Exponential integrators for large-scale stiff matrix Riccati differential equations

## TL;DR

This paper introduces exponential Rosenbrock-type integrators for efficiently solving large-scale stiff matrix Riccati differential equations, demonstrating high accuracy and computational efficiency through numerical comparisons.

## Contribution

It presents novel application of exponential integrators to large-scale stiff matrix Riccati equations, including implementation strategies and low-rank approximation techniques.

## Key findings

- Exponential integrators achieve high accuracy for large-scale problems.
- The methods are computationally efficient compared to traditional approaches.
- Numerical results confirm the effectiveness of the proposed schemes.

## Abstract

Matrix Riccati differential equations arise in many different areas and are particular important within the field of control theory. In this paper we consider numerical integration for large-scale systems of stiff matrix 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 matrix Riccati differential equations.