Low-rank exponential integrators for stiff differential Riccati equations

Abstract

Exponential integrators are an efficient alternative to implicit schemes for the time integration of stiff system of differential equations. In this paper, low-rank exponential integrators of orders one and two for stiff differential Riccati equations are proposed and investigated. The error estimates of the proposed schemes are established. The proposed approach allows to overcome the main difficulties that lay in the interplay of time integration and low-rank approximation in the numerical schemes, which is uncommon in standard discretization of differential equations. Results of numerical experiments demonstrate the validity of the convergence analysis and show the performance of the proposed low-rank approximations with different settings.