Convergence of the backward Euler scheme for the operator-valued Riccati differential equation with semi-definite data

Monika Eisenmann; Etienne Emmrich; Volker Mehrmann

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arXiv · 1803.11152

Convergence of the backward Euler scheme for the operator-valued Riccati differential equation with semi-definite data

Monika Eisenmann·Etienne Emmrich·Volker Mehrmann

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Abstract

For initial value problems associated with operator-valued Riccati differential equations posed in the space of Hilbert--Schmidt operators existence of solutions is studied. An existence result known for algebraic Riccati equations is generalized and used to obtain the existence of a solution to the approximation of the problem via a backward Euler scheme. Weak and strong convergence of the sequence of approximate solutions is established permitting a large class of right-hand sides and initial data.

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Monika Eisenmann, Etienne Emmrich, Volker Mehrmann. 2018-03-29. Convergence of the backward Euler scheme for the operator-valued Riccati differential equation with semi-definite data. https://arxiv.org/abs/1803.11152

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