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

Monika Eisenmann | Zendy; Etienne Emmrich | Zendy; Volker Mehrmann | Zendy

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

Author(s) -

Monika Eisenmann,

Etienne Emmrich,

Volker Mehrmann

Publication year - 2019

Publication title -

evolution equations and control theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.665

H-Index - 19

eISSN - 2163-2480

pISSN - 2163-2472

DOI - 10.3934/eect.2019017

Subject(s) - mathematics , hilbert space , riccati equation , operator (biology) , algebraic riccati equation , sequence (biology) , convergence (economics) , mathematical analysis , limit of a sequence , weak convergence , algebraic number , euler's formula , initial value problem , backward euler method , differential equation , euler equations , limit (mathematics) , biochemistry , chemistry , genetics , computer security , repressor , biology , economic growth , computer science , transcription factor , economics , asset (computer security) , gene

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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