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Journal of Scientific Computing
Published in: Journal of Scientific Computing 2/2023

01-08-2023

Positivity Preserving Exponential Integrators for Differential Riccati Equations

Authors: Hao Chen, Alfio Borzì

Published in: Journal of Scientific Computing | Issue 2/2023

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Abstract

A large class of differential Riccati equations (DREs) satisfy positivity property in the sense that the time-dependent solution preserves for any time its symmetric and positive semidefinite structure. This positivity property plays a crucial role in understanding the wellposedness of the DRE, and whether it could be inherited in the discrete level is a significant issue in numerical simulations. In this paper, we study positivity preserving time integration schemes by means of exponential integrators. The proposed exponential Euler and exponential midpoint schemes are linear and proven to be positivity preserving and unconditionally stable. Sharp error estimates of the schemes are also obtained. Numerical experiments are carried out to illustrate the performance of the proposed integrators.
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Metadata
Title
Positivity Preserving Exponential Integrators for Differential Riccati Equations
Authors
Hao Chen
Alfio Borzì
Publication date
01-08-2023
Publisher
Springer US
Published in
Journal of Scientific Computing / Issue 2/2023
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI
https://doi.org/10.1007/s10915-023-02275-6

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