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Positivity Preserving Exponential Integrators for Differential Riccati Equations


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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The work of Hao Chen was partly supported by the Natural Science Foundation Project of CQ CSTC (No. cstc2021jcyj-msxmX0034). The work of Alfio Borzì was partly supported by the BMBF-Project iDeLIVER : Intelligent MR Diagnosis of the Liver by Linking Model and Data-driven Processes.

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Chen, H., Borzì, A. Positivity Preserving Exponential Integrators for Differential Riccati Equations. J Sci Comput 96, 50 (2023).

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