Low-rank exponential integrators for stiff differential Riccati equations

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 estimat...

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Bibliographic Details
Published inAdvances in computational mathematics Vol. 51; no. 2
Main Authors Chen, Hao, Borzì, Alfio
Format Journal Article
LanguageEnglish
Published New York Springer Nature B.V 01.04.2025
Subjects
Approximation
Differential equations
Error analysis
Integrators
Mathematics
Riccati equation
Time integration
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Summary: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.
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ISSN:1019-7168
1572-9044
DOI:10.1007/s10444-025-10228-w