Year: 2026
Type: preprint
Abstract: Matrix differential Riccati equation (DRE) typically exhibits transient and steady-state phases, posing challenges for fixed-step time integration methods, which may lack accuracy during transients or oversample in steady regimes. In this work, we propose adaptive low-rank matrix-valued exponential integrators for large-scale stiff DRE. The methods combine embedded exponential Rosenbrock-type schemes and adaptive step-size control, enabling an automatic adjustment to the evolving solution dynamics. This improves the accuracy during rapid transient phases while maintaining high accuracy in the steady state. Numerical experiments on benchmark problems demonstrate that the proposed adaptive integrators consistently improve accuracy and computational efficiency compared with fixed-step low-rank schemes.
Source: arXiv (Cornell University)
Authors: Li, Jinyi, Li, Dongping, Yang, Hua
Institutions: Donghua University, Changchun Normal University
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G6849811707, G88672592
OpenAlex ID: W7143543580
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