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Randomised one-step time integration methods for deterministic operator differential equations
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Lie, Han Cheng, Stahn, Martin and Sullivan, T. J. (2022) Randomised one-step time integration methods for deterministic operator differential equations. Calcolo, 59 (1). 13. doi:10.1007/s10092-022-00457-6 ISSN 0008-0624.
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Official URL: http://dx.doi.org/10.1007/s10092-022-00457-6
Abstract
Uncertainty quantification plays an important role in problems that involve inferring a parameter of an initial value problem from observations of the solution. Conrad et al. (Stat Comput 27(4):1065–1082, 2017) proposed randomisation of deterministic time integration methods as a strategy for quantifying uncertainty due to the unknown time discretisation error. We consider this strategy for systems that are described by deterministic, possibly time-dependent operator differential equations defined on a Banach space or a Gelfand triple. Our main results are strong error bounds on the random trajectories measured in Orlicz norms, proven under a weaker assumption on the local truncation error of the underlying deterministic time integration method. Our analysis establishes the theoretical validity of randomised time integration for differential equations in infinite-dimensional settings.
| Item Type: | Journal Article | ||||||
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| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Engineering > Engineering Faculty of Science, Engineering and Medicine > Science > Mathematics |
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| Library of Congress Subject Headings (LCSH): | Differential equations , Numerical analysis , Random dynamical systems | ||||||
| Journal or Publication Title: | Calcolo | ||||||
| Publisher: | Springer | ||||||
| ISSN: | 0008-0624 | ||||||
| Official Date: | 25 February 2022 | ||||||
| Dates: |
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| Volume: | 59 | ||||||
| Number: | 1 | ||||||
| Article Number: | 13 | ||||||
| DOI: | 10.1007/s10092-022-00457-6 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||
| Date of first compliant deposit: | 28 February 2022 | ||||||
| Date of first compliant Open Access: | 28 February 2022 | ||||||
| RIOXX Funder/Project Grant: |
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