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The proposed methods iteratively construct a probability distribution over the solution of deterministic problems, enhancing the information obtained from the numerical simulation. Within this paper, we examine the efficacy of the randomized versions of the implicit Euler method, the midpoint scheme, and exponential integrators of first and second order. By demonstrating the consistency and convergence properties of these solvers, we illustrate their utility in capturing the sensitivity of the solution to numerical errors. Our analysis establishes the theoretical validity of randomized time integration for constrained systems and offers insights into the calibration of probabilistic integrators for practical applications.<\/jats:p>","DOI":"10.1007\/s11222-024-10543-0","type":"journal-article","created":{"date-parts":[[2024,12,16]],"date-time":"2024-12-16T03:48:08Z","timestamp":1734320888000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Probabilistic time integration for semi-explicit PDAEs"],"prefix":"10.1007","volume":"35","author":[{"given":"R.","family":"Altmann","sequence":"first","affiliation":[]},{"given":"A.","family":"Moradi","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,12,16]]},"reference":[{"issue":"4","key":"10543_CR1","doi-asserted-by":"publisher","first-page":"907","DOI":"10.1007\/s11222-020-09926-w","volume":"30","author":"A Abdulle","year":"2020","unstructured":"Abdulle, A., Garegnani, G.: Random time step probabilistic methods for uncertainty quantification in chaotic and geometric numerical integration. 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