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They converge towards <jats:italic>A<\/jats:italic>- or even <jats:italic>L<\/jats:italic>-stable collocation methods, but are often not sufficiently robust themselves. In this paper, a family of SDC methods inspired by an implicit formulation of the Lax\u2013Wendroff method is developed. Compared to fully implicit approaches, the methods have the advantage that they only require the solution of positive definite or semi-definite linear systems. Numerical evidence suggests that the proposed semi-implicit SDC methods with Radau points are <jats:italic>L<\/jats:italic>-stable up to order 11 and require very little diffusion for orders 13 and 15. The excellent stability and accuracy of these methods is confirmed by numerical experiments with 1D conservation problems, including the convection\u2013diffusion, Burgers, Euler and Navier\u2013Stokes equations.<\/jats:p>","DOI":"10.1007\/s10915-025-02857-6","type":"journal-article","created":{"date-parts":[[2025,3,17]],"date-time":"2025-03-17T05:31:00Z","timestamp":1742189460000},"update-policy":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Stable Semi-implicit SDC Methods for Conservation Laws"],"prefix":"10.1007","volume":"103","author":[{"ORCID":"https:\/\/2.zoppoz.workers.dev:443\/https\/orcid.org\/0000-0002-6485-3825","authenticated-orcid":false,"given":"J\u00f6rg","family":"Stiller","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,3,17]]},"reference":[{"issue":"3","key":"2857_CR1","doi-asserted-by":"publisher","first-page":"797","DOI":"10.1137\/0732037","volume":"32","author":"UM Ascher","year":"1995","unstructured":"Ascher, U.M., Ruuth, S.J., Wetton, B.: Implicit\u2013explicit methods for time-dependent partial differential equations. 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