{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,23]],"date-time":"2025-07-23T12:00:11Z","timestamp":1753272011192},"reference-count":18,"publisher":"American Mathematical Society (AMS)","issue":"351","license":[{"start":{"date-parts":[[2025,3,28]],"date-time":"2025-03-28T00:00:00Z","timestamp":1743120000000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/100000015","name":"U.S. Department of Energy","doi-asserted-by":"publisher","award":["DE-SC0023164","FA9550-21-1-0358","883363"],"award-info":[{"award-number":["DE-SC0023164","FA9550-21-1-0358","883363"]}],"id":[{"id":"10.13039\/100000015","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>Implicit-explicit Runge-Kutta (IMEX-RK) schemes are popular methods to treat multiscale equations that contain a stiff part and a non-stiff part, where the stiff part is characterized by a small parameter <inline-formula content-type=\"math\/mathml\">\n<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"epsilon\">\n  <mml:semantics>\n    <mml:mi>\u03b5<\/mml:mi>\n    <mml:annotation encoding=\"application\/x-tex\">\\varepsilon<\/mml:annotation>\n  <\/mml:semantics>\n<\/mml:math>\n<\/inline-formula>. In this work, we prove rigorously the uniform stability and uniform accuracy of a class of IMEX-RK schemes for a linear hyperbolic system with stiff relaxation. The result we obtain is optimal in the sense that it holds regardless of the value of <inline-formula content-type=\"math\/mathml\">\n<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"epsilon\">\n  <mml:semantics>\n    <mml:mi>\u03b5<\/mml:mi>\n    <mml:annotation encoding=\"application\/x-tex\">\\varepsilon<\/mml:annotation>\n  <\/mml:semantics>\n<\/mml:math>\n<\/inline-formula> and the order of accuracy is the same as the design order of the original scheme, i.e., there is no order reduction.<\/p>","DOI":"10.1090\/mcom\/3967","type":"journal-article","created":{"date-parts":[[2024,3,13]],"date-time":"2024-03-13T20:40:04Z","timestamp":1710362404000},"page":"209-240","source":"Crossref","is-referenced-by-count":2,"title":["Uniform accuracy of implicit-explicit Runge-Kutta (IMEX-RK) schemes for hyperbolic systems with relaxation"],"prefix":"10.1090","volume":"94","author":[{"given":"Jingwei","family":"Hu","sequence":"first","affiliation":[]},{"given":"Ruiwen","family":"Shu","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2024,3,28]]},"reference":[{"issue":"4","key":"1","doi-asserted-by":"publisher","first-page":"A2402--A2435","DOI":"10.1137\/19M1303290","article-title":"Implicit-explicit multistep methods for hyperbolic systems with multiscale relaxation","volume":"42","author":"Albi, Giacomo","year":"2020","journal-title":"SIAM J. 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