{"title":"一类中性微分方程 Runge-Kutta 方法的延迟稳定性","authors":"Zheng Wang, Yuhao Cong","doi":"10.1007/s11075-024-01846-4","DOIUrl":null,"url":null,"abstract":"<p>In this paper, a class of Runge-Kutta methods for solving neutral delay differential equations (NDDEs) is proposed, which was first introduced by Bassenne et al. (J. Comput. Phys. <b>424</b>, 109847, 2021) for ODEs. In the study, the explicit Runge-Kutta method is multiplied by an operator, which is a Time-Accurate and highly-Stable Explicit operator (TASE-RK), resulting in higher stability than explicit RK. Recently, the multi-parameter TASE-W method was extended by González-Pinto et al. (Appl. Numer. Math. <b>188</b>, 129–145, 2023). We generalized TASE-RK and TASE-W to NDDEs for the first time. Then, by applying the argument principle, sufficient conditions for delay-dependent stability of TASE-RK and TASE-W combined with Lagrange interpolation for NDDEs are investigated. Finally, numerical examples are carried out to verify the theoretical results.</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Delay-dependent stability of a class of Runge-Kutta methods for neutral differential equations\",\"authors\":\"Zheng Wang, Yuhao Cong\",\"doi\":\"10.1007/s11075-024-01846-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper, a class of Runge-Kutta methods for solving neutral delay differential equations (NDDEs) is proposed, which was first introduced by Bassenne et al. (J. Comput. Phys. <b>424</b>, 109847, 2021) for ODEs. In the study, the explicit Runge-Kutta method is multiplied by an operator, which is a Time-Accurate and highly-Stable Explicit operator (TASE-RK), resulting in higher stability than explicit RK. Recently, the multi-parameter TASE-W method was extended by González-Pinto et al. (Appl. Numer. Math. <b>188</b>, 129–145, 2023). We generalized TASE-RK and TASE-W to NDDEs for the first time. Then, by applying the argument principle, sufficient conditions for delay-dependent stability of TASE-RK and TASE-W combined with Lagrange interpolation for NDDEs are investigated. Finally, numerical examples are carried out to verify the theoretical results.</p>\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2024-05-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s11075-024-01846-4\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11075-024-01846-4","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
Delay-dependent stability of a class of Runge-Kutta methods for neutral differential equations
In this paper, a class of Runge-Kutta methods for solving neutral delay differential equations (NDDEs) is proposed, which was first introduced by Bassenne et al. (J. Comput. Phys. 424, 109847, 2021) for ODEs. In the study, the explicit Runge-Kutta method is multiplied by an operator, which is a Time-Accurate and highly-Stable Explicit operator (TASE-RK), resulting in higher stability than explicit RK. Recently, the multi-parameter TASE-W method was extended by González-Pinto et al. (Appl. Numer. Math. 188, 129–145, 2023). We generalized TASE-RK and TASE-W to NDDEs for the first time. Then, by applying the argument principle, sufficient conditions for delay-dependent stability of TASE-RK and TASE-W combined with Lagrange interpolation for NDDEs are investigated. Finally, numerical examples are carried out to verify the theoretical results.
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Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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