{"title":"后向欧拉多速率公式的稳定性","authors":"S. Skelboe","doi":"10.1137/0910059","DOIUrl":null,"url":null,"abstract":"Stability properties of multirate formulas cannot be analyzed by a scalar test equation but require at least one equation for each different steplength. This paper generalizes the concept of absolute stability and A-stability for backward Euler multirate formulas. Stability theorems for multirate methods with two and three different steplengths are given, while a general result for an arbitrary number of different steplengths is the topic of future research.","PeriodicalId":200176,"journal":{"name":"Siam Journal on Scientific and Statistical Computing","volume":"10 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1989-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"36","resultStr":"{\"title\":\"Stability properties of backward euler multirate formulas\",\"authors\":\"S. Skelboe\",\"doi\":\"10.1137/0910059\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Stability properties of multirate formulas cannot be analyzed by a scalar test equation but require at least one equation for each different steplength. This paper generalizes the concept of absolute stability and A-stability for backward Euler multirate formulas. Stability theorems for multirate methods with two and three different steplengths are given, while a general result for an arbitrary number of different steplengths is the topic of future research.\",\"PeriodicalId\":200176,\"journal\":{\"name\":\"Siam Journal on Scientific and Statistical Computing\",\"volume\":\"10 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1989-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"36\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Siam Journal on Scientific and Statistical Computing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1137/0910059\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Siam Journal on Scientific and Statistical Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1137/0910059","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Stability properties of backward euler multirate formulas
Stability properties of multirate formulas cannot be analyzed by a scalar test equation but require at least one equation for each different steplength. This paper generalizes the concept of absolute stability and A-stability for backward Euler multirate formulas. Stability theorems for multirate methods with two and three different steplengths are given, while a general result for an arbitrary number of different steplengths is the topic of future research.
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