{"title":"用于ode和DAEs的间隔工具","authors":"N. Nedialkov","doi":"10.1109/SCAN.2006.28","DOIUrl":null,"url":null,"abstract":"We overview the current state of interval methods and software for computing bounds on solutions in initial value problems (IVPs)for ordinary differential equations (ODEs). We introduce the VNODE-LP solver for IVP ODEs, a successor of the author's VNODE package. VNODE-LP is implemented entirely using literate programming. A major goal of the VNODE-LP work is to produce an interval solver such that its correctness can be verified by a human expert, similar to how mathematical results are certified for correctness. We also discuss the state in computing bounds on solutions in differential algebraic equations.","PeriodicalId":388600,"journal":{"name":"12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006)","volume":"25 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2006-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"108","resultStr":"{\"title\":\"Interval Tools for ODEs and DAEs\",\"authors\":\"N. Nedialkov\",\"doi\":\"10.1109/SCAN.2006.28\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We overview the current state of interval methods and software for computing bounds on solutions in initial value problems (IVPs)for ordinary differential equations (ODEs). We introduce the VNODE-LP solver for IVP ODEs, a successor of the author's VNODE package. VNODE-LP is implemented entirely using literate programming. A major goal of the VNODE-LP work is to produce an interval solver such that its correctness can be verified by a human expert, similar to how mathematical results are certified for correctness. We also discuss the state in computing bounds on solutions in differential algebraic equations.\",\"PeriodicalId\":388600,\"journal\":{\"name\":\"12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006)\",\"volume\":\"25 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2006-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"108\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SCAN.2006.28\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SCAN.2006.28","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We overview the current state of interval methods and software for computing bounds on solutions in initial value problems (IVPs)for ordinary differential equations (ODEs). We introduce the VNODE-LP solver for IVP ODEs, a successor of the author's VNODE package. VNODE-LP is implemented entirely using literate programming. A major goal of the VNODE-LP work is to produce an interval solver such that its correctness can be verified by a human expert, similar to how mathematical results are certified for correctness. We also discuss the state in computing bounds on solutions in differential algebraic equations.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
