Well-posed, Ill-posed, and Intermediate Problems with Applications
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| Title: | Well-posed, Ill-posed, and Intermediate Problems with Applications |
|---|---|
| Description: | This book deals with one of the key problems in applied mathematics, namely the investigation into and providing for solution stability in solving equations with due allowance for inaccuracies in set initial data, parameters and coefficients of a mathematical model for an object under study, instrumental function, initial conditions, etc., and also with allowance for miscalculations, including roundoff errors. Until recently, all problems in mathematics, physics and engineering were divided into two classes: well-posed problems and ill-posed problems. The authors introduce a third class of problems: intermediate ones, which are problems that change their property of being well- or ill-posed on equivalent transformations of governing equations, and also problems that display the property of being either well- or ill-posed depending on the type of the functional space used. The book is divided into two parts: Part one deals with general properties of all three classes of mathematical, physical and engineering problems with approaches to solve them; Part two deals with several stable models for solving inverse ill-posed problems, illustrated with numerical examples. |
| Authors: | Petrov Yuri P., Valery S. Sizikov |
| Resource Type: | eBook. |
| Subjects: | Differential equations--Numerical solutions, Numerical analysis--Improperly posed problems, Engineering mathematics, Mathematical physics |
| Categories: | MATHEMATICS / Mathematical Analysis, MATHEMATICS / Applied |
| Database: | eBook Collection (EBSCOhost) |
| FullText | Links: – Type: ebook-pdf Text: Availability: 0 |
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| Header | DbId: nlebk DbLabel: eBook Collection (EBSCOhost) An: 174017 RelevancyScore: 998 AccessLevel: 6 PubType: eBook PubTypeId: ebook PreciseRelevancyScore: 998.4384765625 |
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| Items | – Name: Title Label: Title Group: Ti Data: Well-posed, Ill-posed, and Intermediate Problems with Applications – Name: Abstract Label: Description Group: Ab Data: This book deals with one of the key problems in applied mathematics, namely the investigation into and providing for solution stability in solving equations with due allowance for inaccuracies in set initial data, parameters and coefficients of a mathematical model for an object under study, instrumental function, initial conditions, etc., and also with allowance for miscalculations, including roundoff errors. Until recently, all problems in mathematics, physics and engineering were divided into two classes: well-posed problems and ill-posed problems. The authors introduce a third class of problems: intermediate ones, which are problems that change their property of being well- or ill-posed on equivalent transformations of governing equations, and also problems that display the property of being either well- or ill-posed depending on the type of the functional space used. The book is divided into two parts: Part one deals with general properties of all three classes of mathematical, physical and engineering problems with approaches to solve them; Part two deals with several stable models for solving inverse ill-posed problems, illustrated with numerical examples. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Petrov+Yuri+P%2E%22">Petrov Yuri P.</searchLink><br /><searchLink fieldCode="AR" term="%22Valery+S%2E+Sizikov%22">Valery S. Sizikov</searchLink> – Name: TypePub Label: Resource Type Group: TypPub Data: eBook. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Differential+equations--Numerical+solutions%22">Differential equations--Numerical solutions</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis--Improperly+posed+problems%22">Numerical analysis--Improperly posed problems</searchLink><br /><searchLink fieldCode="DE" term="%22Engineering+mathematics%22">Engineering mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+physics%22">Mathematical physics</searchLink> – Name: SubjectBISAC Label: Categories Group: Su Data: <searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Mathematical+Analysis%22">MATHEMATICS / Mathematical Analysis</searchLink><br /><searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Applied%22">MATHEMATICS / Applied</searchLink> |
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| RecordInfo | BibRecord: BibEntity: Classifications: – Code: 518.6 Scheme: ddc Type: prePub Languages: – Code: eng Text: English Subjects: – SubjectFull: Differential equations--Numerical solutions Type: general – SubjectFull: Numerical analysis--Improperly posed problems Type: general – SubjectFull: Engineering mathematics Type: general – SubjectFull: Mathematical physics Type: general Titles: – TitleFull: Well-posed, Ill-posed, and Intermediate Problems with Applications Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Petrov Yuri P. – PersonEntity: Name: NameFull: Valery S. Sizikov – PersonEntity: Name: NameFull: Petrov Yuri P. – PersonEntity: Name: NameFull: Valery S. Sizikov IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Type: published Y: 2005 – D: 04 M: 02 Type: profile Y: 2014 Identifiers: – Type: isbn-print Value: 9789067644327 – Type: isbn-electronic Value: 9783110195309 Numbering: – Type: volume Value: 00049 Titles: – TitleFull: Well-posed, Ill-posed, and Intermediate Problems with Applications Type: main |
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