Well-Posedness of Parabolic Difference Equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
1994
|
| Schriftenreihe: | Operator Theory Advances and Applications
69 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | A well-known and widely applied method of approximating the solutions of problems in mathematical physics is the method of difference schemes. Modern computers allow the implementation of highly accurate ones; hence, their construction and investigation for various boundary value problems in mathematical physics is generating much current interest. The present monograph is devoted to the construction of highly accurate difference schemes for parabolic boundary value problems, based on Padé approximations. The investigation is based on a new notion of positivity of difference operators in Banach spaces, which allows one to deal with difference schemes of arbitrary order of accuracy. Establishing coercivity inequalities allows one to obtain sharp, that is, two-sided estimates of convergence rates. The proofs are based on results in interpolation theory of linear operators. This monograph will be of value to professional mathematicians as well as advanced students interested in the fields of functional analysis and partial differential equations |
| Beschreibung: | 1 Online-Ressource (XIV, 353 p) |
| ISBN: | 9783034885188 9783034896610 |
| DOI: | 10.1007/978-3-0348-8518-8 |
Internformat
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Datensatz im Suchindex
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| any_adam_object | |
| author | Ashyralyev, A. |
| author_facet | Ashyralyev, A. |
| author_role | aut |
| author_sort | Ashyralyev, A. |
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| building | Verbundindex |
| bvnumber | BV042422148 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)869865160 (DE-599)BVBBV042422148 |
| dewey-full | 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
| dewey-search | 515 |
| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-0348-8518-8 |
| format | Electronic eBook |
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| id | DE-604.BV042422148 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:10Z |
| institution | BVB |
| isbn | 9783034885188 9783034896610 |
| language | English |
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| physical | 1 Online-Ressource (XIV, 353 p) |
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| publishDate | 1994 |
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| publisher | Birkhäuser Basel |
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| series2 | Operator Theory Advances and Applications |
| spelling | Ashyralyev, A. Verfasser aut Well-Posedness of Parabolic Difference Equations by A. Ashyralyev, P. E. Sobolevskii Basel Birkhäuser Basel 1994 1 Online-Ressource (XIV, 353 p) txt rdacontent c rdamedia cr rdacarrier Operator Theory Advances and Applications 69 A well-known and widely applied method of approximating the solutions of problems in mathematical physics is the method of difference schemes. Modern computers allow the implementation of highly accurate ones; hence, their construction and investigation for various boundary value problems in mathematical physics is generating much current interest. The present monograph is devoted to the construction of highly accurate difference schemes for parabolic boundary value problems, based on Padé approximations. The investigation is based on a new notion of positivity of difference operators in Banach spaces, which allows one to deal with difference schemes of arbitrary order of accuracy. Establishing coercivity inequalities allows one to obtain sharp, that is, two-sided estimates of convergence rates. The proofs are based on results in interpolation theory of linear operators. This monograph will be of value to professional mathematicians as well as advanced students interested in the fields of functional analysis and partial differential equations Mathematics Global analysis (Mathematics) Numerical analysis Analysis Numerical Analysis Theoretical, Mathematical and Computational Physics Mathematik Differenzengleichung (DE-588)4012264-5 gnd rswk-swf Parabolische Differentialgleichung (DE-588)4173245-5 gnd rswk-swf Padé-Näherung (DE-588)4173060-4 gnd rswk-swf Parabolisches Randwertproblem (DE-588)4319434-5 gnd rswk-swf Differenzenverfahren (DE-588)4134362-1 gnd rswk-swf Parabolisches Randwertproblem (DE-588)4319434-5 s Differenzengleichung (DE-588)4012264-5 s Padé-Näherung (DE-588)4173060-4 s 1\p DE-604 Parabolische Differentialgleichung (DE-588)4173245-5 s Differenzenverfahren (DE-588)4134362-1 s 2\p DE-604 Sobolevskii, P. E. Sonstige oth https://doi.org/10.1007/978-3-0348-8518-8 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Ashyralyev, A. Well-Posedness of Parabolic Difference Equations Mathematics Global analysis (Mathematics) Numerical analysis Analysis Numerical Analysis Theoretical, Mathematical and Computational Physics Mathematik Differenzengleichung (DE-588)4012264-5 gnd Parabolische Differentialgleichung (DE-588)4173245-5 gnd Padé-Näherung (DE-588)4173060-4 gnd Parabolisches Randwertproblem (DE-588)4319434-5 gnd Differenzenverfahren (DE-588)4134362-1 gnd |
| subject_GND | (DE-588)4012264-5 (DE-588)4173245-5 (DE-588)4173060-4 (DE-588)4319434-5 (DE-588)4134362-1 |
| title | Well-Posedness of Parabolic Difference Equations |
| title_auth | Well-Posedness of Parabolic Difference Equations |
| title_exact_search | Well-Posedness of Parabolic Difference Equations |
| title_full | Well-Posedness of Parabolic Difference Equations by A. Ashyralyev, P. E. Sobolevskii |
| title_fullStr | Well-Posedness of Parabolic Difference Equations by A. Ashyralyev, P. E. Sobolevskii |
| title_full_unstemmed | Well-Posedness of Parabolic Difference Equations by A. Ashyralyev, P. E. Sobolevskii |
| title_short | Well-Posedness of Parabolic Difference Equations |
| title_sort | well posedness of parabolic difference equations |
| topic | Mathematics Global analysis (Mathematics) Numerical analysis Analysis Numerical Analysis Theoretical, Mathematical and Computational Physics Mathematik Differenzengleichung (DE-588)4012264-5 gnd Parabolische Differentialgleichung (DE-588)4173245-5 gnd Padé-Näherung (DE-588)4173060-4 gnd Parabolisches Randwertproblem (DE-588)4319434-5 gnd Differenzenverfahren (DE-588)4134362-1 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Numerical analysis Analysis Numerical Analysis Theoretical, Mathematical and Computational Physics Mathematik Differenzengleichung Parabolische Differentialgleichung Padé-Näherung Parabolisches Randwertproblem Differenzenverfahren |
| url | https://doi.org/10.1007/978-3-0348-8518-8 |
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