Difference Schemes with Operator Factors:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
2002
|
| Schriftenreihe: | Mathematics and Its Applications
546 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Two- and three-level difference schemes for discretisation in time, in conjunction with finite difference or finite element approximations with respect to the space variables, are often used to solve numerically nonstationary problems of mathematical physics. In the theoretical analysis of difference schemes our basic attention is paid to the problem of stability of a difference solution (or well posedness of a difference scheme) with respect to small perturbations of the initial conditions and the right hand side. The theory of stability of difference schemes develops in various directions. The most important results on this subject can be found in the book by A.A. Samarskii and A.V. Goolin [Samarskii and Goolin, 1973]. The survey papers of V. Thomee [Thomee, 1969, Thomee, 1990], A.V. Goolin and A.A. Samarskii [Goolin and Samarskii, 1976], E. Tadmore [Tadmor, 1987] should also be mentioned here. The stability theory is a basis for the analysis of the convergence of an approximative solution to the exact solution, provided that the mesh width tends to zero. In this case the required estimate for the truncation error follows from consideration of the corresponding problem for it and from a priori estimates of stability with respect to the initial data and the right hand side. Putting it briefly, this means the known result that consistency and stability imply convergence |
| Beschreibung: | 1 Online-Ressource (X, 384 p) |
| ISBN: | 9789401598743 9789048161188 |
| DOI: | 10.1007/978-94-015-9874-3 |
Internformat
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| 245 | 1 | 0 | |a Difference Schemes with Operator Factors |c by A. A. Samarskii, P. P. Matus, P. N. Vabishchevich |
| 264 | 1 | |a Dordrecht |b Springer Netherlands |c 2002 | |
| 300 | |a 1 Online-Ressource (X, 384 p) | ||
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| 490 | 1 | |a Mathematics and Its Applications |v 546 | |
| 500 | |a Two- and three-level difference schemes for discretisation in time, in conjunction with finite difference or finite element approximations with respect to the space variables, are often used to solve numerically nonstationary problems of mathematical physics. In the theoretical analysis of difference schemes our basic attention is paid to the problem of stability of a difference solution (or well posedness of a difference scheme) with respect to small perturbations of the initial conditions and the right hand side. The theory of stability of difference schemes develops in various directions. The most important results on this subject can be found in the book by A.A. Samarskii and A.V. Goolin [Samarskii and Goolin, 1973]. The survey papers of V. Thomee [Thomee, 1969, Thomee, 1990], A.V. Goolin and A.A. Samarskii [Goolin and Samarskii, 1976], E. Tadmore [Tadmor, 1987] should also be mentioned here. The stability theory is a basis for the analysis of the convergence of an approximative solution to the exact solution, provided that the mesh width tends to zero. In this case the required estimate for the truncation error follows from consideration of the corresponding problem for it and from a priori estimates of stability with respect to the initial data and the right hand side. Putting it briefly, this means the known result that consistency and stability imply convergence | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Operator theory | |
| 650 | 4 | |a Differential equations, partial | |
| 650 | 4 | |a Computer science / Mathematics | |
| 650 | 4 | |a Partial Differential Equations | |
| 650 | 4 | |a Operator Theory | |
| 650 | 4 | |a Computational Mathematics and Numerical Analysis | |
| 650 | 4 | |a Applications of Mathematics | |
| 650 | 4 | |a Mathematical Modeling and Industrial Mathematics | |
| 650 | 4 | |a Informatik | |
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| 700 | 1 | |a Matus, P. P. |e Sonstige |4 oth | |
| 700 | 1 | |a Vabiščevič, P. N. |d ca. 20. Jht. |e Sonstige |0 (DE-588)1067604855 |4 oth | |
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Datensatz im Suchindex
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| author | Samarskij, Aleksandr A. 1919- |
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| author_facet | Samarskij, Aleksandr A. 1919- |
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| author_sort | Samarskij, Aleksandr A. 1919- |
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| bvnumber | BV042424170 |
| classification_tum | MAT 000 |
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| dewey-full | 515.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.353 |
| dewey-search | 515.353 |
| dewey-sort | 3515.353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-94-015-9874-3 |
| format | Electronic eBook |
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| id | DE-604.BV042424170 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:15Z |
| institution | BVB |
| isbn | 9789401598743 9789048161188 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027859587 |
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| spelling | Samarskij, Aleksandr A. 1919- Verfasser (DE-588)107587351 aut Difference Schemes with Operator Factors by A. A. Samarskii, P. P. Matus, P. N. Vabishchevich Dordrecht Springer Netherlands 2002 1 Online-Ressource (X, 384 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 546 Two- and three-level difference schemes for discretisation in time, in conjunction with finite difference or finite element approximations with respect to the space variables, are often used to solve numerically nonstationary problems of mathematical physics. In the theoretical analysis of difference schemes our basic attention is paid to the problem of stability of a difference solution (or well posedness of a difference scheme) with respect to small perturbations of the initial conditions and the right hand side. The theory of stability of difference schemes develops in various directions. The most important results on this subject can be found in the book by A.A. Samarskii and A.V. Goolin [Samarskii and Goolin, 1973]. The survey papers of V. Thomee [Thomee, 1969, Thomee, 1990], A.V. Goolin and A.A. Samarskii [Goolin and Samarskii, 1976], E. Tadmore [Tadmor, 1987] should also be mentioned here. The stability theory is a basis for the analysis of the convergence of an approximative solution to the exact solution, provided that the mesh width tends to zero. In this case the required estimate for the truncation error follows from consideration of the corresponding problem for it and from a priori estimates of stability with respect to the initial data and the right hand side. Putting it briefly, this means the known result that consistency and stability imply convergence Mathematics Operator theory Differential equations, partial Computer science / Mathematics Partial Differential Equations Operator Theory Computational Mathematics and Numerical Analysis Applications of Mathematics Mathematical Modeling and Industrial Mathematics Informatik Mathematik Matus, P. P. Sonstige oth Vabiščevič, P. N. ca. 20. Jht. Sonstige (DE-588)1067604855 oth Mathematics and Its Applications 546 (DE-604)BV008163334 546 https://doi.org/10.1007/978-94-015-9874-3 Verlag Volltext |
| spellingShingle | Samarskij, Aleksandr A. 1919- Difference Schemes with Operator Factors Mathematics and Its Applications Mathematics Operator theory Differential equations, partial Computer science / Mathematics Partial Differential Equations Operator Theory Computational Mathematics and Numerical Analysis Applications of Mathematics Mathematical Modeling and Industrial Mathematics Informatik Mathematik |
| title | Difference Schemes with Operator Factors |
| title_auth | Difference Schemes with Operator Factors |
| title_exact_search | Difference Schemes with Operator Factors |
| title_full | Difference Schemes with Operator Factors by A. A. Samarskii, P. P. Matus, P. N. Vabishchevich |
| title_fullStr | Difference Schemes with Operator Factors by A. A. Samarskii, P. P. Matus, P. N. Vabishchevich |
| title_full_unstemmed | Difference Schemes with Operator Factors by A. A. Samarskii, P. P. Matus, P. N. Vabishchevich |
| title_short | Difference Schemes with Operator Factors |
| title_sort | difference schemes with operator factors |
| topic | Mathematics Operator theory Differential equations, partial Computer science / Mathematics Partial Differential Equations Operator Theory Computational Mathematics and Numerical Analysis Applications of Mathematics Mathematical Modeling and Industrial Mathematics Informatik Mathematik |
| topic_facet | Mathematics Operator theory Differential equations, partial Computer science / Mathematics Partial Differential Equations Operator Theory Computational Mathematics and Numerical Analysis Applications of Mathematics Mathematical Modeling and Industrial Mathematics Informatik Mathematik |
| url | https://doi.org/10.1007/978-94-015-9874-3 |
| volume_link | (DE-604)BV008163334 |
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