Formal Algorithmic Elimination for PDEs / by Daniel Robertz
| データ種別 | 電子書籍 |
|---|---|
| 出版者 | Cham : Springer International Publishing : Imprint: Springer |
| 出版年 | 2014 |
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| 書誌ID | OB01024697 |
|---|---|
| 本文言語 | 英語 |
| 一般注記 | Introduction -- Formal Methods for PDE Systems -- Differential Elimination for Analytic Functions -- Basic Principles and Supplementary Material -- References -- List of Algorithms -- List of Examples -- Index of Notation -- Index. License restrictions may limit access Summary: Investigating the correspondence between systems of partial differential equations and their analytic solutions using a formal approach, this monograph presents algorithms to determine the set of analytic solutions of such a system and conversely to find differential equations whose set of solutions coincides with a given parametrized set of analytic functions. After giving a detailed introduction to Janet bases and Thomas decomposition, the problem of finding an implicit description of certain sets of analytic functions in terms of differential equations is addressed. Effective methods of varying generality are developed to solve the differential elimination problems that arise in this context. In particular, it is demonstrated how the symbolic solution of partial differential equations profits from the study of the implicitization problem. For instance, certain families of exact solutions of the Navier-Stokes equations can be computed |
| 著者標目 | *Robertz, Daniel SpringerLink (Online service) |
| 統一書名標目 | Lecture Notes in Mathematics, |
| 件 名 | LCSH:Mathematics LCSH:Algebra LCSH:Field theory (Physics) LCSH:Differential equations, partial FREE:Mathematics FREE:Field Theory and Polynomials FREE:Commutative Rings and Algebras FREE:Associative Rings and Algebras FREE:Partial Differential Equations |
| 分 類 | LCC:QA161.A-161.Z LCC:QA161.P59 DC23:512.3 |
| 巻冊次 | ISBN:9783319114453 RefWorks出力（各巻） print ; ISBN:9783319114446 RefWorks出力（各巻） |
| 資料種別 | 機械可読データファイル |
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