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＜電子ブック＞
Formal Algorithmic Elimination for PDEs / by Daniel Robertz
(Lecture Notes in Mathematics. ISSN:16179692 ; 2121)

版	1st ed. 2014.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2014
本文言語	英語
大きさ	VIII, 283 p. 6 illus., 3 illus. in color : online resource
著者標目	*Robertz, Daniel author SpringerLink (Online service)
件　名	LCSH:Algebraic fields LCSH:Polynomials LCSH:Commutative algebra LCSH:Commutative rings LCSH:Associative rings LCSH:Associative algebras LCSH:Differential equations FREE:Field Theory and Polynomials FREE:Commutative Rings and Algebras FREE:Associative Rings and Algebras FREE:Differential Equations
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 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 HTTP:URL=https://doi.org/10.1007/978-3-319-11445-3

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