Formal Algorithmic Elimination for PDEs

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...

Descripción completa

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Robertz, Daniel (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cham : Springer International Publishing : Imprint: Springer, 2014.
Edición:1st ed. 2014.
Colección:Lecture Notes in Mathematics, 2121
Temas:
Algebraic fields.
Polynomials.
Commutative algebra.
Commutative rings.
Associative rings.
Associative algebras.
Differential equations.
Field Theory and Polynomials.
Commutative Rings and Algebras.
Associative Rings and Algebras.
Differential Equations.
Acceso en línea:Texto Completo

MARC

LEADER 00000nam a22000005i 4500
001 978-3-319-11445-3
003 DE-He213
005 20220112234247.0
007 cr nn 008mamaa
008 141013s2014 sz | s |||| 0|eng d
020 |a 9783319114453  |9 978-3-319-11445-3 
024 7 |a 10.1007/978-3-319-11445-3  |2 doi 
050 4 |a QA247-247.45 
050 4 |a QA161.P59 
072 7 |a PBF  |2 bicssc 
072 7 |a MAT002010  |2 bisacsh 
072 7 |a PBF  |2 thema 
082 0 4 |a 512.3  |2 23 
100 1 |a Robertz, Daniel.  |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
245 1 0 |a Formal Algorithmic Elimination for PDEs  |h [electronic resource] /  |c by Daniel Robertz. 
250 |a 1st ed. 2014. 
264 1 |a Cham :  |b Springer International Publishing :  |b Imprint: Springer,  |c 2014. 
300 |a VIII, 283 p. 6 illus., 3 illus. in color.  |b online resource. 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
347 |a text file  |b PDF  |2 rda 
490 1 |a Lecture Notes in Mathematics,  |x 1617-9692 ;  |v 2121 
505 0 |a 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. 
520 |a 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. 
650 0 |a Algebraic fields. 
650 0 |a Polynomials. 
650 0 |a Commutative algebra. 
650 0 |a Commutative rings. 
650 0 |a Associative rings. 
650 0 |a Associative algebras. 
650 0 |a Differential equations. 
650 1 4 |a Field Theory and Polynomials. 
650 2 4 |a Commutative Rings and Algebras. 
650 2 4 |a Associative Rings and Algebras. 
650 2 4 |a Differential Equations. 
710 2 |a SpringerLink (Online service) 
773 0 |t Springer Nature eBook 
776 0 8 |i Printed edition:  |z 9783319114460 
776 0 8 |i Printed edition:  |z 9783319114446 
830 0 |a Lecture Notes in Mathematics,  |x 1617-9692 ;  |v 2121 
856 4 0 |u https://doi.uam.elogim.com/10.1007/978-3-319-11445-3  |z Texto Completo 
912 |a ZDB-2-SMA 
912 |a ZDB-2-SXMS 
912 |a ZDB-2-LNM 
950 |a Mathematics and Statistics (SpringerNature-11649) 
950 |a Mathematics and Statistics (R0) (SpringerNature-43713) 

Ejemplares similares