Formal algorithmic elimination for PDEs / Daniel Robertz
Tipo de material: TextoSeries Lecture notes in mathematics ; 2121.Detalles de publicación: Cham : Springer, 2014 Descripción: VIII, 283 p. ; 24 cmISBN: 9783319114446Tema(s): Ecuaciones en derivadas parciales | Algoritmos computacionalesResumen: 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.Tipo de ítem | Biblioteca de origen | Signatura | URL | Estado | Fecha de vencimiento | Código de barras | Reserva de ítems |
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Monografías | 02. BIBLIOTECA CAMPUS PUERTO REAL | 517.95/ROB/for (Navegar estantería(Abre debajo)) | Texto completo | Prestado | 31/01/2025 | 374419255X |
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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.
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