Formal algorithmic elimination for PDEs [electronic resource] / Daniel Robertz.

Formal algorithmic elimination for PDEs [electronic resource] / Daniel Robertz.

9783319114446
3319114441
9783319114453 electronic book
331911445X electronic book

Cham [Switzerland] : Springer, [2014]

English

1 online resource (viii, 283 pages) : illustrations

QA192 .R62 2014eb

512.9/4

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.

Includes bibliographical references and index.

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Description based on online resource; title from PDF title page (SpringerLink, viewed October 23, 2014)

Lecture notes in mathematics (Springer-Verlag) ; 2121.

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