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Formal Algorithmic Elimination for Pdes by Daniel Robertz

Formal Algorithmic Elimination for Pdes

by Daniel Robertz
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Book cover type: Paperback
  • ISBN13: 9783319114446
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Publication Date:
  • Pages: 283
  • Original Price: EUR 49.99
  • Language: English
  • Edition: 2014
  • Item Weight: 450 grams
  • BISAC Subject(s): Algebra / Abstract, Differential Equations / General, and Algebra / General

From the Back Cover

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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