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Formal algorithmic elimination for PDEs / Daniel Robertz.

By: Series: Lecture notes in mathematics ; 2121Publication details: Switzerland : Springer, 2014.Description: viii, 283 p. : illustrations ; 24 cmISBN:
  • 9783319114446
Subject(s): DDC classification:
  • 512.94 23 R652
Contents:
1. Introduction -- 2. Formal Methods for PDE Systems -- 3. Differential Elimination for Analytic Functions -- A. Basic Principles and Supplementary Material -- References -- List of Algorithms -- List of Examples -- Index of Notation -- Index.
Summary: 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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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 512.94 R652 (Browse shelf(Opens below)) Available 136437
Total holds: 0

Includes bibliographical references and index.

1. Introduction --
2. Formal Methods for PDE Systems --
3. Differential Elimination for Analytic Functions --
A. Basic Principles and Supplementary Material --
References --
List of Algorithms --
List of Examples --
Index of Notation --
Index.

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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