Texts & Monographs in Symbolic Computation

Loewy Decomposition of Linear Differential Equations

Authors: Schwarz, Fritz

  • Most advanced and most complete text on closed form solutions of linear partial differential equations 
  • Provides more than 50 worked out examples and exercises including solutions 
  • The results described in the book may be applied for determining Lie symmetries of nonlinear differential equations
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eBook $109.00
price for USA (gross)
  • ISBN 978-3-7091-1286-1
  • Digitally watermarked, DRM-free
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  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.00
price for USA
  • ISBN 978-3-7091-1285-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $139.00
price for USA
  • ISBN 978-3-7091-1687-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

The central subject of the book is the generalization of Loewy's decomposition - originally introduced by him for linear ordinary differential equations - to linear partial differential equations. Equations for a single function in two independent variables of order two or three are comprehensively discussed. A complete list of possible solution types is given. Various ad hoc results available in the literature are obtained algorithmically. The border of decidability for generating a Loewy decomposition are explicitly stated. The methods applied may be generalized in an obvious way to equations of higher order, in more variables or systems of such equations.

Reviews

From the reviews:

“This monograph pretends to describe the start point for developing a systematic way for solving linear partial differential equations (PDE’s) based on the Loewy’s decomposition method, working in an proper ring of differential operators and including algorithmic alternatives for several problems considered in classic literature. … this monograph is truly a guide book for the problem of decomposing differential operators, written in a very clear and objective language, and providing the necessary tools towards more general problems.” (Ana Rita Martins, Zentralblatt MATH, Vol. 1261, 2013)


Table of contents (8 chapters)

  • Loewy’s Results for Ordinary Differential Equations

    Schwarz, Fritz

    Pages 1-20

  • Rings of Partial Differential Operators

    Schwarz, Fritz

    Pages 21-59

  • Equations with Finite-Dimensional Solution Space

    Schwarz, Fritz

    Pages 61-79

  • Decomposition of Second-Order Operators

    Schwarz, Fritz

    Pages 81-90

  • Solving Second-Order Equations

    Schwarz, Fritz

    Pages 91-118

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-3-7091-1286-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.00
price for USA
  • ISBN 978-3-7091-1285-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $139.00
price for USA
  • ISBN 978-3-7091-1687-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Loewy Decomposition of Linear Differential Equations
Authors
Series Title
Texts & Monographs in Symbolic Computation
Copyright
2012
Publisher
Springer-Verlag Wien
Copyright Holder
Springer-Verlag Wien
eBook ISBN
978-3-7091-1286-1
DOI
10.1007/978-3-7091-1286-1
Hardcover ISBN
978-3-7091-1285-4
Softcover ISBN
978-3-7091-1687-6
Series ISSN
0943-853X
Edition Number
1
Number of Pages
XVI, 232
Topics