© 2012

Loewy Decomposition of Linear Differential Equations


  • 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


Part of the Texts & Monographs in Symbolic Computation book series (TEXTSMONOGR)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Fritz Schwarz
    Pages 21-59
  3. Fritz Schwarz
    Pages 81-90
  4. Fritz Schwarz
    Pages 91-118
  5. Fritz Schwarz
    Pages 119-147
  6. Fritz Schwarz
    Pages 149-175
  7. Fritz Schwarz
    Pages 177-179
  8. Back Matter
    Pages 181-230

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.


Computer Algebra Software Differential Algebra Partial Differential Equations

Authors and affiliations

  1. 1.Institute SCAIFraunhofer GesellschaftSankt AugustinGermany

Bibliographic information


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)