Loewy Decomposition of Linear Differential Equations

  • Fritz Schwarz

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

  • Fritz Schwarz
    • 1
  1. 1.Institute SCAIFraunhofer GesellschaftSankt AugustinGermany

Bibliographic information