Loewy Decomposition of Linear Differential Equations

• Main Author: Schwarz, Fritz (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Vienna : Springer Vienna : Imprint: Springer, 2012.
• Series: Texts & Monographs in Symbolic Computation, A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria,
• Subjects: Computer science.; Computer science > Mathematics.; Partial differential equations.; Applied mathematics.; Engineering mathematics.; Computer Science.; Symbolic and Algebraic Manipulation.; Partial Differential Equations.; Appl.Mathematics/Computational Methods of Engineering.
• Physical Description: XVI, 232 p. online resource.
• ISBN: 9783709112861
• ISSN: 0943-853X

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.