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.

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 comprehensi...

Table of Contents:

• Loewy's results for ordinary differential equations
• Rings of partial differential operators
• Equations with finite-dimensional solution space
• Decomposition of second-order operators
• Solving second-order equations
• Decomposition of third-order operators
• Solving third-order equations
• Summary and conclusions
• Solutions to the exercises
• Solving Riccati equations
• The method of Laplace
• Equations with Lie symmetries.