Loewy Decomposition of Linear Differential Equations

• Κύριος συγγραφέας: Schwarz, Fritz (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Vienna : Springer Vienna : Imprint: Springer, 2012.
• Σειρά: Texts & Monographs in Symbolic Computation, A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria,
• Θέματα: 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 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. 

 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.