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Loewy Decomposition of Linear Differential Equations [electronic resource] / by Fritz Schwarz.

By: Schwarz, Fritz [author.].
Contributor(s): SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Texts & Monographs in Symbolic Computation, A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria: Publisher: Vienna : Springer Vienna : Imprint: Springer, 2012Description: XV, 230 p. 1 illus. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783709112861.Subject(s): Computer science | Algebra -- Data processing | Differential equations, partial | Engineering mathematics | Computer Science | Symbolic and Algebraic Manipulation | Partial Differential Equations | Appl.Mathematics/Computational Methods of EngineeringDDC classification: 005.131 Online resources: Click here to access online
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.
In: Springer eBooksSummary: 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.
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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.

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.

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