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Loewy Decomposition of Linear Differential Equations / by Fritz Schwarz.
- Format:
- Book
- Author/Creator:
- Schwarz, Fritz, 1941- author.
- Series:
- Computer Science (Springer-11645)
- Texts & Monographs in Symbolic Computation, A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria,. 0943-853X
- Texts & Monographs in Symbolic Computation, A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria, 0943-853X
- Language:
- English
- Subjects (All):
- Computer science--Mathematics.
- Computer science.
- Differential equations, Partial.
- Applied mathematics.
- Engineering mathematics.
- Symbolic and Algebraic Manipulation.
- Partial Differential Equations.
- Mathematical and Computational Engineering.
- Local Subjects:
- Symbolic and Algebraic Manipulation.
- Partial Differential Equations.
- Mathematical and Computational Engineering.
- Physical Description:
- 1 online resource (XVI, 232 pages).
- Edition:
- First edition 2012.
- Contained In:
- Springer eBooks
- Place of Publication:
- Vienna : Springer Vienna : Imprint: Springer, 2012.
- System Details:
- text file PDF
- Summary:
- 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.
- 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.
- Other Format:
- Printed edition:
- ISBN:
- 978-3-7091-1286-1
- 9783709112861
- Access Restriction:
- Restricted for use by site license.
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