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Titlebook: Loewy Decomposition of Linear Differential Equations; Fritz Schwarz Book 2012 Springer-Verlag Wien 2012 Computer Algebra Software.Differen

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书目名称Loewy Decomposition of Linear Differential Equations
编辑Fritz Schwarz
视频video
概述Most advanced and most complete text on closed form solutions of linear partial differential equations.Provides more than 50 worked out examples and exercises including solutions.The results described
丛书名称Texts & Monographs in Symbolic Computation
图书封面Titlebook: Loewy Decomposition of Linear Differential Equations;  Fritz Schwarz Book 2012 Springer-Verlag Wien 2012 Computer Algebra Software.Differen
描述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.
出版日期Book 2012
关键词Computer Algebra Software; Differential Algebra; Partial Differential Equations
版次1
doihttps://doi.org/10.1007/978-3-7091-1286-1
isbn_softcover978-3-7091-1687-6
isbn_ebook978-3-7091-1286-1Series ISSN 0943-853X Series E-ISSN 2197-8409
issn_series 0943-853X
copyrightSpringer-Verlag Wien 2012
The information of publication is updating

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Equations with Finite-Dimensional Solution Space,constants. In other words, its general solution has the structure of a finite-dimensional vector space over constants like in the ordinary case. At first the Loewy decomposition of such systems in two independent variables containing derivatives of order not higher than three are discussed. Subsequently they are applied for finding its solutions.
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Solving Homogeneous Third-Order Equations,he structure of the solutions of linear pde’s on page 91 apply here as well. Similar as for second-order equations, various cases differing by leading derivatives are distinguished. As opposed to second-order equations, third-order equations have virtually never been treated in the literature before.
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