Loewy Decomposition of Linear Differential Equations (häftad)
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Format
Häftad (Paperback / softback)
Språk
Engelska
Antal sidor
232
Utgivningsdatum
2014-10-15
Upplaga
2012 ed.
Förlag
Springer Verlag GmbH
Illustrationer
XVI, 232 p.
Dimensioner
234 x 156 x 13 mm
Vikt
354 g
Antal komponenter
1
Komponenter
1 Paperback / softback
ISBN
9783709116876

Loewy Decomposition of Linear Differential Equations

av Fritz Schwarz
Häftad,  Engelska, 2014-10-15
1136
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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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From the reviews: This monograph pretends to describe the start point for developing a systematic way for solving linear partial differential equations (PDEs) based on the Loewys decomposition method, working in an proper ring of differential operators and including algorithmic alternatives for several problems considered in classic literature. this monograph is truly a guide book for the problem of decomposing differential operators, written in a very clear and objective language, and providing the necessary tools towards more general problems. (Ana Rita Martins, Zentralblatt MATH, Vol. 1261, 2013)

Innehållsförteckning

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.

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