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Loewy Decomposition of Linear Differential Equations, PDF eBook

Loewy Decomposition of Linear Differential Equations PDF

Part of the Texts & Monographs in Symbolic Computation series

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Description

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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