Hier finden Sie wissenschaftliche Publikationen aus den Fraunhofer-Instituten.

Loewy Decomposition of Linear Differential Equations

: Schwarz, Fritz

Wien: Springer, 2012, XV, 230 S.
Texts & Monographs in Symbolic Computation
ISBN: 978-3-7091-1285-4
ISBN: 3-7091-1285-0
ISBN: 978-3-7091-1286-1 (eBook)
Fraunhofer SCAI ()
Computer Algebra Software; Differential Algebra; partial differential equations

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.