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.
- Mathematics, Computers + Internet
- Applied, Data Processing/General, Differential Equations
- Springer-Verlag New York Inc
- July 16, 2012
- September 29, 2012
- Fritz Schwarz