Springer Loewy Decomposition of Linear Differential Equations (Texts & Monographs in Symbolic Computation)

As the most complete text on closed form solutions of linear partial differential equations, this book’s coverage of the generalization of Loewy's decomposition includes more than fifty worked out examples and exercises in addition to their solutions. Review From the reviews: “This monograph pretends to describe the start point for developing a systematic way for solving linear partial differential equations (PDE’s) based on the Loewy’s 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) From the Back Cover 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.