Loewy Decomposition of Linear Differential Equations

丛 书 名：Texts & Monographs in Symbolic Computation

版本说明：1

作     者：Fritz Schwarz 

I S B N：(纸本) 3709112850 

出 版 社：Springer Publishing Company  Incorporated 

出 版 年：2012年

页      数：XVI, 232页

主 题 词：Symbolic and Algebraic Manipulation Differential Equations Mathematical and Computational Engineering Applications 

摘      要：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.