Details:
Title  Solving Linear Boundary Value Problems Via Noncommutative Gröbner Bases  Author(s)  Bruno Buchberger, Heinz W. Engl, Markus Rosenkranz  Type  Article in Journal  Abstract  A new approach for symbolically solving linear boundary value problems is presented. Rather than using generalpurpose tools for obtaining parametrized solutions of the underlying ODE and fitting them against the specified boundary conditions (which may be quite expensive), the problem is interpreted as an operator inversion problem in a suitable Banach space setting. Using the concept of the oblique MoorePenrose inverse, it is possible to transform the inversion problem into a system of operator equations that can be attacked by virtue of noncommutative Gröbner bases. The resulting operator solution can be represented as an integral operator having the classical Green's function as its kernel. Although, at this stage of research, we cannot yet give an algorithmic formulation of the method and its domain of admissible inputs, we do believe that it has promising perspectives of automation and generalization; some of these perspectives are discussed.  Keywords  Linear Boundary Value Problems, Green's Function, MoorePenrose Equations, Symbolic Solution  Length  18  ISBN  1563504X  ISSN  00036811  Copyright  Taylor & Francis Ltd. 
File 
 URL 
http://journalsonline.tandf.co.uk/link.asp?id=tcafaga405dqr8j9 
Language  English  Journal  Applicable Analysis  Volume  82  Number  7  Pages  655675  Publisher  Taylor & Friends  Year  2003  Translation 
No  Refereed 
Yes  Organization 
Johannes Kepler University Linz 
