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TitleSolving Linear Boundary Value Problems Via Non-commutative Gröbner Bases
Author(s) Bruno Buchberger, Heinz W. Engl, Markus Rosenkranz
TypeArticle in Journal
AbstractA new approach for symbolically solving linear boundary value problems is presented. Rather than using general-purpose 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 Moore-Penrose inverse, it is possible to transform the inversion problem into a system of operator equations that can be attacked by virtue of non-commutative 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.
KeywordsLinear Boundary Value Problems, Green's Function, Moore-Penrose Equations, Symbolic Solution
Length18
ISBN1563-504X
ISSN0003-6811
CopyrightTaylor & Francis Ltd.
File
URL http://journalsonline.tandf.co.uk/link.asp?id=tcafaga405dqr8j9
LanguageEnglish
JournalApplicable Analysis
Volume82
Number7
Pages655-675
PublisherTaylor & Friends
Year2003
Translation No
Refereed Yes
Organization Johannes Kepler University Linz
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