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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
CopyrightTaylor & Francis Ltd.
URL http://journalsonline.tandf.co.uk/link.asp?id=tcafaga405dqr8j9
JournalApplicable Analysis
PublisherTaylor & Friends
Translation No
Refereed Yes
Organization Johannes Kepler University Linz