Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10325823 | Journal of Symbolic Computation | 2012 | 21 Pages |
Abstract
The main part of the paper then describes our symbolic analysis approach to linear boundary problems, which hinges on three basic principles: (1)Â Differentiation as well as integration is treated axiomatically, setting up an algebraic data structure that can encode the problem statement (differential equation and boundary conditions) and suitable symbolic expressions for their solution (Green's operators qua integral operators). (2)Â boundary problems are introduced as pairs consisting of an epimorphism on a vector space (abstract differential operator) and a subspace of its dual (abstract boundary conditions). (3)Â Operator algebras are treated by noncommutative polynomials, modulo Groebner bases for certain relation ideals.
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Artificial Intelligence
Authors
Bruno Buchberger, Markus Rosenkranz,