کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
10325823 | 677079 | 2012 | 21 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Transforming problems from analysis to algebra: A case study in linear boundary problems
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موضوعات مرتبط
مهندسی و علوم پایه
مهندسی کامپیوتر
هوش مصنوعی
پیش نمایش صفحه اول مقاله
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چکیده انگلیسی
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.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Symbolic Computation - Volume 47, Issue 6, June 2012, Pages 589-609
Journal: Journal of Symbolic Computation - Volume 47, Issue 6, June 2012, Pages 589-609
نویسندگان
Bruno Buchberger, Markus Rosenkranz,