Symbolic Analysis for Boundary Problems: From Rewriting to Parametrized Gröbner Bases

DOI10.1007/978-3-7091-0794-2_13zbMath1250.65104arXiv1210.2950OpenAlexW1797309904MaRDI QIDQ2912125

Markus Rosenkranz, Bruno Buchberger, Loredana Tec, Georg Regensburger

Publication date: 14 September 2012

Published in: Texts & Monographs in Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.2950

zbMATH Keywords

ordinary differential equationsintegro-differential operatorsintegro-differential algebraslinear boundary problemsintegro-differential polynomials

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Integral operators (45P05) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Linear boundary value problems for ordinary differential equations (34B05) Nonstandard topology (54J05)

Related Items (16)

Divided powers and composition in integro-differential algebras ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Green's functions for reducible functional differential equations ⋮ Algorithmic operator algebras via normal forms in tensor rings ⋮ On integro-differential algebras. ⋮ Monads and distributive laws for Rota-Baxter and differential algebras ⋮ Transforming problems from analysis to algebra: a case study in linear boundary problems ⋮ Computing Polynomial Solutions and Annihilators of Integro-Differential Operators with Polynomial Coefficients ⋮ On rings of differential Rota–Baxter operators ⋮ Constructions of Free Commutative Integro-Differential Algebras ⋮ Composing and Factoring Generalized Green’s Operators and Ordinary Boundary Problems ⋮ A noncommutative algebraic operational calculus for boundary problems ⋮ Automatic pre- and postconditions for partial differential equations ⋮ Normal Forms for Operators via Gröbner Bases in Tensor Algebras ⋮ An algebraic study of multivariable integration and linear substitution

Uses Software

• gfun
• Maple
• Plural
• REDUCE
• Theorema

This page was built for publication: Symbolic Analysis for Boundary Problems: From Rewriting to Parametrized Gröbner Bases