On integro-differential algebras

L Guo, G Regensburger, M Rosenkranz - Journal of Pure and Applied …, 2014 - Elsevier
The concept of integro-differential algebra has been introduced recently in the study of
boundary problems of differential equations. We generalize this concept to that of integro …

[图书][B] Symbolic analysis for boundary problems: From rewriting to parametrized Gröbner bases

M Rosenkranz, G Regensburger, L Tec, B Buchberger - 2012 - Springer
We review our algebraic framework for linear boundary problems (concentrating on ordinary
differential equations). Its starting point is an appropriate algebraization of the domain of …

A Maple package for integro-differential operators and boundary problems

A Korporal, G Regensburger… - ACM Communications in …, 2011 - dl.acm.org
Introduction. We present a Maple package for computing in algebras of integro-differential
operators. This provides the appropriate algebraic setting for treating boundary problems [7] …

ISSAC 2012 software demonstrations: Symbolic computation for ordinary boundary problems in maple

A Korporal, G Regensburger… - ACM Communications in …, 2013 - dl.acm.org
We present a new version of the Maple package IntDiffOp [6, 7] for Symbolic Computation
with boundary problems for linear ordinary differential equations. The solution of boundary …

Transforming problems from analysis to algebra: a case study in linear boundary problems

B Buchberger, M Rosenkranz - Journal of Symbolic Computation, 2012 - Elsevier
In this paper, we summarize our recent work on establishing, for the first time, an algorithm
for the symbolic solution of linear boundary problems. We put our work in the frame of Wen …

An algebraic study of multivariable integration and linear substitution

M Rosenkranz, X Gao, L Guo - arXiv preprint arXiv:1503.01694, 2015 - arxiv.org
We set up an algebraic theory of multivariable integration, based on a hierarchy of Rota-
Baxter operators and an action of the matrix monoid as linear substitutions. Given a suitable …

Regular and singular boundary problems in Maple

A Korporal, G Regensburger, M Rosenkranz - Computer Algebra in …, 2011 - Springer
We describe a new maple package for treating boundary problems for linear ordinary
differential equations, allowing two-/multi-point as well as Stieltjes boundary conditions. For …

A Symbolic Approach to Boundary Problems for Linear Partial Differential Equations: Applications to the Completely Reducible Case of the Cauchy Problem with …

M Rosenkranz, N Phisanbut - … CASC 2013, Berlin, Germany, September 9 …, 2013 - Springer
We introduce a general algebraic setting for describing linear boundary problems in a
symbolic computation context, with emphasis on the case of partial differential equations …

[PDF][PDF] A symbolic framework for general polynomial domains in theorema: Applications to boundary problems

L Tec - ACM Commun. Comput. Algebra, 2011 - Citeseer
In this thesis, we present a symbolic framework for working with general polynomial
domains, targeted at dealing with linear boundary problems on the operator level. We …

Constructions of free commutative integro-differential algebras

X Gao, L Guo - Algebraic and Algorithmic Aspects of Differential and …, 2014 - Springer
In this survey, we outline two recent constructions of free commutative integro-differential
algebras. They are based on the construction of free commutative Rota-Baxter algebras by …