Skip to main content

A symbolic framework for operations on linear boundary problems

Rosenkranz, Markus and Regensburger, Georg and Tec, Loredana and Buchberger, Bruno (2009) A symbolic framework for operations on linear boundary problems. In: Gerdt, V.P. and Mayr, E.W. and Vorozhtsov, E.V., eds. Proceedings of the 11th International Workshop on Computer Algebra in Scientific Computing. Lecture Notes in Computer Science, 5743 . Springer, pp. 269-283. ISBN 978-3-642-04102-0. (doi:10.1007/978-3-642-04103-7_24) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:29967)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided.
Official URL
http://dl.acm.org/citation.cfm?id=1691130

Abstract

We describe a symbolic framework for treating linear boundary

problems with a generic implementation in the Theorema system. For

ordinary differential equations, the operations implemented include computing

Green’s operators, composing boundary problems and integro-differential

operators, and factoring boundary problems. Based on our

factorization approach, we also present some first steps for symbolically

computing Green’s operators of simple boundary problems for partial

differential equations with constant coefficients. After summarizing the

theoretical background on abstract boundary problems, we outline an

algebraic structure for partial integro-differential operators. Finally, we

describe the implementation in Theorema, which relies on functors for

building up the computational domains, and we illustrate it with some

sample computations including the unbounded wave equation.

Item Type: Book section
DOI/Identification number: 10.1007/978-3-642-04103-7_24
Uncontrolled keywords: Linear boundary problem; Green’s operator; Integro-Differential Operator; Ordinary Differential Equation; Wave Equation
Subjects: Q Science > QA Mathematics (inc Computing science) > QA150 Algebra
Q Science > QA Mathematics (inc Computing science) > QA372 Ordinary differential equations
Q Science > QA Mathematics (inc Computing science) > QA 76 Software, computer programming,
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Markus Rosenkranz
Date Deposited: 27 Jul 2012 15:36 UTC
Last Modified: 16 Nov 2021 10:07 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/29967 (The current URI for this page, for reference purposes)
  • Depositors only (login required):