A Noncommutative Algebraic Operational Calculus for Boundary Problems

Rosenkranz, Markus, Korporal, Anja (2013) A Noncommutative Algebraic Operational Calculus for Boundary Problems. Mathematics in Computer Science, 7 (2). pp. 201-227. ISSN 1661-8270. (doi:10.1007/s11786-013-0154-9) (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)

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Official URL
http://dx.doi.org/10.1007/s11786-013-0154-9

Abstract

We set up a left ring of fractions over a certain ring of boundary problems for linear ordinary differential equations. The fraction ring acts naturally on a new module of generalized functions. The latter includes an isomorphic copy of the differential algebra underlying the given ring of boundary problems. Our methodology employs noncommutative localization in the theory of integro-differential algebras and operators. The resulting structure allows to build a symbolic calculus in the style of Heaviside and Mikusinski, but with the added benefit of incorporating boundary conditions where the traditional calculi allow only initial conditions. Admissible boundary conditions include multiple evaluation points and nonlocal conditions. The operator ring is noncommutative, containing all integrators initialized at any evaluation point.

Item Type: Article
DOI/Identification number: 10.1007/s11786-013-0154-9
Uncontrolled keywords: Linear boundary value problems; Mikusinski calculus; Operational calculus; Ordinary differential equations; Green’s operators; Factorization; Differential algebra
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: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: Markus Rosenkranz
Date Deposited: 14 May 2013 17:39 UTC
Last Modified: 29 May 2019 10:11 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/33900 (The current URI for this page, for reference purposes)
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