Solving and factoring boundary problems for linear ordinary differential equations in differential algebras

Rosenkranz, Markus and Regensburger, Georg (2008) Solving and factoring boundary problems for linear ordinary differential equations in differential algebras. Journal of Symbolic Computation, 43 (8). pp. 515-544. ISSN 0747-7171. (The full text of this publication is not available from this repository)

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Official URL
http://dx.doi.org/10.1016/j.jsc.2007.11.007

Abstract

We present a new approach for expressing and solving boundary problems for linear ordinary differential equations in the language of differential algebras. Starting from an algebra with a derivation and integration operator, we construct an algebra of linear integro-differential operators that is expressive enough for specifying regular boundary problems with arbitrary Stieltjes boundary conditions as well as their solution operators. On the basis of these structures, we define a new multiplication on regular boundary problems in such a way that the resulting Green's operator is the reverse composition of the constituent Green's operators. We provide also a method for lifting any factorization of the underlying differential operator to the level of boundary problems. Since this method only needs the computation of initial value problems, it can be used as an effective alternative for computing Green's operators in the case where one knows how to factor the given differential operators.

Item Type: Article
Uncontrolled keywords: Linear boundary value problems; Ordinary differential equations; Green’s operators; Factorization; Differential algebra; Noncommutative Gröbner bases
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 > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: Markus Rosenkranz
Date Deposited: 27 Jul 2012 16:25
Last Modified: 30 Jul 2012 08:28
Resource URI: http://kar.kent.ac.uk/id/eprint/29971 (The current URI for this page, for reference purposes)
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