Rosenkranz, Markus and Buchberger, Bruno and Engl, Heinz W.
(2003)
*Solving linear boundary value problems via non-commutative Groebner bases.*
Applicable Analysis , 82
(7).
pp. 655-675.
ISSN 0003-6811.
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Official URL http://dx.doi.org/10.1080/0003681031000118981 |

## Abstract

A new approach for symbolically solving linear boundary value problems is presented. Rather than using general-purpose tools for obtaining parametrized solutions of the underlying ODE and fitting them against the specified boundary conditions (which may be quite expensive), the problem is interpreted as an operator inversion problem in a suitable Banach space setting. Using the concept of the oblique Moore-Penrose inverse, it is possible to transform the inversion problem into a system of operator equations that can be attacked by virtue of non-commutative Groebner bases. The resulting operator solution can be represented as an integral operator having the classical Green's function as its kernel. Although, at this stage of research, we cannot yet give an algorithmic formulation of the method and its domain of admissible inputs, we do believe that it has promising perspectives of automation and generalization; some of these perspectives are discussed.

Item Type: | Article |
---|---|

Uncontrolled keywords: | Linear boundary value problems, Green's function, Moore-Penrose equations, symbolic solution |

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 18:00 |

Last Modified: | 30 Jul 2012 08:37 |

Resource URI: | https://kar.kent.ac.uk/id/eprint/29978 (The current URI for this page, for reference purposes) |

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