Rosenkranz, Markus and Serwa, Nitin
(2015)
*
Green's Functions for Stieltjes Boundary Problems.
*
In: Robertz, Daniel, ed.
Proceedings of the 2015 ACM on International Symposium on Symbolic and Algebraic Computation.
ISSAC International Symposium on Symbolic and Algebraic Computation
.
ACM, New York, USA, pp. 315-321.
ISBN 978-1-4503-3435-8.
(doi:10.1145/2755996.2756681)
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Official URL http://dx.doi.org/10.1145/2755996.2756681 |

## Abstract

Stieltjes boundary problems generalize the customary class of well-posed two-point boundary value problems in three independent directions, regarding the specification of the boundary conditions: (1) They allow more than two evaluation points. (2) They allow derivatives of arbitrary order. (3) Global terms in the form of definite integrals are allowed. Assuming the Stieltjes boundary problem is regular (a unique solution exists for every forcing function), there are symbolic methods for computing the associated Green's operator.

In the classical case of well-posed two-point boundary value problems, it is known how to transform the Green's operator into the so-called Green's function, the representation usually preferred by physicists and engineers. In this paper we extend this transformation to the whole class of Stieltjes boundary problems. It turns out that the extension (1) leads to more case distinction, (2) implies ill-posed problems and hence distributional terms, (3) has apparently no effect on the structure of the Green's function.

Item Type: | Book section |
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DOI/Identification number: | 10.1145/2755996.2756681 |

Uncontrolled keywords: | Linear boundary problems; Green's functions; Stieltjes boundary conditions |

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: | 16 Jun 2015 08:07 UTC |

Last Modified: | 23 Sep 2019 11:53 UTC |

Resource URI: | https://kar.kent.ac.uk/id/eprint/49024 (The current URI for this page, for reference purposes) |

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