tutorial

Symbolic Computation with Integro-Differential Operators

Author:

Georg RegensburgerAuthors Info & Claims

ISSAC '16: Proceedings of the 2016 ACM International Symposium on Symbolic and Algebraic Computation

Pages 17 - 18

https://doi.org/10.1145/2930889.2930942

Published: 20 July 2016 Publication History

Abstract

The algebraic and algorithmic study of integro-differential algebras and operators has only started in the past decade. Integro-differential operators allow us in particular to study initial value and boundary problems for linear ODEs from an algebraic point of view. Differential operators already provide a rich algebraic structure with a wealth of results and algorithmic methods. Adding integral operators and evaluations, many new phenomena appear, including zero devisors and non-finitely generated ideals. In this tutorial, we give an introduction to symbolic methods for integro-differential operators and boundary problems developed over the last years. In particular, we discuss normal forms, basic algebraic properties, and the computation of polynomial solutions for ordinary integro-differential equations with polynomial coefficients. We will also outline methods for manipulating and solving linear boundary problems and illustrate them with an implementation.

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Cited By

Cluzeau TPoor JQuadrat ARaab CRegensburger G(2018)Symbolic Computation for Integro-Differential-Time-Delay Operators with Matrix CoefficientsIFAC-PapersOnLine10.1016/j.ifacol.2018.07.21551:14(153-158)Online publication date: 2018
https://doi.org/10.1016/j.ifacol.2018.07.215
Chen SKauers M(2017)Some open problems related to creative telescopingJournal of Systems Science and Complexity10.1007/s11424-017-6202-930:1(154-172)Online publication date: 14-Feb-2017
https://doi.org/10.1007/s11424-017-6202-9

Index Terms

Symbolic Computation with Integro-Differential Operators
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
2. Mathematics of computing
  1. Mathematical software

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Information

Published In

cover image ACM Conferences

ISSAC '16: Proceedings of the 2016 ACM International Symposium on Symbolic and Algebraic Computation

July 2016

434 pages

ISBN:9781450343800

DOI:10.1145/2930889

General Chairs:
Sergei Abramov
Russian Academy of Sciences, Russia
,
Eugene Zima
Wilfrid Laurier University, Canada
,
Program Chair:
Xiao-Shan Gao
Chinese Academy of Sciences, China

Copyright © 2016 Owner/Author.

Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the Owner/Author.

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SIGSAM: ACM Special Interest Group on Symbolic and Algebraic Manipulation

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Association for Computing Machinery

New York, NY, United States

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Published: 20 July 2016

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Austrian Science Fund (FWF)

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ISSAC '16

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SIGSAM

ISSAC '16: International Symposium on Symbolic and Algebraic Computation

July 20 - 22, 2016

ON, Waterloo, Canada

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Cited By

Cluzeau TPoor JQuadrat ARaab CRegensburger G(2018)Symbolic Computation for Integro-Differential-Time-Delay Operators with Matrix CoefficientsIFAC-PapersOnLine10.1016/j.ifacol.2018.07.21551:14(153-158)Online publication date: 2018
https://doi.org/10.1016/j.ifacol.2018.07.215
Chen SKauers M(2017)Some open problems related to creative telescopingJournal of Systems Science and Complexity10.1007/s11424-017-6202-930:1(154-172)Online publication date: 14-Feb-2017
https://doi.org/10.1007/s11424-017-6202-9

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