Publication result detail

Multiple Integral Computations Using Taylor Series

CHALOUPKA, J.; KUNOVSKÝ, J.; MARTINKOVIČOVÁ, A.; ŠÁTEK, V.; THONHOFER, E.

Original Title

Multiple Integral Computations Using Taylor Series

English Title

Multiple Integral Computations Using Taylor Series

Type

Paper in proceedings (conference paper)

Original Abstract

The paper is a part of student cooperation in AKTION project (Austria-Czech) and deals with possibilities of numerical solution of initial value problems of ordinary differential equations (ODEs). The Taylor series method with automatic computation of higher Taylor series terms is used for solution of multiple integrals.

A Multiple integral of a continuous function of n variables can be computed by n-ary integration of the function fixing the remaining variables. These simple integrals can be solved as a ODEs, thus introducing a problem of parallel solving of a growing number of equations with respect to n and the required precision.

English abstract

The paper is a part of student cooperation in AKTION project (Austria-Czech) and deals with possibilities of numerical solution of initial value problems of ordinary differential equations (ODEs). The Taylor series method with automatic computation of higher Taylor series terms is used for solution of multiple integrals.

A Multiple integral of a continuous function of n variables can be computed by n-ary integration of the function fixing the remaining variables. These simple integrals can be solved as a ODEs, thus introducing a problem of parallel solving of a growing number of equations with respect to n and the required precision.

Keywords

Differential equations, Multiple integrals, Taylor series method, Stiff systems, TKSL, MATLAB

Key words in English

Differential equations, Multiple integrals, Taylor series method, Stiff systems, TKSL, MATLAB

Authors

CHALOUPKA, J.; KUNOVSKÝ, J.; MARTINKOVIČOVÁ, A.; ŠÁTEK, V.; THONHOFER, E.

RIV year

2015

Released

10.04.2015

Publisher

American Institute of Physics

Location

Rhodes

ISBN

978-0-7354-1287-3

Book

12th International Conference of Numerical Analysis and Applied Mathematics

ISBN

0094-243X

Periodical

AIP conference proceedings

Volume

2015

Number

1648

State

United States of America

Pages from

1

Pages to

4

Pages count

4

URL

http://dx.doi.org/10.1063/1.4913137

BibTex

@inproceedings{BUT111569,
  author="Jan {Chaloupka} and Jiří {Kunovský} and Alžbeta {Martinkovičová} and Václav {Šátek} and Elvira {Thonhofer}",
  title="Multiple Integral Computations Using Taylor Series",
  booktitle="12th International Conference of Numerical Analysis and Applied Mathematics",
  year="2015",
  journal="AIP conference proceedings",
  volume="2015",
  number="1648",
  pages="1--4",
  publisher="American Institute of Physics",
  address="Rhodes",
  doi="10.1063/1.4913137",
  isbn="978-0-7354-1287-3",
  issn="0094-243X",
  url="http://dx.doi.org/10.1063/1.4913137"
}