Publication detail

Numerical Integration of Multiple Integrals Using Taylor's Polynomial

CHALOUPKA, J. KUNOVSKÝ, J. ŠÁTEK, V. VEIGEND, P. MARTINKOVIČOVÁ, A.

Original Title

Numerical Integration of Multiple Integrals Using Taylor's Polynomial

English Title

Numerical Integration of Multiple Integrals Using Taylor's Polynomial

Type

conference paper

Language

en

Original Abstract

The paper concentrates on a new method of numerical computation of multiple integrals. Equations based on Taylor polynomial are derived. Multiple integral of a continuous function of n-variables is numerically integrated step by step by reducing its dimension. First, integration formulas for a function of two variables are derived. Formulas for function of n-variables are generalized using composition. Numerical derivatives for Taylor terms are repeatedly computed from simple integrals. Finally method is demonstrated on an exponential function of two-variables and a new approach to determine a number of Taylor terms is discussed.

English abstract

The paper concentrates on a new method of numerical computation of multiple integrals. Equations based on Taylor polynomial are derived. Multiple integral of a continuous function of n-variables is numerically integrated step by step by reducing its dimension. First, integration formulas for a function of two variables are derived. Formulas for function of n-variables are generalized using composition. Numerical derivatives for Taylor terms are repeatedly computed from simple integrals. Finally method is demonstrated on an exponential function of two-variables and a new approach to determine a number of Taylor terms is discussed.

Keywords

Multiple Integrals, Numerical Integration, Taylor's Polynomial, Modern Taylor Series Method

RIV year

2015

Released

21.07.2015

Publisher

SciTePress - Science and Technology Publications

Location

Colmar

ISBN

978-989-758-120-5

Book

Proceedings of the 5th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

Edition

NEUVEDEN

Edition number

NEUVEDEN

Pages from

163

Pages to

171

Pages count

9

URL

BibTex


@inproceedings{BUT119827,
  author="Jan {Chaloupka} and Jiří {Kunovský} and Václav {Šátek} and Petr {Veigend} and Alžbeta {Martinkovičová}",
  title="Numerical Integration of Multiple Integrals Using Taylor's Polynomial",
  annote="The paper concentrates on a new method of numerical computation of multiple
integrals. Equations based
on Taylor polynomial are derived. Multiple integral of a continuous function of
n-variables is numerically
integrated step by step by reducing its dimension. First, integration formulas
for a function of two variables
are derived. Formulas for function of n-variables are generalized using
composition. Numerical derivatives for
Taylor terms are repeatedly computed from simple integrals. Finally method is
demonstrated on an exponential
function of two-variables and a new approach to determine a number of Taylor
terms is discussed.",
  address="SciTePress - Science and Technology Publications",
  booktitle="Proceedings of the 5th International Conference on Simulation and Modeling Methodologies, Technologies and Applications",
  chapter="119827",
  edition="NEUVEDEN",
  howpublished="print",
  institution="SciTePress - Science and Technology Publications",
  year="2015",
  month="july",
  pages="163--171",
  publisher="SciTePress - Science and Technology Publications",
  type="conference paper"
}