Numerical Integration of Multiple Integrals using Taylor Polynomial

Jan Chaloupka, Jiří Kunovský, Václav Šátek, Petr Veigend, Alžbeta Martinkovičová

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.

References

  1. F. Khaksar Haghani, F. Soleymani. (2014). A New HighOrder Stable Numerical Method for Matrix Inversion. The Scientific World Journal, Volume 2014
  2. A. Jordan, Z. Maorong. (2005). A Software Package for the Numerical Integration of ODEs by Means of HighOrder Taylor Methods. Experimental Mathematics, Vol. 14, No. 1
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Paper Citation


in Harvard Style

Chaloupka J., Kunovský J., Šátek V., Veigend P. and Martinkovičová A. (2015). Numerical Integration of Multiple Integrals using Taylor Polynomial . In Proceedings of the 5th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH, ISBN 978-989-758-120-5, pages 163-171. DOI: 10.5220/0005539701630171


in Bibtex Style

@conference{simultech15,
author={Jan Chaloupka and Jiří Kunovský and Václav Šátek and Petr Veigend and Alžbeta Martinkovičová},
title={Numerical Integration of Multiple Integrals using Taylor Polynomial},
booktitle={Proceedings of the 5th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,},
year={2015},
pages={163-171},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005539701630171},
isbn={978-989-758-120-5},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 5th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,
TI - Numerical Integration of Multiple Integrals using Taylor Polynomial
SN - 978-989-758-120-5
AU - Chaloupka J.
AU - Kunovský J.
AU - Šátek V.
AU - Veigend P.
AU - Martinkovičová A.
PY - 2015
SP - 163
EP - 171
DO - 10.5220/0005539701630171