<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The tasks involving repeated integral occur from time to time in technical practice. This paper introduces the research of authors in the field of repeated integrals within the required class of functions. Authors focus on the definite integral over repeated integral and they develop a tool for its computation. It involves two principal steps, analytical and numerical step.</p><p>In the analytical step, the definite integral over a repeated integral is decomposed into <italic>n</italic> integrals and then the Cauchy form is used for further rearrangement. Numerical step involves Gauss type integration slightly modified by the authors. Several examples illustrating the operation of both analytical and numerical steps of the method are provided in the paper.</p></abstract>

The tasks involving repeated integral occur from time to time in technical practice. This paper introduces the research of authors in the field of repeated integrals within the required class of functions. Authors focus on the definite integral over repeated integral and they develop a tool for its computation. It involves two principal steps, analytical and numerical step.In the analytical step, the definite integral over a repeated integral is decomposed into n integrals and then the Cauchy form is used for further rearrangement. Numerical step involves Gauss type integration slightly modified by the authors. Several examples illustrating the operation of both analytical and numerical steps of the method are provided in the paper.

Computation of Definite Integral Over Repeated Integral

Dept. of Structural Mechanics, Faculty of Civil Engineering

Dept. of Mathematics, Faculty of Civil Engineering

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Computation of Definite Integral Over Repeated Integral"}

The tasks involving repeated integral occur from time to time in technical practice. This paper introduces the research of authors in the field of repeated...

Computation of Definite Integral Over Repeated Integral

Published Online: Mar 12, 2019

Page range: 141 - 154

Received: Sep 17, 2018

DOI: https://doi.org/10.2478/tmmp-2018-0026

Keywords
repeated integral, repeated integral decomposition, Cauchy form for repeated integrals, Gauss and Lobatto quadrature and cubature

© 2018 Katarína Tvrdá et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Computation of Definite Integral Over Repeated Integral

Published Online: Mar 12, 2019

Page range: 141 - 154

Received: Sep 17, 2018

DOI: https://doi.org/10.2478/tmmp-2018-0026

Keywordsrepeated integral, repeated integral decomposition, Cauchy form for repeated integrals, Gauss and Lobatto quadrature and cubature

© 2018 Katarína Tvrdá et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
repeated integral, repeated integral decomposition, Cauchy form for repeated integrals, Gauss and Lobatto quadrature and cubature