<abstract xmlns="http://www.w3.org/1999/xhtml">

In this paper, we propose an approximation technique to compute multiple integrals of a non-negative real continuous function over a hyper-rectangle Ω of ℝ<italic>n</italic>. The main idea is to use a reducing transformation procedure obtained by using α-dense curves. First, the region Ω<italic>f</italic> whose measure represents the value of the integral, is densified by a specific curve <italic>ℓ</italic>α(<italic>t</italic>) of finite length. Therefore, the multiple integral can be approached by a simple integral corresponding to <italic>ℓ</italic>α (<italic>t</italic>). Some numerical examples are given.
</abstract>

In this paper, we propose an approximation technique to compute multiple integrals of a non-negative real continuous function over a hyper-rectangle Ω of ℝn. The main idea is to use a reducing transformation procedure obtained by using α-dense curves. First, the region Ωf whose measure represents the value of the integral, is densified by a specific curve ℓα(t) of finite length. Therefore, the multiple integral can be approached by a simple integral corresponding to ℓα (t). Some numerical examples are given.

Efficient α-Dense Curve Strategies for Multiple Integrals over Hyper-rectangle Regions

Laboratory of Fundamental and Numerical Mathematics (LMFN)

Department of Mathematics, University Ferhat Abbas Setif 1

Laboratory of Fundamental and Numerical Mathematics (LMFN), Department of Basic Education in Technology

Annals of West University of Timisoara - Mathematics and Computer Science

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

In this paper, we propose an approximation technique to compute multiple integrals of a non-negative real continuous function over a hyper-rectangle Ω of ℝn....

Efficient α-Dense Curve Strategies for Multiple Integrals over Hyper-rectangle Regions

Published Online: Jul 05, 2024

Page range: 85 - 97

Received: Feb 19, 2024

Accepted: Jun 18, 2024

DOI: https://doi.org/10.2478/awutm-2024-0006

Keywords
Numerical integration, α-dense curves, reducing transformation

© 2024 Mohamed Rahal et al., published by Sciendo

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

Efficient α-Dense Curve Strategies for Multiple Integrals over Hyper-rectangle Regions

Published Online: Jul 05, 2024

Page range: 85 - 97

Received: Feb 19, 2024

Accepted: Jun 18, 2024

DOI: https://doi.org/10.2478/awutm-2024-0006

KeywordsNumerical integration, α-dense curves, reducing transformation

© 2024 Mohamed Rahal et al., published by Sciendo

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

Keywords
Numerical integration, α-dense curves, reducing transformation