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Approximating multiple integrals over non-rectangular compact set using α-dense curves
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Approximating multiple integrals over non-rectangular compact set using α-dense curves
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Journal Article
Approximating multiple integrals over non-rectangular compact set using α-dense curves
2024
Overview
In this paper, we develop a method for approximating multiple integrals. The domain of integration Ω is assumed to be a non-rectangular compact of ℝⁿ. The main idea is the dimensionality reduction procedure based on the use of parametric α-dense curves ℓα(t). First, the region whose measure represents the value of the integral, is densified using new results, by a certain α-dense curve of finite length. The multiple integral of a positive continuous function f over Ω is approximated by a unique single integral corresponding to ℓα(t). Some numerical examples are given.
Publisher
University of Nis, Faculty of Sciences and Mathematics
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