Approximating multiple integrals via α‐dense curves

Abstract

This paper is intended to provide a numerical method for computing integrals of several variables. The method is based on a intuitive geometric idea relative to the meaning of densifying a domain in Rⁿ⁺¹(n≥1) by a curve h(t), contained in that domain, say K, with a very small density α (this must be interpreted as the following property: for any point of K there exists a point of the curve at distance less or equal than α).Thus, the method states that any area, volume, etc, can be computed as the limit of the length of a certain curve, densifying that domain, multiplied by a power of its density. Therefore, the computation of a multiple integral of a nonnegative continuous function can be approached by a simple integral corresponding to the length of the curve h(t) and certain power of its density.

Citation

Mora, G., Cherruault, Y., Benabidallah, A. and Tourbier, Y. (2002), "Approximating multiple integrals via α‐dense curves", Kybernetes, Vol. 31 No. 2, pp. 292-304. https://doi.org/10.1108/03684920210419010