A Multidimensional Analogue of the Simpson's Formula of Integral
Kazuyuki Fujii (Yokohama City University)
TL;DR
This paper introduces a multidimensional analogue of Simpson's formula for numerical integration, extending a classical one-dimensional method to higher dimensions, which could benefit applications in mathematics and physics.
Contribution
The paper presents a novel, simple, and elegant multidimensional Simpson's formula, filling a gap in numerical integration methods for multiple variables.
Findings
Provides a new multidimensional Simpson's formula
The formula is simple and potentially useful in mathematical physics
Extends classical numerical integration techniques to higher dimensions
Abstract
The Simpson's formula is obtained by approximating the integral of a function on some interval by the integral of the quadratic polynomial determined by the function. However, a multidimensional analogue of the formula has not been given as far as we know. In this paper such a formula is given. Our formula is simple and beautiful, so it may be convenient in Mathematics or Mathematical Physics.
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