ADAPTIVE QUADRATURE METHOD TO APPROXIMATE DOUBLE INTEGRALS OVER NON-RECTANGULAR REGIONS

Abstract

Recently, in an early publication [1], the author presented an algorithm to approximate double integral over a rectangle basing on the adaptive quadrature method. This method has the upper hand comparing with many other approaches due to its low cost and high efficiency. In that paper, even the algorithm was constructed strictly for approximating double integrals over rectangles only, it can be also extended to treat the case of non-rectangular regions. Nevertheless, for non-rectangular regions, it is not somewhat practical to program such an algorithm because of the consumption a large amount of RAM to store data of values for functions taking on the boundary of the region. The storage is performed at many steps in each repeating loop. This shortcoming often makes the program implement awkwardly. This paper aims to revise the aforementioned algorithm to be more efficient.