AN ALGORITHM TO APPROXIMATE DOUBLE INTEGRALS BY USING ADAPTIVE QUADRATURE METHOD

Abstract

For the numerical integration in one variable, the Adaptive quadrature is a well-known method, which is superior in the sense of reducing the number of the evaluations of the function than other methods using equally-space nodes, and thus increases the accuracy of the approximation. This method takes the functional variation into account when controlling the subdivision of the given interval into suitable step sizes, in which the subintervals with larger variation have smaller step sizes in regarding that the obtained approximation is within a given specified tolerance. That is, this procedure distributes the error uniformly into equal subintervals. In this article, we develop an algorithm applying Adaptive quadrature method, which bases on the Composite Simpson’s rule, to approximate double integrals over a general region in the plane. We will prove that this algorithm works for double integrals. Besides, the article gives the pseudocode for the algorithm and an interesting example to illustrate the use of the algorithm. The examples is implemented by using Matlab code.