An optimization approach to numerical integration in two dimensions

In this paper, we propose an efficient approach to numerical integration of functions of two variables, where a grid set with a fixed number of vertic es is to be chosen such that the error between the numerical integral and t he exact integral is minimized. Two schemes are first developed for suffici ently smooth functions. One is based on barycenter rule on a rectangular pa rtition, while the other is on a triangular partition. A scheme for non-suf ficiently smooth functions is also developed. For illustration, several exa mples are solved by using the proposed schemes. (C) 2000 Published by Elsev ier Science Inc. All rights reserved.