Numerical method for evaluation double integrals with continuous integrands by using mid point rule when the number of subintervals at the two dimensions are not equal

Abstract

The main aim of this search is to derive method to find the values of the double integrals numerically its integrands continuous in the region of the integrals by using Midpoint two dimensions (interior x and exterior y ) and how to find the general form of the on the ruleerrors (correction terms) and we will improve the results by using Romberg acceleraion from correction terms that we found it when the number of subintervals (n) that divided interval integral on the interior dimension x equal to twice the number of subintervals (m) on the exterior dimension y ,that is mean (h_1=1/2 h_2 ) when h_1 means the distances between the ordinates on the x axis and h_2 means the distances between the ordinates on the y axis and we denote to this method by 〖 M〗_i(h_i ) and we can depend on this method to calculate the double integrals because it gave high accuracy in the results by few subintervals.