طريقه عددية لحساب التكاملات الثنائية ذات المكاملات المعتلة و المعتلة المشتقة باستخدام قاعدة النقطة الوسطى عندما تكون إعداد الفترات الجزئية على البعدين غير متساوية

The main aim of this search is to derive method to find the values of the double integrals numerically its integrands have singularity at partial derivatives or the integrands are singular in one point or more of region of the integrals by using midpoint rule on the two dimensions (interior and exterior ) and how to find the general form of the errors (correction terms) with improve the result by using Romberg acceleration[1],[5]by depending on the correction terms that we found it when the number of subintervals (n) that divided integral interval on the interior dimension not equal to the number of subintervals (m) on the exterior dimension , that is mean 1 2 (h  h ) when means the distances between the ordinates on the axis and is the distances between the ordinates on the axis and we denote to this method by and we can depend on it to calculate the double integrals because it gave high accuracy in results by few subintervals (we will take particular case when n m  2 , that is mean 1 2 1 ( ) 2 h h  to able us to use Romberg acceleration on the integrals that we study it ) .