طريقة عددية لحساب التكاملات الثنائية ذات المكاملات المعتلة المشتقة و المعتلة باستخدام قاعدة سمبسون عندما تكون عدد الفترات الجزئية على البعدين غير متساوية

Abstract EN

The main aim of this research is to derive numerical rule to calculate values of double integrals its integrands have singular partial derivatives and singular integrals at one end of limits region of integration by using Simpson's rule with two dimensions (on the interior x and exterior y), and to find correction terms (formula of error) for it, and using Romberg acceleration to improve the results of integrations by depending on correction terms that we found when the number of subintervals (m) on the dimension y equal to twice of subintervals (n) on the dimension x,((n),(m) even integers number), precisel y when h1=2h2 where h1 is the distance between ordinates on x-axis and h2 the distance between ordinates on y-axis .

we will use the symbol ( sim2) to indicate this Simpson's rule with two dimensions and symbolized the base with Romberg acceleration the symbol ( Rsim2 ) and we can depend on this rule to calculate like these integrals because it gave high accuracy on the results with respect to the analytical values of integration with little subintervals.