Derivation of formulaes evaluating double integrals and their error formulaes using Mid-point and Simpson‘s methods

Abstract

The main aim of this search is to find the values of the double integrals numerically, Its integrals either continuous or continuous but its partial derivatives are singular or the integrals are singular in one point or more of region of the integrals and to find the general form of the errors (correction terms ) to any case of the behavior of integrands with different style that another researchers used it Mohammed [14] , Alttai [10] and Dayaa [12] .And by using the correction terms that we found it , we applied it to find the values of double integrals for each case of cases of integrands ,we yields that the two methods with Romberg acceleration canbe able on it to find the values of double integrals numerically with high accuercy little subintervals and smaller times that the above researchers needed to it.