Numerically approach for calculate of double integrals

Abstract

        The main aim of this thesis to find values of the double and triple integrals numerically with continuous integrands or improper (singular) of the partial derivatives or improper at one point or more of region of the integration .

Also in this thesis , we find general formula of the errors by using behaviour of the integrands and new approach is different on the previous approached by Mohammed [13] , Alttai [10] , Dayaa [11] and others .

We have introduced three theorems (cases) to find the correction errors bounds with respect to the double integration for all case of the integrand by depending on these correction errors .

We calculated the double integral and found the method is composition method of using midpoint rule on the two dimensions interior and exterior with applying Romberg acceleration method on it when the number of subintervals of interval of interior integral equal to the number of subintervals of interval of exterior integral  such that  is the distances between coordinates of  and is the distances between coordinates of such that we can depend on it to calculate the double integrations , and given higher accuracy in the results by few subintervals and time less than the request time for the researchers in the same subject .