Evaluation of Double integrals with Continuous Integrands by using Acceleration Methods Aitken‘ s with Rule.

Abstract

      The main aim of this research is to evaluate the value of double integrations whose integrands continuous function numerically by using   rule (this rule compound from Simpson‘s rule on the exterior dimension Y and Mid point rule on the interior dimension X) when the number of subintervals on the interior dimension equal to the number of subintervals on the exterior dimension , that is mean  where as means the distances between ordinates on the X-axis and  means the distances between ordinates on the Y-axis . And to improve the results we applied Aitken‘s acceleration over the Yielded values from the SM rule to accelerate the convergence of the approximate to the real value of integrations and we named this method (ASM) and we got good resulte with respect to the accuracy and speed of convergence to the analytic ( real ) values by using little subintervals.