Evaluation of Triple Integrals with Continuous Integrands Numerically by Using Two Methods AI(MMS) and RO(MMS) and comparison Between them

Abstract

       The main aim of this  paper is to evaluate the triple integrals with continuous integrands numerically by using two  method obtained  from two accelerations Aitken‘s and Romberg with the combination rule from( two rules Mid- point rule on  both two dimensions of exterior Z and middle dimension  Y and Simpson‘s rule on the interior dimension X, denoted by MMS) where the number of divisions on the exterior dimension is equal to the number of divisions on the middle dimension and equal to the number of divisions on the interior dimension where we have introduced theorem with proof to find this rule and the correction error bounds with respect  its and to improve the results we used two accelerations mentioned with rule MMS and we shall call these two methods AI(MMS) and RO(MMS) where we got high accuracy in the results by few subintervals relatively and short time .