Driving Two Numerical Methods to Evaluate the Triple Integrals R(MSM),R(SMM) and Compare Between Them

Abstract

The main objective of present work is the conclusion of two new numerical methods to evaluate the triple integrals with continuous integrands and their partial derivatives are continuous too, the first method through using Mid-point rule on the interior dimension X, Simpson's rule on the middle dimension Y and Mid-point rule on the exterior dimension Z, which denoted by the symbol MSM. The second method by using Mid-point rule on both two dimensions of interior X and middle dimension Y and Simpson's rule on the exterior dimension Z which denoted by SMM, where the number of divisions on the three dimensions are equals. We have concluded two theorems with their proves to find their rules and the correction terms that we found it and to improve the results we used Romberg acceleration which denoted by R(MSM),R(SMM) where we got high accuracy in the results by little sub-intervals relatively and short time.