Two Numerical ways RO (SuMM) and RO (MSuSu)) to Evaluate triple integrals

Abstract

The main goal of this research to calculate the triple integrals which has continuous functions numerically by two methods are RO(SuMM) and RO(SuMM)that obtained by Romberg acceleration with two composite rules. The first rule is the Mid-point method on the first dimension X and the second dimension Y with a suggested method on the third dimension Z and, which is denoted by SuMM. The second rule is a suggested method on the first dimension X and the second dimension Y with the Mid-point method on the third dimension Z and, which is denoted by MSuSu. Where the number of divisions on these three dimensions is exactly the Sam. We represented two theorems with their proofs to find such rules and the correction terms (the error terms) for each of rule Therefore, we obtained high accuracy results in a relatively few sub intervals and short time. Subject Classification: 65XX