Evaluation of triple integrals with Continuous Integrands numerically by Newton-Cotes Formulas
Abstract
The main aim of this search is to derivation numerically new rule to find the values of
the triple integrals, Its integrands continuous in region of the integration and derivation
the errors (correction terms ) and to improve the results of the triple integrals we used
Romberg accelerating method by depending on these correction terms that we found, this
method (composition method of applying Romberg acceleration method on the obtained
values of applying Mid-point rule on the dimension z and Simpson’s rule on the
dimension y and Trapezoidal Rule on the dimension x, when the number of subintervals
of interval of interior dimension equal to the number of subintervals of interval of middle
dimension and equal to the number of subintervals of exterior dimension) such that
h  h  h , h is the distances between the ordinates on the x– axis, h is the distances
between the ordinates on the y- axis and h is the distances between the ordinates on the
z– axis ,and we indicate this method by (RMST) , we can depend on it to calculate the
triple integrals when it integrands continuous on the region of integration and give higher
accuracy in the results by few subintervals.
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