Evaluation of Triple Integrals with Singular Partial Derivatives or Singular Integrands in both Ends of the Region of Integration by Numerically Method of Newton-Cotes Composite Formulas (MTS)

The main aimof this research is evaluation thevalues of the triple dimension integrals numerically, when its integrands are either continuous with singular partial derivatives or singular in all ends of the region of integration. Through this derivation the errors (correction terms) to the numerically method (MTS) such that the letter S refer to Simpson’s rule on the dimension x and the letter T refer to Trapezoidal Rule on the dimension x and the letter M refer to Mid-point rule on the dimension z and to improve the results of the triple integrals weused Romberg’s accelerating method by depending on these correction terms that we found, andwe indicate this method by (RMTS), we can depend on it to calculate the triple integrals when its integrands singular or continuous with singular partial derivatives or singular in all ends of the region of integration and give higher accuracy inthe results by few sub intervals.