الخلاصة

In this research we used a new method to calculate approximate values for quadratic integrations with continuous integrators. We have chosen the midpoint rule as the best method of dealing with impairment problems as well as being simple in application and will be applied to four dimensions when the number of partial periods divided by the internal integration period [a,b] is equal to the number of partial periods to which the middle integration period [c,d] is divided, equal to the number of partial periods to which the middle integration period [e,f] is divided, and is also equal to the number of partial periods to which the external integration period [q,r]. That is, (h1=h2=h3=h4), then we apply the Romberg Integration on the resulting values accelerating the Convergence and getting better results. We are going to give this method the symbol R(4M), where R is the Romberg Accelerating Method, and (4M) is the midpoint rule on the four dimensions.