Numerical Method for Evaluation of Double Integrals with continuous Integrands by using Trapezoidal rule and Romberg acceleration when the number of subintervals at the two dimensions are unequal

Abstract

The main of this research is to find the values of the double integrals numerically by using Trapezoidal method for two dimensions it's integrands are continuous in region of integral and derives error form (correction terms) when number of subintervals on both dimensions are unequal and we will study and apply special case on well choosen integrals when numbers of subintervals on dimension  equals to twice of numbers of subintervals on dimension  in other word   means that and we will improve the results by using Romberg acceleration [3] and [4] .High accuraceg in results had appeared of the choosen  integals by using alittle number of subintervals , thus , It can be depend on this way in calculating like these integrals. We will give asymbole for this rule (method) , indicates to Trapezoidal rule on both dimensions, indicates to Romberg acceleration.