Using An Accelerating Method With The Trapezoidal And Mid-Point Rules To Evaluate The Double Integrals With Continuous Integrands Numerically

Abstract

In this research we have used a compound method which is composed of Trapezoidal and Mid-Point Rules to evaluate the approximate values of the double Integrals with Continuous Integrands because of the resultant approximate values are fast when approximating from the true values of integrals if compared with other Newton -Cotes formulas. [ S.S. Sastry, 2008". The symbol of this rule is TM, in this method 2n is, the number of subintervals [a,b], equivalent to 2m ( the number of subintervals of [c,d] and (h=ћ), we accelerate the resultant approximate to the true values of integrals through applying Aitken's accelerate on the compound rule TM to procure a new method we called it A(TM) where the symbol A indicates to the Aitken’s acceleration method and the symbol TM ( y indicates to the Trapezoidal rule on the external and x indicates to the Mid-point rule on the internal dimensions).

Keywords: double integrals, Trapezoidal and Mid-Point Rules and Newton-Cotes