Derivation of composite rules for numerical calculation of double integrals using Romberg acceleration to improve results

Abstract

     The main goal of this work is to find numerical value of a double integral where the integrand is continuous, by derivation composite rules and its correction terms. Depending on these terms we improve these values by using Romberg acceleration, after that we used these rules to find the values of integral with continuous integrands on the region of integral and we compare these results with composite rule of trapezoidal on the two dimensions (exterior and interior), the resulting values are better if accuracy and number of sub-intervals are taken in account.