Numerical Analysis of Double Integral of Trigonometric Function Using Romberg Method

Abstract

In general, solving the two-fold integral of trigonometric functions is not easy to do analytically. Therefore, we need a numerical method to get the solution. Numerical methods can only provide solutions that approach true value. Thus, a numerical solution is also called a close solution. However, we can determine the difference between the two (errors) as small as possible. Numerical settlement is done by consecutive estimates (iteration method). The numerical method used in this study is the Romberg method. Romberg's integration method is based on Richardson's extrapolation expansion, so that there is a calculation of the integration of functions in two estimating ways I (h1) and I (h2) resulting in an error order on the result of the completion increasing by two, so it needs to be reviewed briefly about how the accuracy of the method. The results of this study indicate that the level of accuracy of the Romberg method to the analytical method (exact) will give the same value, after being used in several simulations.