Solving The Double Integrals By Extending Simpson’s 3/8 Rule

Abstract

In this thesis, we have solved the double integrals by extending Simpson’s 3/8 rule on the regions that are either vertically or horizontally simple, (or both). The given region of integration is discretized and the integrand is evaluated as the functional values at each grid point (ordered pairs) on the discretized region of integration. Finally, we applied the composite Simpson’s 3/8 rule on the 𝑥-direction and applied again the same on the 𝑦- direction or vice versa. The error analysis of the double integrals by extending Simpson’s 3/8 rule is also discussed in this thesis. Examples are taken in order to check the validity of the method; and it is shown that the method is more accurate as we have considered more mesh points.