Numerical Approximation of Surface Integrals Using Mixed Cubature Adaptive Scheme

This research described the development of a new mixed cubature rule for evaluation of surface integrals over rectangular domains. Taking the linear combination of Clenshaw-Curtis 5- point rule and Gauss-Legendre 3-point rule ( each rule is of same precision i.e. precision 5) in two dimensions the mixed cubature rule of higher precision was formed (i.e. precision 7). This method is iterative in nature and relies on the function values at uneven spaced points on the rectangle of integration. Also as supplement, an adaptive cubature algorithm is designed in order to reinforce our mixed cubature rule. With the illustration of numerical examples this mixed cubature rule is turned out to be more powerful when compared with the constituents standard cubature procedures both in adaptive and non-adaptive environment.