Generalized differential and integral quadrature and their application to solve boundary layer equations

Based on the work of generalized differential quadrature (GDQ), a global method of generalized integral quadrature (GIQ) is developed in this paper for approximating an integral of a function over a part of the closed domain. GIQ approximates the integral of a function over the part of the whole closed domain by a linear combination of all the functional values in the whole domain with higher order of accuracy. The weighting coefficients of GIQ can be easily determined from those of GDQ. Applications of GDQ and GIQ to solve boundary layer equations demonstrated that accurate numerical results can be obtained using just a few grid points.