Efficient and stable generation of higher-order pseudospectral integration matrices

The main purpose of this work is to provide new higher-order pseudospectral integration matrices (HPIMs) for the Chebyshev-type points, and present an exact, efficient, and stable approach for computing the HPIMs. The essential idea is to reduce the computation of HPIMs to that of higher-order Chebyshev integration matrices (HCIMs), and take a very simple and recursive way to compute the HCIMs efficiently and stably. Extensive numerical results show that the new approach for computing the HPIMs has better stability than that of the recently derived Elgindy’s approach for large number of Chebyshev-type points.