On spline-based differential quadrature

In the paper Barrera et al. (2014), a boolean sum differential quadrature method (DQM) was proposed by combining a spline interpolation operator having a fundamental function with minimal compact support and a spline quasi-interpolation operator reproducing the polynomials in the spline space. It is a general framework that provides results that differ from the ones obtained by defining specific schemes with structures which depend on the degree of the B-spline to be considered. The main drawback of these boolean sum DQMs is that the number of evaluation points increases quickly with the degree of the B-spline due to the use of a quasi-interpolation operator. We propose a different construction avoiding this problem and derive explicit results for low degree B-splines.