Construction of compact finite difference schemes by classic differential quadrature

Abstract

Using classic differential quadrature formulae and uniform grids, this paper systematically constructs a variety of high-order finite difference schemes, and some of these schemes are consistent with the so-called boundary value methods. The derived difference schemes enjoy the same stability and accuracy properties with correspondent differential quadrature methods but have a simpler form of calculation; thus, they can be seen as a compact format of classic differential quadrature methods. Through systematic Fourier stability analysis, the characteristics such as the dissipation, dispersion and resolution of the different schemes were studied and compared.