Construction of Compact Finite Difference Schemes by Classic Differential Quadrature

• Main Authors: Fangzong Wang, Mingshuai Pan, Yong Wang
• Format: Article
• Language: English
• Published: MDPI AG 2017-03-01
• Series: Applied Sciences
• Subjects: compact finite difference scheme; differential quadrature methods; grids; boundary value methods; Fourier stability analysis
• Online Access: http://www.mdpi.com/2076-3417/7/3/284

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.