A family of high order finite difference schemes with good spectral resolution
This paper presents a family of finite difference schemes for the first and second derivatives of smooth functions. The schemes are Hermitian and symmetric and may be considered as a more general version of the standard compact (Padé) schemes. They are different from the standard Padé schemes in that the first and second derivatives are evaluated simultaneously. For the same stencil width, the proposed schemes are two orders higher in accuracy, and have significantly better spectral representation. Eigenvalue analysis, and numerical solutions of the one-dimensional advection equation are used to demonstrate the numerical stability of the schemes. \(\copyright\) Academic Press.
scientific article; zbMATH DE number 1212280