Banded, stable, skew-symmetric differentiation matrices of high order

Differentiation matrices play an important role in the space discretization of first-order partial differential equations. This work considers grids on a finite interval and treats homogeneous Dirichlet boundary conditions. Differentiation matrices of orders up to $6$ are derived that are banded, stable and skew symmetric. To achieve these desirable properties, nonequidistant grids are considered.