Banded, stable, skew-symmetric
differentiation matrices of high order
Ernst Hairer and Arieh Iserles
Abstract. Differentiation matrices play an important role in the space discretization of
first order partial differential equations. The present 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,
non-equidistant grids are considered.
Key Words. Differentiation matrices, space discretisation
of PDEs, structure preservation, geometric numerical integration.