Diagonal-norm summation by parts operators for finite difference approximations of third and fourth derivatives

High-order accurate finite difference operators for third and fourth derivatives are derived. The closures are based on the summation-by-parts (SBP) framework, thereby guaranteeing linear stability. Stability for nonlinear equations that support a convex extension can be achieved if the SBP operators are based on a diagonal norm. The boundary conditions are imposed using a penalty technique. The accuracy and stability properties of the newly derived SBP operators are demonstrated for both linear and nonlinear dispersive wave propagation problems.