Difference equations, serving as the discrete analogue to differential equations, have long been a linchpin in the study of dynamic systems. These equations define sequences recursively, and their ...

We survey many old and new results on solutions of the following pair of adjoint differential-difference equations: \begin{align*} \tag{1} up'(u) = - ap(u) - bp(u - 1 ...

This paper develops two local mesh-free methods for designing stencil weights and spatial discretization, respectively, for parabolic partial differential equations (PDEs) of ...