Difference equations, as discrete analogues of differential equations, form a fundamental mathematical framework for describing systems that evolve incrementally over time or space. Coupled with ...

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 ...

Sometimes, it’s easy for a computer to predict the future. Simple phenomena, such as how sap flows down a tree trunk, are straightforward and can be captured in a few lines of code using what ...