In his doctoral thesis, Michael Roop develops numerical methods that allow finding physically reliable approximate solutions ...

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 ...

Applying a few simplifying assumptions and constructing a set of ordinary differential equations leads to a model that ...

Physics-informed neural networks (PINNs) have shown remarkable prospects in solving forward and inverse problems involving ...

The study of differential-difference equations and boundary value problems occupies an essential niche in applied mathematics, linking the theory of differential operators with discrete translation ...