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 ...

Computational fluid dynamics (CFD) is a branch of physics that utilizes numerical methods and algorithms to analyze and predict the behavior of fluids and gases under various conditions. This field ...

In many biological and physical systems, feedback mechanisms depend on a set of thresholds associated with the state variables. Each feedback has a characteristic time scale. We suggest that ...

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