Reaction–diffusion dynamics lie at the heart of understanding pattern formation in complex systems, ranging from chemical reactions and biological patterning to engineering applications. At its core, ...

Mathematical modelling has emerged as an indispensable tool in understanding and optimising biosensor performance and reaction-diffusion processes. By coupling differential equations that describe ...

Observing nature shows that many temporal and spatial structures are not formed by the outside, but rather by the respective system itself. To study these self-organizing processes is the subject of ...

In the past few decades, the use of phase field-modeling equations for mathematical modeling has progressed. Phase separation has been studied extensively in thermodynamics and materials engineering, ...

Porous media play a critical role in various industrial fields due to their complex pore networks and considerable specific surface areas. The transport and reaction phenomena within porous media are ...

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