Numerical methods for nonlocal and fractional models

Understand

Partial differential equations (PDEs) are used, with huge success, to model phenomena arising across all scientific and engineering disciplines.

• However, across an equally wide swath, there exist situations in which PDE models fail to adequately model observed phenomena or are not the best available model for that purpose.
• On the other hand, in many situations, nonlocal models that account for interaction occurring at a distance have been shown to more faithfully and effectively model observed phenomena that involve possible singularities and other anomalies.
• In this article, we consider a generic nonlocal model, beginning with a short review of its definition, the properties of its solution, its mathematical analysis, and specific concrete examples.