Mathematicians finally understand the behavior of an important class of differential equations that describe everything from ...

A partial differential equation (PDE) is a mathematical equation that involves multiple independent variables, an unknown function that is dependent on those variables, and partial derivatives of the ...

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 ...

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 ...

This addendum corrects an error in the notation of earlier versions of our paper "Partial differential equation representations of derivatives with bilateral ...