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 ...

Partial differential equations (PDE) describe the behavior of fluids, structures, heat transfer, wave propagation, and other physical phenomena of scientific and engineering interest. This course ...

In this topic, our goal is to utilise and further develop the theory of non-linear PDEs to understand singular phenomena arising in geometry and in the description of the physical world. Particular ...

Calculation: A representation of a network of electromagnetic waveguides (left) being used to solve Dirichlet boundary value problems. The coloured diagrams at right represent the normalized ...

We derive a partial differential equation (PDE) representation for the value of financial derivatives with bilateral counterparty risk and funding costs. The model is very general in that the funding ...

The Navier-Stokes equations describe simple, everyday phenomena, like water flowing from a garden hose, yet they provide a million-dollar mathematical challenge. Physics contains equations that ...