Partial differential equations (PDEs) form the mathematical backbone for models in physics, engineering, biology and finance. They express relationships between the rates of change of a multivariable ...

Two new approaches allow deep neural networks to solve entire families of partial differential equations, making it easier to model complicated systems and to do so orders of magnitude faster. In high ...

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 ...

Introductory course on using a range of finite-difference methods to solve initial-value and initial-boundary-value problems involving partial differential equations. The course covers theoretical ...

My research interests are in applied and computational mathematics. I am interested in developing and analyzing high-order numerical methods for solving partial differential equations and fractional ...

Neuromorphic computers, inspired by the architecture of the human brain, are proving surprisingly adept at solving complex mathematical problems that underpin scientific and engineering challenges.