Partial differential equations (PDEs) are a class of mathematical problems that represent the interplay of multiple variables, and therefore have predictive power when it comes to complex physical ...

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 ...

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 ...

Runge-Kutta methods applied to stiff systems in singular perturbation form are shown to give accurate approximations of phase portraits near hyperbolic stationary points. Over arbitrarily long time ...

We investigate the asymptotic properties as t → ∞ of the following differential equation in the Hilbert space H: $\ddot x(t) + a(t)\dot x(t) + \nabla G(x(t)) = 0,t \ge 0,$ where the map \[\mathbb{R}_ ...

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 ...

Mathematics is the language that lets us describe the universe. Galileo Galilei was already convinced of that in the 16th century. But even everyday phenomena such as the melting of an ice cube in a ...