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 ...

Partial differential equations can describe everything from planetary motion to plate tectonics, but they’re notoriously hard to solve. Unless you’re a physicist or an engineer, there really isn’t ...

Maths Class 12 Differential Equations MCQs: The Central Board of Secondary Education conducts the annual board exams for class 12, which are considered among the most important for students. The ...

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 ...

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 ...

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 ...

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}_ ...

Earlier this year, Mathematician Ian Stewart came out with an excellent and deeply researched book titled "In Pursuit of the Unknown: 17 Equations That Changed the World" that takes a look at the most ...