Harmonic functions, defined as twice continuously differentiable functions satisfying Laplace’s equation, have long been a subject of intense study in both pure and applied mathematics.

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.

Waveguide-based structures can solve partial differential equations by mimicking elements in standard electronic circuits. This novel approach, developed by researchers at Newcastle University in the ...

Facebook researchers built a new neural network that can solve complex mathematical equations, even those dealing with calculus. Here's how it works.

Partial differential equations can describe everything from planetary motion to plate tectonics, but they’re notoriously hard to solve.

This study focuses on the numerical resolution of backward stochastic differential equations with data dependent on a jump-diffusion process. We propose and analyse a numerical scheme based on ...

Mathematicians have found solutions to a 140-year-old, 7-dimensional equation that were not known to exist for more than a century despite its widespread use in modeling the behavior of gases.

One breakthrough came in 2010, when Dominic Berry, now at Macquarie University in Sydney, built the first algorithm for solving linear differential equations exponentially faster on quantum, rather ...

Existence of positive periodic solutions of third-order differential equations is established using an explicit Green's function and a fixed-point theorems on cones. Rocky Mountain Journal of ...