Heun functions, which generalise the well‐known hypergeometric functions, are solutions to the Heun differential equation – a second‐order linear differential equation with four regular ...

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 ...

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.

A new definition of a guiding function for functional differential equations is given, which is sometimes better for applications than the known one by Mawhin. We then prove an existence result for ...

Motivated essentially by several recent works on interesting generalizations of the first-order Volterra-type integro-differential equation governing the unsaturated behavior of the free electron ...

The method of characteristics for solving first order quasilinear equations will be discussed. The three main types of linear second order partial differential equations will be considered: parabolic ...

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

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 ...

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.