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 ...

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.

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 ...

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 ...