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.

The Characteristics and capabilities of the best codes for solving the initial value problem for ordinary differential equations are studied. Only codes which are readily available, portable, and very ...

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 ...

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

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 ...

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 ...