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 ...

Parameter embedding methods, also known as continuation methods, are robust and accurate numerical techniques employed to solve non-linear algebraic equations. They are used to solve equations that ...

We crunch numbers and use basic binary compute to determine what happens next in a linear pattern or sequence using classical algorithms. But nonlinear differential equations are tougher.

We study the compactness of a sequence of weak solutions to the (p-th power) nonlinear Klein-Gordon equation with uniform natural energy bounds. A refinement of the Rellich's Theorem of compact ...

A UNSW Sydney mathematician has discovered a new method to tackle algebra's oldest challenge—solving higher polynomial equations.