A while back, [Chris Lu] was studying how analog circuits, specifically op-amps can be used to perform mathematical operations and wondered if they could be persuaded to solve differential equations, ...

Stochastic nonlinear wave equations and Schrödinger equations represent a fascinating confluence of probability theory and the analysis of partial differential equations. By incorporating random ...

Dissipative wave equations constitute an extensive class of partial differential equations wherein damping terms play a pivotal role in governing the long-term dynamics of the system. Recent ...

This is a preview. Log in through your library . Abstract We consider an initial-boundary value problem for ${\partial _t}u - \partial _t^{ - \alpha }{\nabla ^2}u = f\left( x \right)$ , that is, for a ...

SIAM Journal on Numerical Analysis, Vol. 54, No. 2 (2016), pp. 1093-1119 (27 pages) A fully discrete approximation of the semilinear stochastic wave equation driven by multiplicative noise is ...

Pressure waves propagating through bubble-containing liquids in tubes experience considerable attenuation. Researchers have now derived an equation describing this phenomenon, demonstrating that ...

According to quantum mechanics, the physics theory that describes the zoo of subatomic particles, all matter can be described as both particles and waves. But is it real? When you purchase through ...

The Born rule, which connects the math of quantum theory to the outcomes of experiments, has been derived from simpler physical principles. The new work promises to give researchers a better grip on ...