Functional integral equations constitute a broad class of problems in which an unknown function appears under an integral sign. These equations play a pivotal role in modelling complex phenomena in ...

SIAM Journal on Applied Mathematics, Vol. 75, No. 3 (2015), pp. 929-952 (24 pages) We present a new class of well-conditioned integral equations for the solution of two and three dimensional ...

For the integral equation $\mathrm{u}\left(\mathrm{x}\right)={\int }_{0}^{1}\mathrm{K}(\mathrm{x},\mathrm{y})\times \mathrm{u}\left(\mathrm{y}\right)\mathrm{d}\mathrm ...

Engineers have designed a metamaterial device that can solve integral equations. The device works by encoding parameters into the properties of an incoming electromagnetic wave; once inside, the ...

Analogue computer: Brian Edwards (left), Nader Engheta (centre) and Nasim Mohammadi Estakhri show-off their microwave protoype. (Courtesy: Eric Sucar/University of Pennsylvania) Metamaterials have ...

Studies properties and solutions of partial differential equations. Covers methods of characteristics, well-posedness, wave, heat and Laplace equations, Green's functions, and related integral ...

The Schrödinger equation rewrote the rules of matter and forever changed the field of chemistry. Donald Truhlar, a chemist at the University of Minnesota, calls it the “greatest advance of the 20th ...