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 ...

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 ...

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 ...

Boundary integral equation (BIE) methods have emerged as a robust computational framework for addressing problems in elasticity analysis by reformulating partial differential equations into equivalent ...

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 ...

Integral equations in various scientific theories and their relation to differential equations. Methods of solving linear problems with Hilbert Schmidt, Cauchy, and Wiener-Hopf type kernels; ...

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 ...

Methods for solving linear, ordinary, and partial differential equations of mathematical physics. Green's functions, distribution theory, integral equations, transforms, potential theory, diffusion ...