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 ...

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; ...

Purdue faculty dedicate countless hours to exploring the frontiers of their respective fields, pushing the boundaries of knowledge and contributing to the ever-evolving landscape of academia. To ...

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 ...

Glenn Bruda, a 17-year-old high school student, is credited with the discovery of a novel calculus formula that he has named the Maclaurin Integration technique. (Photo courtesy of Jennifer Bruda) ...