Electromagnetic integral equations offer a powerful framework for modelling wave propagation and scattering phenomena by recasting Maxwell’s equations into formulations involving integrals over ...

Fast direct solvers have emerged as a transformative approach in the numerical resolution of integral equations pivotal to electromagnetic analysis. These methods are designed to resolve the dense ...

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 ...

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; ...

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 ...

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 ...

Description: Banach and Hilbert spaces; linear operators; spectral theory of compact linear operators; applications to linear integral equations and to regular Sturm-Liouville problems for ordinary ...