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 ...

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

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 ...

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 ...

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; ...