An integral equation formulation of the <i>N</i>-body dielectric spheres problem. Part I: numerical analysis

In this article, we analyse an integral equation of the second kind that represents solution N interacting dielectric spherical particles undergoing mutual polarisation. A traditional analysis can not quantify scaling stability constants- and thus approximation error- with respect to number involved spheres. We develop a new priori error demonstrates -independent continuous discrete formulations equation. Consequently, obtain convergence rates are independent .