Numerical analysis of an unbounded operator arising from an electro-magnetic interior scattering problem (Q1607582)

The paper is devoted to the numerical solution of second kind equations involving the integral operator with the singular kernel \(|s-t|^-1 (f(s)-f(t))\) over the unit interval. The mapping properties of this operator are studied in the normed space \(X\) of all uniformly Hölder continuous functions. The numerical solution uses a simple Nyström method. The author shows that the discretizations, which are not compact, converge pointwise to the singular operator in \(X\). This together with some properties of the discrete matrices is used to prove the convergence of Nyström's method. The paper contains also results of numerical experiments using the analyzed method and similar methods.