On the well-posedness of Pocklington's equation for a straight wire antenna and convergence of numerical solutions

In this paper we describe some recent mathematical results concerning Pockl ington's integro-differential equation for the current induced on a straigh t, thin wire by an incident harmonic electromagnetic field. These results s how that this equation is well-posed in suitable function spaces and descri be the continuity and smoothness properties of the solution compared with t he incident field. We also describe some new rigorous convergence results f or a simple Galerkin type numerical solution method for the equation.