The use of the frill generator in thin-wire integral equations

For a frill-generator feed, certain fundamental mathematical properties of Hallenʹs and Pocklingtonʹs equations with the approximate kernel are stated and derived. For a particular moment-method procedure (Galerkinʹs method with pulse functions applied to Hallenʹs equation), the consequences to the numerical solutions are carefully examined. Generalizations to other numerical methods with subsectional basis functions are discussed. Many of our results come from studying the simpler problem of the infinite dipole analytically and applying the understanding thus obtained to the case of the finite dipole.