Differences between extended-integral-equation and method-of-auxiliary-sources solutions of a simple scattering problem

The auxiliary surface current, determined by applying the Method of Auxiliary Sources (MAS) to scattering problems by perfect conductors, may exhibit a certain form of oscillations, which are inherent to MAS and are independent of the word-length and the numerical-integration routines. The purpose of the present work is to demonstrate analytically that the “extended integral equation” (which is similar to the MAS one with the main difference that the unknown is the actual surface current on the scatterer) does not exhibit oscillations of the type described above. Hence, oscillations occurring in the extended integral equation are likely to be due to finite word-length or numerical integration errors.