In this paper methods based on the boundary integral equations of Brakhage and Werner, Leis, Panich, Kussmaul and Burton and Miller for the solution of the exterior Helmholtz equation are considered. Each of these equations contain a weighting parameter. The relationship between the choice of weighting parameter, the condition of the linear system of equations derived through collocation, and the error in the solution is studied. The problem of choosing the free parameter to minimise the resulting error is discussed.
This paper was based on chapter 4 of the PhD
and the contents of this paper were published as the following journal paper