  Three types of boundary integral equation (BIE) methods are employed to
obtain closed-form solutions of a wave-scattering problem which are compared to
the exact, closed-form (reference), solution deriving from the
separation-of-variables technique. The problem involves either Dirichlet (D) or
Neumann (N) boundary conditions (BC) for a scatterer that is a circular
cylinder submitted to one or two incident waves. The three BIE methods lead to
different expressions for the traction (for D-BC) or boundary displacement (for
N-BC) by which numerous resonances are predicted whose frequency of occurrence
differs from one method to another. This is interpreted as being the sign that
the three methods are generally-defective and the resonances are 'spurious'.
This 'disease' is cured by combining two BIE into one in such a way that the
resulting BIE gives rise to a closed-form solution identical to the exact
reference solution devoid of spurious resonances.
