  In this paper, new boundary differential equations for the two-dimensional
exterior scattering problem have been derived. It has been shown that the
Helmholtz equation can be reduced to an inhomogeneous Bessel's equation in a
body-fitted coordinate system. By imposing the Sommerfeld radiation condition
to the general solution of the Bessel's equation, an integro-differential
equation, which is equivalent to the original Helmholtz equation, can be
obtained. The boundary differential equation can then be established by use of
the integration by parts to get rid of the integral in the integro-differential
equation for high frequency problems. Numerical examples have been presented to
demonstrate the validity of the new boundary differential equations.
