  Green's function of the problem describing steady forward motion of bodies in
an open ocean in the framework of the linear surface wave theory (the function
is often referred to as Kelvin's wave source potential) is considered. Methods
for numerical evaluation of the so-called `single integral' (or, in other
words, `wavelike') term, dominating in the representation of Green's function
in the far field, are developed. The difficulty in the numerical evaluation is
due to integration over infinite interval of the function containing two
differently oscillating factors and the presence of stationary points. This
work suggests two methods to approximate the integral and its derivatives.
First of the methods is based on the idea suggested by D.Levin in 1982 ---
evaluation of the integral is converted to finding a particular slowly
oscillating solution of an ordinary differential equation. To overcome
well-known numerical instability of Levin's collocation method, an alternative
type of collocation is used; it is based on a barycentric Lagrange
interpolation with a clustered set of nodes. The second method for evaluation
of the wavelike term involves application of the steepest descent method and
Clenshaw--Curtis quadrature. The methods are numerically tested and compared
for a wide variety of parameters.
