  As one of the fitting methods, the polynomial approximation is effective to
process sophisticated problem. In this paper, we employ this approach to handle
the scattering of scalar field around the Schwarzschild-de Sitter black-hole.
The complex relationship between tortoise coordinate and radial coordinate is
replaced by the approximate polynomial. The Schr$\ddot{o}$dinger-like equation,
the real boundary conditions and the polynomial approximation construct a full
Sturm-Liouville type problem. Then this boundary value problem can be solved
numerically according to two limiting cases: the first one is the Nariai
black-hole whose horizons are close to each other, the second one is when the
horizons are widely separated. Compared with previous results (Brevik and
Tian), the field near the event horizon and cosmological horizon can have a
better description.
