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

Real Scalar Field Scattering with Polynomial Approximation around Schwarzschild-de Sitter Black-hole