In this paper, the real scalar field equation in Schwarzschild-de Sitter spacetime is solved numerically with high precision. A method called 'polynomial' approximation is introduced to derive the relation between the tortoise coordinate x and the radius r. This method is different from the 'tangent' approximation [1] and leads to more accurate result. The Nariai black hole is then discussed in details. We find that the wave function is harmonic only near the horizons as I. Brevik and B. Simonsen [1] found. Howerver the wave function is not harmonic in the region of the potential peak, with amplitude increasing instead. Furthermore, we also find that, when cosmological constant decreases, the potential peak increases, and the maximum wave amplitude increases.

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By generalizing the method of I. Brevik et al. the scalar field equation between the outer black hole horizon and the cosmological horizon in the extreme Reissner-Nordström-de Sitter (RNdS) geometry is solved. The field amplitude, as well as the potential, is shown graphically by introducing the "tangent " approximation, which is more exact than that used by I. Brevik et al., of the tortoise coordinate. There are two limiting cases of our special interest. The first one is when the cosmological horizon is very close to the outer horizon of the "black hole." The second one is when they are far apart. And the reflection and transmission coefficients are worked out in the two cases respectively.

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