  In our previous work, we have proposed two methods for computing the
luminosity distance d_{L}^{\Lambda} in LCDM model. In this paper, two effective
quadrature algorithms, known as Romberg Integration and composite Gaussian
Quadrature, are presented to calculate the luminosity distance d_{L}^{CPL} in
the Chevallier-Polarski-Linder parametrization(CPL) model. By comparing the
efficiency and accuracy of the two algorithms, we find that the second is more
promising. Moreover, we develop another strategy adapted for approximating
d_{L}^{\Lambda} in flat LCDM universe. To some extent, our methods can make
contributions to the recent numerical stimulation for the investigation of dark
energy cosmology.
