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.Comment: 12 pages, 3 figures, 3 tables, version accepted for publication in
JCAP (http://iopscience.iop.org/1475-7516/2011/11/047
