Quadrature algorithms to the luminosity distance with a time-dependent   dark energy model
  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. 
Nan-Nan Yue, De-Zi Liu, Xiao-Xing Pei, Fang-Fang Zhu, Tong-Jie Zhang   and Zhi-Liang Yang
astro-ph.CO