Can the CDCC calculation be improved?

The Continuum Discretized Coupled Channels method of including breakup effects in the calculation of nuclear reactions, when applied to unstable nuclei, requires the inclusion of a large number of coupled channels, and the numerical computational effort increases correspondingly. The computing time with traditional finite difference techniques [1] scales with the cube of the number of channels $N$. The scaling with a new spectral integral method ($SIEM$) [2] of solving coupled equations is likewise $N^{3}$. However, the structure of the matrices that occur in the numerical algorithm of the $SIEM$ is different from that of the finite difference methods, and lends itself well to iterative solutions, reducing the numerical complexity to $N^ {2}$ times the number of required iterations. Various iterative schemes will be considered, and their convergence properties will be examined. \bigskip\newline[1] \ I. J. Thompson, code FRESCO, Comp. Phys. Rep. \textbf{7}, 167 (1988);\newline[2] \ R. A. Gonzales, S. -Y. Kang, I. Koltracht and G. Rawitscher, J. of Comput. Phys. \textbf{153}, 160 (1999).