Abstract
We are concerned with an efficient numerical solution of linear equations at each time-stepping of the trapezoidal rule applied to a system of ordinary differential equations (ODEs), which is assumed to be linear with a constant coefficient matrix of large dimension. By referring to the idea of the deflated CG method by Y. Saad et al, the present paper describes a method to share several computational costs in the CG process over a number of computational steps. It can suppress increase of the memory usage as well as reduce the total number of CG iteration. Numerical examples depict its efficiency.
