This is an interesting paper. The authors continue their study of the convergence of dynamic iteration methods for large systems of initial value problems. They consider the initial value problem &xdot; + A x = f , x ( 0 ) = x 0 , t > 0 , where A is an n × n complex matrix. With the splitting A = : M - N they obtain the iteration scheme &xdot; n + Mx n = Nx n - 1 + f , x n ( 0 ) = x 0 , which is discretized using linear multistep methods.
The paper shows how the study of the interaction between the splitting of the system into subsystems and the time discretization method chosen can be reduced to a graphical test. This test relates the set of convergence of the splitting of the matrix to the stability region of the discretization method.
