The application of the quasistationary derivatives method for calculating analytical solutions of spatial kinetics problems

The quasistationary derivatives method is applied in the paper to improve efficiency of numerical algorithms used for calculating analytical solutions of spatial kinetics problems. A one-dimensional problem (BSS-6) published in the ANL Benchmark Problem Book is considered. According to the approach used by the authors of BSS-6, the system of reactor kinetics equations is presented by a system of ordinary differential equations (ODE) obtained after approximation of the diffusion operator by a finite-difference scheme, thus the analytical solution is calculated on the basis of the solution of the full eigenvalue problem. The difficulty is that the matrix of this stiff system is ill-conditioned, therefore standard subroutines for solving problems of linear algebra appear to be unstable numerically here because of the round-off error. The quasistationary derivatives method is used as a preconditioning procedure to diminish the condition number of the system matrix. (author)