Application of Explicit Cyclic Schemes Using Chebyshev Polynomials in Problems on Spatial Kinetics of Nuclear Reactors

Two explicit cyclic algorithms have been constructed in this paper for the problem on spatial kinetics of nuclear reactors. The first algorithm is based on explicit cyclic schemes with varying time steps proposed earlier by V. I. Lebedev to solve stiff problems [1,2]. The second algorithm is based on the method of local iterations proposed by O.V. Lokutsievskiy and V.O. Lokutsievskiy for the parabolic equation [3] and further developed by V. T. Zhukov [4]. The application of these algorithms for neutron kinetics is an urgent problem, because they allow to overcome the well known disadvantages of simple explicit schemes (too rigid requirements on time steps that result in big computing times) and yet to retain their logical simplicity important for parallel techniques. Numerical experiments allow to drive at the conclusion that the application of the explicit cyclic schemes with parameters determined by Chebyshev polynomials is very promising and their efficiency is comparable to the widely used implicit schemes yet retaining logical simplicity characteristic for the explicit schemes.