Application of Alternating-Direction Implicit Methods to the Space-Dependent Kinetics Equations

An approximate solution-of the multigroup neutron diffusion kinetics equations with delayed neutrons in two-dimensional geometry can be obtained by matrix splitting methods based on an Alternating-Direction Implicit (ADI) scheme. The method is shown to be consistent and numerically stable. An exponential transformation of the semi-discrete equations reduces the truncation error so that the method becomes usable for practical computations. The results of numerical experiments are presented to illustrate the accuracy and stability of the method. These results indicate that another splitting method based on an Alternating-Direction Explicit scheme is slightly superior.