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A general class of two-step alternating-direction semi-implicit methods is proposed for the approximate solution of the semidiscrete form of the space-dependent reactor kinetics equations. An exponential transformation of the semi-discrete equations is described which has been found to significantly reduce the truncation error when several alternating-direction semi-implicit methods are applied to the transformed equations. A subset of this class is shown to be a consistent approximation to the differential equations and to be numerically stable. Specific members of this subset are compared in one-and two-dimensional numerical experiments. An "optimum" method, termed the NSADE (Non-Symmetric Alternating-Direction Explicit) method is extended to three-dimensional geometries. Subsequent three-dimensional numerical experiments confirm the truncation error, accuracy, and stability properties of this method.

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 useable 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 AlternatingDirection Explicit scheme is slightly superior.

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