Alternating Direction Methods for the Reactor Kinetics Equations

A class of finite difference methods known as alternating semi-implicit techniques is presented for the solution of the multigroup diffusion theory reactor kinetics equations in two space dimensions. A subset of the above class is shown to be consistent with the differential equations and numerically stable. An exponential transformation of the semidiscrete equations is shown to reduce the truncation error of the above methods so that they become practical methods for two-dimensional problems. A variety of numerical experiments are presented which illustrate the truncation error, convergence rate, and stability of a particular member of the above class.