A Matrix exponential technique to solve neutron diffusion equations in heterogeneous assemblies.

Abstract

In this thesis we present a method to generate the natural spacial modes of an atomic reactor model from the time-dependent multi group neutron diffusion equations. In chapter H> an original method called the MEX theory is outlined which finds the eigenvalues and associated eigenvectors of a linear operator derived from this set of equations. The MEX theory generates these eigenvalues in terms of a product of matrix exponential functions. This is hopefully an improvement over the finite difference methods commonly used. Two computer programs were written during the course of the research and results from a test problem are presented in chapter Possible extensions and improvements to the MEX theory are indicated in chapter 6 and a discussion of the mathematical characteristics of the relevant operators is found in the appendix.