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

摘要

In this thesis we present a method to generatethe natural spacial modes of an atomic reactor model fromthe time-dependent multi group neutron diffusion equations.In chapter H> an original method called the MEX theory isoutlined which finds the eigenvalues and associated eigenvectorsof a linear operator derived from this set ofequations. The MEX theory generates these eigenvalues interms of a product of matrix exponential functions. Thisis hopefully an improvement over the finite differencemethods commonly used.Two computer programs were written during thecourse of the research and results from a test problemare presented in chapter Possible extensions andimprovements to the MEX theory are indicated in chapter 6and a discussion of the mathematical characteristics ofthe relevant operators is found in the appendix.