Abstract
The multiplication of neutrons in a nuclear system is typically quantified by an eigenvalue for the system that determines if the system supports sustaining chain reactions. Using neutron diffusion theory, this chapter presents a numerical method for solving these socalled k-eigenvalue problems. The equations are discretized in 1-D geometry and the inverse power iteration method is applied to the resulting generalized eigenvalue problem. A justification of the inverse power method is given in terms of the properties of matrices, and an implementation based on LU factorization with Python is given. The numerical solution is computed for several test problems and compared with analytic solutions where possible.
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