# Multigroup Neutron Diffusion Equation

Let us consider a 1D reactor core which is divided into various energy groups and different regions having constant material properties. The discretization of the reactor core into various groups is shown in Figure 7.1.

Using the previous procedure, the shape functions are multiplied with Equation 7.6, and we will have

Integrating Equation 7.11 over the domain, we get

Further simplification of Equation 7.13 gives a system of algebraic equations. In matrix form, these algebraic equations look like

Here,

[K_{?}] is the stiffness matrix for the coupled neutron diffusion equation {ф} is the fuzzy neutron flux vector

In steady case [Q], the matrix is zero.

# Bibliography

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