The multi-group integro-differential equations of the neutron diffusion kinetics. Solutions with the progressive polynomial approximation in multi-slab geometry

The multi-group integro-differential equations of the neutron diffusion kinetics (IDE-NDK) was presented and solved numerically in multi-slab geometry with the use of the progressive polynomial approximation. Four applications were computed: a positive ramp, a negative ramp, a sinusoidal and an instantaneous change of thermal macroscopic cross-sections in an 120 slab-nuclear reactor for a 2 prompt-group model. The results showed good accuracy for the developed non-iterative algorithms. It was shown the advantage of using the IDE-NDK over the traditional partial differential equations of the neutron diffusion kinetics from an accuracy point of view. Finite difference algorithms were also developed to obtain initial conditions and to make desired comparisons.