Application of Backward Differentiation Formulas to Neutron Kinetics Problems

Abstract

The neutron kinetics equations belong to the class of stiff equations for numerical time integration schemes. In this work, the accuracy and speed of algorithms based on backward differentiation formulas (BDFs) are studied with regard to point and spatial neutron kinetics problems. Using a BDF algorithm with the automatic selection of time step and order, solutions to a number of model problems with both a positive and negative reactivity insertion are analyzed. Plots of numerical cost dependences on local and global errors are presented. The results indicate that algorithms based on BDFs are highly efficient and that their application to nuclear reactor simulation is justified.