A numerical solution to the nonlinear point kinetics equations using Magnus expansion

• The linear and nonlinear neutron point kinetic equation with Newtonian temperature feedback has been considered.
• We construct the exponential form of the solution using the Magnus expansion.
• The Magnus expansion is tested for step, ramp, sinusoidal and temperature feedback reactivity insertions.
• Results are in a good agreement with other available methods in the open literature.

The solution of point kinetics equations can predict the neutron density variation during the operation of a nuclear reactor, which is very important in reactor safety and analysis. The point kinetics equations are coupled nonlinear ordinary differential equations, which are stiff and difficult to solve. In this paper, the Magnus expansion is proposed to solve the neutron point kinetics equations. It is convenient to construct the exponential form of the solution with the Magnus expansion. The present method is tested using a variety of cases with step, ramp, sinusoidal and temperature feedback reactivity insertions. The results indicate that the method is accurate for thermal and fast reactors.