An analytical solution of the point kinetics equations with time-variable reactivity by the decomposition method

In this work, we report an analytical solution for the point kinetics equations by the decomposition method, assuming that the reactivity is an arbitrary function of time. The main idea initially consists in the determination of the point kinetics equations solution with constant reactivity by just using the well-known solution results of the first-order system of linear differential equations in matrix form with constant matrix entries. Applying the decomposition method, we are able to transform the point kinetics equations with time-variable reactivity into a set of recursive problems similar to the point kinetics equations with constant reactivity, which can be straightly solved by the mentioned technique. For illustration, we also report simulations for constant, linear and sinusoidal reactivity time functions as well comparisons with results in literature.