On an analytical representation for the solution of the neutron point kinetics equation free of stiffness

• We develop an analytical solution for the point kinetics equation free of stiffness.
• We use the decomposition method to construct a recursive system for neutron density and precursors concentration.
• We present numerical results for constant, step, ramp, quadratic and sine shape reactivity functions.

In this work, we report on an analytical representation for the solution of the neutron point kinetics equation, free of stiffness and assuming that reactivity is a continuous or sectionally continuous function of time. To this end, we cast the point kinetics equation in a first order linear differential equation. Next, we split the corresponding matrix into a diagonal matrix plus a matrix that contains the remaining terms. Expanding the neutron density and the delayed neutron precursor concentrations in a truncated series allows one to construct a recursive system in form of a first order matrix differential equation with source. The initialization of the recursion procedure is of diagonal form and has no source but satisfies the initial conditions. The remaining equations are subject to null initial conditions and include the time-dependent diagonal elements together with the off-diagonal elements as a source term. The solution is obtained in an analytical representation which may be evaluated for any time value, because it is free of stiffness. We present numerical simulations and comparisons against results from the literature for a constant, a step, a ramp, a quadratic, and a sine shaped reactivity function.