A nonstiff solution for the stochastic neutron point kinetics equations

TL;DR

This paper introduces Double-DDM, a novel nonstiff method for solving stochastic neutron point kinetics equations, enabling direct computation of neutron and precursor densities over time with high accuracy.

Contribution

The paper presents Double-DDM, an adaptation of the diagonalization-decomposition method, providing a nonstiff solution for stochastic neutron kinetics without incremental time stepping.

Findings

Results agree with established methods

Effective for constant, linear, and sinusoidal reactivities

Allows direct calculation at any time point

Abstract

We propose an approach to solve the stochastic neutron point kinetics equations using an adaptation of the diagonalization-decomposition method (DDM). This new approach (Double-DDM) yields a nonstiff solution for the stochastic formulation, allowing the calculation of the neutron and precursor densities at any time of interest without the need of using progressive time steps. We use Double-DDM to compute results for stochastic problems with constant, linear, and sinusoidal reactivities. We show that these results strongly agree with those obtained by other approaches established in the literature. We also compute and analyze the first four statistical moments of the solutions.