Analytical representation of the solution of the point reactor kinetics equations with adaptive time step

• We develop an analytical solution to the point reactor kinetics equations in the integral formulation.
• We use an analytic criterion for time step control, based on the desired accuracy.
• We apply the solution to several prescribed reactivity inputs.
• Results show this method is highly accurate and suitable for benchmarking purposes.

An explicit analytical solution is developed for the point reactor kinetics equations in the integral formulation from low-order Taylor series expansions of neutron density and reactivity functions. Numerical instability, resulting from the stiff nature of the nonlinear ordinary differential equations, is controlled through the use of variable time steps determined by requiring that, in each step, the relative neutron density truncation error be within a specified tolerance. As a result, the accumulated error over a number of time steps is kept within acceptable limits. Neutron densities and precursor concentrations obtained in this way were computed for a number of different reactivity insertions including step, ramp, and oscillatory changes, and compared with several methods available in the literature, with excellent agreement with the more accurate solutions. The method, named ITS2, provides a simple, yet accurate, analytical approximation to the reactor kinetics equations with prescribed reactivity and arbitrary number of delayed groups, the only possible limitation being the number of time steps needed when extreme accuracy is demanded in specific transient situations.