Keywords: closed–form solutions, point kinetics equations, reactivity feedback, decomposition method, temperature feedback, time–dependent reactivity, neutron density, nonlinear ODEs, ordinary differential equations, numerical simulation, nuclear reactors, nuclear energy, nuclear power
On a closed–form solution of the point kinetics equations with reactivity feedback of temperature
An analytical solution of the point kinetics equations to calculate time–dependent reactivity by the decomposition method has recently appeared in the literature. In this paper, we consider the neutron point kinetics equations together with temperature feedback effects. To this end, point kinetics is perturbed by a temperature equation that depends on the neutron density, obtaining a second–order non–linear ordinary differential equation. This equation is then solved by the decomposition method by expanding the neutron density in a series and expressing the non–linear terms by Adomian polynomials. Upon substituting these expansions into the non–linear ordinary equation, we construct a recursive set of linear problems that can be solved and resulting in an exact analytical representation for the solution. We also report numerical simulations and comparison against literature results.