Solution of the point reactor kinetics equations with temperature feedback by the ITS2 method

The ITS2 method is used to solve the point-reactor kinetics equations in the integral formulation with arbitrary number of delayed neutron groups and Newtonian temperature feedback. The method is based on low-order Taylor series expansions of neutron density and reactivity functions and uses variable time steps to control the numerical instabilities resulting from the stiff nature of the governing equations. Time steps are determined through an analytic criterion relating their magnitudes to the maximum admissible truncation error in the neutron-density expansion series. Temperature feedback is included in the reactivity as a function of the neutron density for different input types, including step change with adiabatic temperature feedback and compensated ramp functions. An iterative procedure is applied to determine the time steps while simultaneously updating the reactivity function. Numerical results show the ITS2 method is highly accurate for solving point reactor dynamics problems with temperature feedback.