Numerical instability of time-discretized one-point kinetic equations

The one-point kinetic equations with numerical errors induced by the explicit, implicit and Crank±Nicolson integration methods are derived. The zero-power transfer functions based on the present equations are demonstrated to investigate the numerical stability of the discretized systems. These demonstrations indicate unconditional stability for the implicit and Crank± Nicolson methods but present the possibility of numerical instability for the explicit method. An upper limit of time mesh spacing for the stability is formulated and several numerical calculations are made to con®rm the validity of this formula.