Abstract: This paper presents the numerical method for solving the rate equations of electron's average occupation probabilities by using multiple-time-scale perturbation theory.It is especially suitable for lower levels of elements, Since in that case the transition between neighbouring bound energy levels could be considered as fast, the others as slow. Under some reasonable physical assumptions the method leads to the analytic expressions for P_n as functions of the number of free electron, n_s.As a result, in stead of solvingstrong stitff ordinary ditferential equations of (dp_n)/(dt), we just need solving thedifferential equation for n_e and the algebraical equations for P_n. Therefore the problem is much simplified with avoiding the computation of Jacobi iaverse matrix which generally appears is the implicit schemes.