Abstract
A general expression for a special type of functions has been introduced, which allows us to approximate the exponential function in an economical manner. Also, the different cases of Padé approximation are perturbed so that the resulting approximations have a smaller minimum maximum error on the desired interval especially at large transient time steps. In addition, the Padé approximations and the resulting perturbed ones are applied to the solution of the point kinetics equations of nuclear reactor with different types of reactivity. The results of the approximations developed show large correction effects at small transients and perform quite well at large transients. Also, the factorization methods based on using temporarily the complex plane with the analytical inversion are applied to obtain the general solution of the point kinetics equations.