Generalized power series method with step size control for neutron kinetics equations

Based on the power series method (PWS), a generalized power series method (GPWS) has been introduced for solving the point reactor kinetics equations. The stiffness of the kinetics equations restricts the time interval to a small increment, which in turn restricts the PWS method within a very small constant step size. The traditional PWS method has been developed using a new formula that can control the time step at each step while transient proceeds. Two solvers of the PWS method using two successive orders have been used to estimate the local truncation errors. The GPWS method has employed these errors and some other constraints to produce the largest step size allowable at each step while keeping the error within a specific tolerance. The proposed method has resolved the stiffness point kinetics equations in a very simple way with step, ramp and zigzag ramp reactivities. The generalized method has turned out to represent a fast and accurate computational technique for most applications. The method is seemed to be valid for a time interval that is much longer than the time interval used in the conventional numerical integration, and is thus useful in reducing computing time. The method constitutes an easy-to-implement algorithm that provides results with high accuracy for most applications where, the reactor kinetics equations are reduced to a differential equation in a matrix form convenient for explicit power series solution. Results obtained by GPWS method: attest the power of the theoretical analysis, they demonstrate that the convergence of the iteration scheme can be accelerated, and the resulting computing time can be greatly reduced while maintaining computational accuracy. The point kinetics equations have been solved as a preliminary simple case aimed at testing the applicability of the GPWS method to solve point kinetics equations with feedback or, space kinetics problems.