Cálculo da Exponencial Matricial via Método de Aproximação de Padé do modelo da Cinética Pontual de Nêutrons com reatividade dependente do tempo

Abstract

In this work, a solution of the Neutron Point Kinetics Equations is presented using the Padé Approximation Method. Through this methodology, the matrix exponential of the coefficients of the aforementioned equations is solved, overcoming its stiffness characteristic. Six groups of delayed neutron precursors are considered in this model for different types of reactivities: constant, ramp, quadratic, sinusoidal and zig-zag. For cases with temporal dependency, Piecewise Constant Approximation is used. It consists in approximating reactivity by a constant value in a short time interval together with the analytical continuation, which uses the solution from the previous step as initial condition to the next interval. The results obtained are compared with those in the literature using graphs and tables. In addition, the issue of computational time is also handled and the residual term is analyzed, using the differential equation itself and the maximum norm as an estimate for error control.