Mathematical treatment for two-point reactor kinetics model of reflected systems

An appropriate precise mathematical model of physical systems has to be developed to predict the dynamic behavior of reflected systems, which comprise core and reflector regions. The present paper developed an accurate and economic mathematical method based on the fundamental matrix to describe the spectrum behavior for one- and two-point kinetics model with multi-group of delayed neutrons. The developed method utilizes the eigenvalues and eigenvectors of the coefficient matrix for the homogeneous linear differential equations resulting from the stiff system of coupled partial differential equations in two-point kinetics model. Moreover, the inverse of the fundamental matrix is calculated analytically. It was evident that the fundamental matrix method is proven to be an excellent solution for cases in which the reactivity is represented by a series of steps and improves accuracy for more general cases of time varying reactivity including Newtonian temperature feedback. The stability of the system is analyzed for different types of reactivity. Finally, the numerical results obtained with these algorithms are applied and verified for different applications of reflected reactors.