An efficient technique for the point reactor kinetics equations with Newtonian temperature feedback effects

Abstract

The point reactor kinetics equations of multi-group of delayed neutrons in the presence Newtonian temperature feedback effects are a system of stiff nonlinear ordinary differential equations which have not any exact analytical solution. The efficient technique for this nonlinear system is based on changing this nonlinear system to a linear system by the predicted value of reactivity and solving this linear system using the fundamental matrix of the homogenous linear differential equations. The nonlinear point reactor kinetics equations are rewritten in the matrix form. The solution of this matrix form is introduced. This solution contains the exponential function of a variable coefficient matrix. This coefficient matrix contains the unknown variable, reactivity. The predicted values of reactivity in the explicit form are determined replacing the exponential function of the coefficient matrix by two kinds, Backward Euler and Crank Nicholson, of the rational approximations. The nonlinear point kinetics equations changed to a linear system of the homogenous differential equations. The fundamental matrix of this linear system is calculated using the eigenvalues and the corresponding eigenvectors of the coefficient matrix. Stability of the efficient technique is defined and discussed. The efficient technique is applied to the point kinetics equations of six-groups of delayed neutrons with step, ramp, sinusoidal and the temperature feedback reactivities. The results of these efficient techniques are compared with the traditional methods.