Numerical treatment for the point reactor kinetics equations using theta method, eigenvalues and eigenvectors

Highlights: •Theta method is treated for solving the matrix form of the point reactor kinetics equations. •Treatment theta method is based on the eigenvalues and the eigenvectors of the coefficient matrix. •Treatment theta method is applied to solve the point kinetics equations with step, ramp, sinusoidal and pulse reactivities. •The results of the treatment theta method are compared with the traditional methods. •Comparisons substantiate the accuracy of the treatment theta method. -- Abstract: The point reactor kinetics model is a stiff system of linear/nonlinear ordinary differential equations. In fact, the numerical solutions of this stiff model need a smaller time step intervals within various computational schemes. The aim of this work is an accurate numerical solution without need to the smaller time step intervals. Theta method is the most popular, simplest and widely used method for solving the first order ordinary differential equations. In light of this fact, theta method is treated for solving the matrix form of this model via the eigenvalues and corresponding eigenvectors of the coefficient matrix. In this work, the matrix form of the stiff point kinetics equations with multi-group of delayed neutrons is introduced. The treatment theta method is applied to solve the stiff point kinetics equations with six groups of delayed neutrons. The performance of the treatment theta method is evaluated in several case studies involving step, ramp, sinusoidal and pulse reactivities. The results of the treatment theta method are more accurate than the theta method comparing with the conventional methods.