A novel mathematical model for two-energy groups of the point kinetics reactor dynamics

• Fundamental matrix for the two-energy group of the point kinetics equations is introduced.
• Merging the piecewise constant functions over a partition in time into the fundamental matrix.
• The results confirm the theoretical analysis and indicate the range of applicability.
• Stiff linear and/or nonlinear differential equations for I-group of delayed neutrons are solved.
• The great advantage is that the method remains valid for full space-time kinetics.

The point kinetics equations for reactor dynamic systems are normally described and treated for one-energy group, which modeled as stiff coupled differential equations, and their solution by the conventional explicit methods will give a stable consistent result only for very small time steps. A novel analytical formulation is constructed and converged to high accuracy from the merger of the piecewise constant functions over a partition in time into the fundamental matrix for the two-energy group of the point kinetics equations. The resulting system of stiff linear and/or nonlinear differential equations for an arbitrary number of delayed neutrons is solved exactly over each time step. Through analytical inversion technique of the fundamental matrix and the stability of the method, we demonstrate its high accuracy for a variety of imposed reactivity insertions found in the literature for three dimensional homogeneous reactors. From knowledge of how the error term behaves the computational results indicate that the method is efficient and accurate for multi-dimensional homogeneous reactors.