Solution of two-dimensional space-time multigroup reactor kinetics equations by generalized Padé and cut-product approximations

New methods based on the class of Padé and cut-product approximations are applied to the solution of the multigroup diffusion theory reactor kinetics equations in two space dimensions. The methods are shown to be consistent and numerically stable. The stability of the developed approximations is studied and it is in general A(α)-stable, where 0 ⩽ α ⩽ π/2 and therefore they are quite efficient in the presence of extreme stiffness, as shown by numerical results for some typical test cases. The system of stiff coupled differential equations is represented in a matrix form and due to the particular structure of this matrix, new algorithm based on the back-substitution is proposed for analytical inversion of the “A” matrix. The method has been tested for different benchmark problems. The results indicated that this method can allow much larger time steps and thus save much computational time as compared to the other conventional methods.