Efficient computational system for transient neutron diffusion model via finite difference and theta methods

• Efficient computational system (ECS) for transient neutron diffusion model is presented.
• ECS is based on finite difference, theta method, eigenvalues and eigenvectors of coefficient matrix.
• ECS is applied to multi-dimensional homogenous and TWIGL reactors.
• The results of ECS are in agreement with the results of traditional methods.
• ECS is reduced the computational time CPU by about 30% comparing with faster reference method.

The space–time neutron diffusion equations with two energy groups and average one group of delayed neutrons are a system of stiff partial differential equations. The efficient computational system is presented to solve the neutron diffusion equations based on finite difference and theta methods. Finite difference method is used to reduce the partial differential equations to the ordinary differential equations. These ordinary differential equations are rewritten in a matrix form. Theta method is developed using the eigenvalues and corresponding eigenvectors of the coefficient matrix. These eigenvalues and the corresponding eigenvectors are calculated analytically. The efficient computational system is applied to multi-dimensional transient neutron diffusion equations with two energy groups and one group of delayed neutrons in the homogenous and heterogenous nuclear reactors. The results of the proposed method are in agreement with the results of traditional methods. The efficient computational system reduces the computational time (CPU) by about 30%30% compared with the faster reference method. So, the efficient computational system is considered a fast technique more than theta method and traditional numerical codes.