Numerical Solution of One-Speed One-Dimensional Diffusion Equation based on Finite Difference and Source Iteration

Numerical methods are in favor to solve the impenetrable diffusion equations for neutron transport in contrast to using the analytical approach. This work applied a finite difference scheme and inverse power iteration to solve the one-group diffusion problem numerically for a one-dimensional slab containing fissile materials and heavy water. Both numerical and analytical solutions were obtained for comparison. MATLAB was employed to perform iterations and the minimum mesh size search. The effect of the initial guess on the accuracy and computational efficiency was investigated. Arguably, there is an appreciable acceleration for convergence by more intuitive initial estimations, as evidenced by the comparative results in the iteration counts decreasing from 799 to 8 by means of a random sampling method in place of the conventional initial guess method based on uniform flux when searching for the minimum size of the mesh necessary to meet the prescriptive accuracy.