A New Method for the Numerical Solution of the Two-Dimensional Neutron Diffusion Equation

A new method for the numerical solution of the two-dimensional diffusion equation was developed, namely, the analytic solutions in neighboring mesh regions were discretely connected at the mesh points to obtain a five-point linear equation similar to the conventional finite-difference equation. A series of test calculations performed for thermal and fast reactors shows that the new method effectively reduces the number of mesh points, and hence computation time and memory, required to attain the same computational accuracy as does the conventional finite-difference method.