Error analysis of the multidimensional nodal integral method for solving the neutron diffusion equation

This paper presents an error analysis of the Nodal Integral Method (NIM) applied to the two-dimensional neutron diffusion equation. The geometry of the problem under consideration consists of a homogeneous material unit square. This geometry is transformed by scaling out the diffusion length. The NIM formalism is presented then used to solve the neutron diffusion equation in this specific problem. The Maximum Principle is proved to be valid for the NIM formalism and an error analysis is performed by applying the Maximum Principle to the truncation error and a comparison function. Results show that the convergence order for the NIM solution to the exact solution is O(a2), where a is half the scaled length of a computational cell, and a bound on the error is derived. Numerical results are also presented in verification of this result. (authors)