Discrete Diffusion Equation Research Articles

Convergence properties of eigenvalues of space discretized diffusion equations

A theorem is presented in this paper to establish the convergence of eigenvalues of space discretized Diffusion equation. The computational results confirm this.

Transience and Solvability of a Non-Linear Diffusion Equation

This paper is concerned with the existence of bounded solutions to an operator inequality which is a non-linear version of a discrete time diffusion equation. Here, the solvability of the inequality will be closely related to the transience of a corresponding random walk. In particular, the inequality will generally be solvable in three or more dimensions, but not in one or two dimensions if appropriate moment conditions hold. 1. The basic equation and initialization. Let Q be a probability measure

Errors in Perturbation Calculations

Exact and first-order perturbation formulas that give changes in the eigenvalue of the discrete multigroup neutron diffusion equation are obtained. Various errors arising during the evaluation of these formulas are discussed. It is shown that for exact theory to give greater precision than first-order theory the fluxes must be sufficiently well converged to display the changes in them due to the perturbation. The reader is encouraged to assess the likely outcome of errors in his own calculations.