Transiente diffusion equation: an alternative finite difference approach

Abstract

This work is concerned with development of an alternative finite difference method approach to the solution of the transient diffusion equation. In this approach is assumed that the potential function has a linear variation in some time interval. Thus an integral with respect to time is carried out in the initial diffusion equation. A constant time weighting function is adopted. The time integration reduces the order of the time derivative that appears in the initial equation. Two numerical examples are presented to verify the accuracy and applicability of the proposed approaches. The results are compared with the standard corresponding analytical solutions.