Locally explicit schemes for three-dimensional diffusion with a non-local boundary specification

Abstract

Two finite difference schemes based on the classical three-point forward time centred space (FTCS) method and the five-point FTCS formula, are used to solve the three-dimensional time dependent diffusion equation with a non-local boundary specification. In these methods locally one-dimensional (LOD) procedures are used to extend the one-dimensional techniques to solve the three-dimensional problem. Numerical integration procedures are also employed to overcome the non-local boundary specification. Results from some numerical experiments are presented, including error estimates derived in the maximum norm. The results of numerical testing show that the LOD techniques give better results than the fully explicit schemes. The CPU times used for the procedures developed in this article are also reported.