Implicit locally one-dimensional methods for two-dimensional diffusion with a non-local boundary condition

Two new second-order finite difference techniques based upon the classical 3-point backward time centered space (BTCS) method and the Crank-Nicolson s cheme, and also a fourth-order finite difference scheme based on Crandall's method for one-dimensional diffusion, are used to solve the two-dimensiona l time dependent diffusion equation with non-local boundary conditions. In these cases locally one-dimensional (LOD) techniques are used to extend the one-dimensional techniques to solve the two-dimensional problem. The stabi lity properties and truncation error of these methods are discussed and the results of a numerical experiment for these three methods are presented. E rror estimates are also tabulated. The results of numerical testing shows t hat these schemes uses less central processor (CPU) time than the fully imp licit schemes. (C) 1999 IMACS/Elsevier Science B.V. All rights reserved.