New explicit finite difference schemes for two-dimensional diffusion subject to specification of mass

Two different explicit finite difference schemes for the numerical solution of the diffusion equation on a rectangular region, subject to local or non local boundary conditions, the latter involving a double integral to simula te specification of mass in a curved region, are compared. These schemes, t he two-dimensional 9-point Forward Time Centered Space (FTCS) explicit form ula [Noye & Hayman, J Comp Math 42, 1992, 223-236] and the locally one-dime nsional (LOD) method based on the classical one-dimensional FTCS formula [N oye & Hayman, J Comp Math 51, 1994, 215-228], are economical to use, are ge nerally second-order, have bounded ranges of stability, and can be shown to be identical at grid points in the interior of the solution domain. Howeve r, results obtained are different, unless a special boundary treatment is u sed with the LOD method. Then the LOD method is more efficient. Some numeri cal tests are presented for both cases, and accuracy and Central Processor (CP) time needed for the nonlocal problem are found to be superior than tho se for the method of Cannon et al. [Cannon et al., Appl Anal J 50, 1993, 1- 19]. (C) 1999 John Wiley & Sons,Inc.