A weighted group explicit method for the diffusion equation (Q1064755)

New explicit methods for the finite difference solution of the diffusion equation are derived. The new methods used stable asymmetric approximations to the partial differential equation which, when coupled in groups of two adjacent points on the grid, result in implicit equations which can be easily converted to explicit form and which offer many advantages. By judicious use of alternating, this strategy on the grid points of the domain results in an algorithm which possesses unconditional stability. The merit of this approach is that it also results in more accurate solutions because of truncation error cancellations. The stability, consistency, convergence, and truncation error of the new method are briefly discussed and the results of numerical experiments presented.