NEW EXPLICIT METHODS FOR THE NUMERICAL SOLUTION OF DIFFUSION PROBLEMS
David J. Evans
In this survey paper, Part 1 is concerned with new explicit methods for the finite difference solution of a parabolic partial differential equation in 1 space dimension. The new methods use stable asymmetric approximations to the partial differential equation which when coupled in groups of 2 adjacent points on the grid result in implicit equations which can be easily converted to explicit form which in turn 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 results in more accurate solutions because of truncation error cancellations. The stability, consistency, convergence and truncation error of the new method is discussed and the results of numerical experiments presented.
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