Abstract
Abstract In the usual finite difference calculations of magnetic field effects the accuracy decreases and the number of required discretization points increases with decreasing magnetic interaction. By matching the numerical results with the asymptotic analytic solution we obtain a consistently high accuracy for a very small number of discretization points (of the order of 10) independent of the size of the magnetic interaction. The matching is incorporated into the standard algorithm by changing one of the boundary conditions which becomes spin dependent. A simple rule is given for the optimal position of the matching boundary condition. The method is tested both for free diffusion and for diffusion in a strong Coulombic field.
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