IMPROVED FINITE-DIFFERENCE CALCULATION OF MAGNETIC-FIELD EFFECTS - INCLUSION OF ANALYTIC ASYMPTOTICS

In the usual finite difference calculations of magnetic field effects the accuracy decreases and the number of required discretization point s increases with decreasing magnetic interaction. By matching the nume rical results with the asymptotic analytic solution we obtain a consis tently high accuracy for a very small number of discretization points (of the order of 10) independent of the size of the magnetic interacti on. The matching is incorporated into the standard algorithm by changi ng one of the boundary conditions which becomes spin dependent. A simp le rule is given for the optimal position of the matching boundary con dition. The method is tested both for free diffusion and for diffusion in a strong Coulombic field.