The convergence of the particle method for the Vlasov-Poisson system with equally spaced initial data points

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A proof of convergence of particle methods is given for the Vlasov-Poisson system in three dimensions. This proof applies to some classes of initial functions not included in previous analyses of this problem. A semidiscrete problem is considered discretized in space but not in time with equally spaced initial data points. The convergence is proved for initial functions that are two and three times differentiable. Error estimates are obtained for these cases that depend on the two parameters, the interparticle distance and the mollification parameter in the approximate electric field. To gain further insight into the form such error bounds may take some computations are then done on the one dimensional Vlasov-Poisson system. Experimentally determined error bounds are obtained for particle-in-cell methods. Based on the computed error estimates in one dimension some conclusions are drawn regarding the accuracy of the type of error bounds obtained for the system in three dimensions. Copyright © 2001 by Marcel Dekker, Inc.

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Transport Theory and Statistical Physics

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