A New Numerical Method for Kinetic Equations in Several Dimensions

We present first results of anumerical method solving inhomogeneous partial differential equation of first order with a conservationproperty. The method is based on the Finite Particle Schemes for homogeneous PDE's of the first orderas the Vlasov-Poisson system in kinetic theory. The inhomogeneity is redefined as a flux. For theassociated 'velocity-field' given by the Radon-Nikodym derivative of the flux, we give a numericalapproximation. Together with the 'velocity-field' given by the derivative terms of first order this givesthe right hand side of the equations of motion of the particles. The computation can be done in a veryefficient way and the results are in good agreement with the exact solution.