We present first results of a numerical method solving inhomogeneous partial differential equation of first order with a conservation property. The method is based on the Finite Particle Schemes for homogeneous PDE's of the first order as the Vlasov-Poisson system in kinetic theory. The inhomogeneity is redefined as a flux. For the associated 'velocity-field' given by the Radon-Nikodym derivative of the flux, we give a numerical approximation. Together with the 'velocity-field' given by the derivative terms of first order this gives the right hand side of the equations of motion of the particles. The computation can be done in a very efficient way and the results are in good agreement with the exact solution.
A New Numerical Method for Kinetic Equations in Several Dimensions
MOTTA, Santo;
1991-01-01
Abstract
We present first results of a numerical method solving inhomogeneous partial differential equation of first order with a conservation property. The method is based on the Finite Particle Schemes for homogeneous PDE's of the first order as the Vlasov-Poisson system in kinetic theory. The inhomogeneity is redefined as a flux. For the associated 'velocity-field' given by the Radon-Nikodym derivative of the flux, we give a numerical approximation. Together with the 'velocity-field' given by the derivative terms of first order this gives the right hand side of the equations of motion of the particles. The computation can be done in a very efficient way and the results are in good agreement with the exact solution.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
