We present first results of a numerical method solving inhomogeneous partial differential equation of the 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 ridefined 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-filed" given by the derivative terms of the first order this gives the right hand side of the equation of motion of the particles. The computation can be done in a very efficient way and results are in good agreement with the exact solution.
A New Numerical Method for Kinetic Equation in Several Dimensions
MOTTA, Santo;
1992-01-01
Abstract
We present first results of a numerical method solving inhomogeneous partial differential equation of the 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 ridefined 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-filed" given by the derivative terms of the first order this gives the right hand side of the equation of motion of the particles. The computation can be done in a very efficient way and 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.
