On the Chang and Cooper scheme applied to a linear Fokker-Planck equation

We show that for a particular linear Fokker-Planck operator, the explicit Chang and Cooper scheme is positive and entropy satisfying under a CFL criterion when the initial condition is positive. Then, we deduce that the distribution given by the explicit Chang and Cooper scheme converges toward a discrete Maxwellian equilibrium.

Keywords

Kinetic equation, Fokker-Planck-Landau operator, explicit Chang and Cooper scheme, positive and entropy satisfying scheme

2010 Mathematics Subject Classification

65M06, 65M12, 82C40, 82D10

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Published 1 January 2010