The MWF method: A convergence theorem for homogeneous one-dimensional case

The MWF numerical method for kinetic equations was presented by S. Motta and J. Wick in 1992 and recently extended by the authors to systems of kinetic equations. The basic idea of the method consists in rewriting the kinetic equation in a conservation law in divergence form, redefining the collisions as a flux and formally to transform the problem into a collisionless one. In all tested cases, the numerical results are in agreement with the exact solutions but a convergence proof of the method, to the best of our knowledge, is missing.In this paper we present our investigation on the sufficient conditions that the collision operator may satisfy, to guarantee a convergence proof of the method in the homogeneous one-dimensional case. This investigation is of both theoretical and applied interest.