Numerical analysis of the weighted particle method applied to the semiconductor Boltzmann equation

Summary The semiconductor Boltzmann equation involves an integral operator, the kernel of which is a measure supported by a surface. This feature introduces some singularities of the exact solution, which makes the numerical approximation of this equation difficult. This paper is devoted to the error analysis of the weighted particle method (introduced by Mas-Gallic and Raviart [14]) applied to the space homogeneous semiconductor Boltzmann equation. The results are commented in view of the practical use of the method. This paper is closely related to [12], where results of numerical simulations on both test and real problems are given.