This work introduces a numerical fixed point method to approximate the solutions of a Vlasov-Poisson-Boltzmann boundary value problem which arises when modeling a bi-species collisional sheath. Our method relies on the exact integration of the transport equations by means of the characteristic curves. A special care is given about the choice of a suitable phase space discretization together with the use of adequate quadrature formulas so as to ensure that the numerical fixed point method is stable. Numerical experiments are carried out in order to illustrate the effects of the various physical parameters that are in the scope of the analysis. Some results going beyond the scope of the analysis are also given.

这项工作引入了一种数值不动点方法，以近似模拟双物种碰撞鞘时出现的Vlasov-Poisson-Boltzmann边值问题的解决方案。我们的方法依靠特征曲线对运输方程进行精确积分。要特别注意选择合适的相空间离散化以及使用适当的正交公式，以确保数值定点方法稳定。为了说明分析范围内各种物理参数的影响，进行了数值实验。还给出了一些超出分析范围的结果。