中文摘要：

在这个工作，我们为计算在被非线性的 Poisson-Boltzmann 方程管理的二个同样地控告的球形的粒子之间的静电的相互作用建议一个有效数字方法。非线性的问题被一个单调解决导致线性化的方程的一个序列的反复的方法。一个修改中央有限差别计划被开发用一个一致笛卡儿的格子在一个外面的不规则的领域上解决线性化的方程。与一致格子，方法简单，并且作为后果，多，格子解答者能被采用加快集中。有在一个控告的圆柱的毛孔限制的二个孤立的范围和二个范围的盒子的数字实验用建议方法被执行。我们的数字计划被发现有效，数字结果在对以前的出版结果的好同意被发现。

英文摘要：

In this work, we propose an efficient numerical method for computing the electrostatic interaction between two like-charged spherical particles which is governed by the nonlinear Poisson-Boltzmann equation. The nonlinear problem is solved by a monotone iterative method which leads to a sequence of linearized equations. A modified central finite difference scheme is developed to solve the linearized equations on an exterior irregular domain using a uniform Cartesian grid. With uniform grids, the method is simple, and as a consequence, multigrid solvers can be employed to speed up the convergence. Numerical experiments on cases with two isolated spheres and two spheres confined in a charged cylindrical pore are carried out using the proposed method. Our numerical schemes are found efficient and the numerical results are found in good agreement with the previous published results.