TY - JOUR
T1 - A Finite Difference Scheme for Solving the Nonlinear Poisson-Boltzmann Equation Modeling Charged Spheres
AU - Zhong-Hua Qiao, Zhi-Lin Li & Tao Tang
JO - Journal of Computational Mathematics
VL - 3
SP - 252
EP - 264
PY - 2006
DA - 2006/06
SN - 24
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8750.html
KW - Nonlinear Poisson-Boltzmann equation, Electrostatic interaction, Irregular
domain, Monotone iterative method, Multigrid solver.
AB - <p style="text-align: justify;">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.</p>