Finite difference scheme for solving the nonlinear Poisson-Boltzmann equation modeling charged spheres

Zhonghua Qiao, Zhi Lin Li, Tao Tang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

28 Citations (Scopus)


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 to be efficient and the numerical results are found in good agreement with the previous published results.
Original languageEnglish
Pages (from-to)252-264
Number of pages13
JournalJournal of Computational Mathematics
Issue number3
Publication statusPublished - 1 May 2006
Externally publishedYes


  • Electrostatic interaction
  • Irregular domain
  • Monotone iterative method
  • Multigrid solver
  • Nonlinear Poisson-Boltzmann equation

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Computational Mathematics

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