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Solving the finite‐difference non‐linear Poisson–Boltzmann equation
Author(s) -
Luty Brock A.,
Davis Malcolm E.,
McCammon J. Andrew
Publication year - 1992
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.540130911
Subject(s) - poisson–boltzmann equation , poisson's equation , partial differential equation , boltzmann equation , discrete poisson equation , mathematics , finite difference method , differential equation , mathematical analysis , finite difference , laplace's equation , physics , quantum mechanics , ion
The Poisson–Boltzmann equation can be used to calculate the electrostatic potential field of a molecule surrounded by a solvent containing mobile ions. The Poisson–Boltzmann equation is a non‐linear partial differential equation. Finite‐difference methods of solving this equation have been restricted to the linearized form of the equation or a finite number of non‐linear terms. Here we introduce a method based on a variational formulation of the electrostatic potential and standard multi‐dimensional maximization methods that can be used to solve the full non‐linear equation. © 1992 by John Wiley & Sons, Inc.