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Solving the finite‐difference, nonlinear, Poisson–Boltzmann equation under a linear approach
Author(s) -
Zhexin Xiang,
Yunyu Shi,
Yinwu Xu
Publication year - 1995
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.540160207
Subject(s) - poisson–boltzmann equation , nonlinear system , poisson's equation , partial differential equation , mathematics , mathematical analysis , boltzmann equation , poisson distribution , physics , quantum mechanics , ion , statistics
Electrostatic interactions are among the key factors in determining the structure and function of biomolecules. Simulating such interactions involves solving the Poisson equation and the Poisson‐Boltzmann (P‐B) equation in the molecular interior and exterior region, respectively. The P‐B equation is a nonlinear partial differential equation. The central processing unit (CPU) time for solving the full nonlinear P‐B equation has been severalfold greater than the equivalent linear case. Here a simple method is proposed to solve the full nonlinear P‐B equation under a linear approach, which has been tested both on a spherical case and on small molecules. Results show that our method converges rapidly even under highly charged cases. With this method, the CPU time for solving the full nonlinear P‐B equation is somewhat less than the equivalent linear case in our calculations. © 1995 by John Wiley & Sons, Inc.