A Newton-like iterative method implemented in the DelPhi for solving the nonlinear Poisson-Boltzmann equation

Chuan Li; Mark McGowan; Emil Alexov; Shan Zhao

doi:10.3934/mbe.2020331

A Newton-like iterative method implemented in the DelPhi for solving the nonlinear Poisson-Boltzmann equation

Math Biosci Eng. 2020 Sep 21;17(6):6259-6277. doi: 10.3934/mbe.2020331.

Authors

Chuan Li¹, Mark McGowan², Emil Alexov³, Shan Zhao²

Affiliations

¹ Department of Mathematics, West Chester University of Pennsylvania, West Chester, Pennsylvania 19383, USA.
² Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487, USA.
³ Department of Physics and Astronomy, Clemson University, Clemson, South Carolina 29634, USA.

Abstract

DelPhi is a popular scientific program which numerically solves the Poisson-Boltzmann equation (PBE) for electrostatic potentials and energies of biomolecules immersed in water via finite difference method. It is well known for its accuracy, reliability, flexibility, and efficiency. In this work, a new edition of DelPhi that uses a novel Newton-like method to solve the nonlinear PBE, in addition to the already implemented Successive Over Relaxation (SOR) algorithm, is introduced. Our tests on various examples have shown that this new method is superior to the SOR method in terms of stability when solving the nonlinear PBE, being able to converge even for problems involving very strong nonlinearity.

Keywords: DelPhi; Newton method; Poisson-Boltzmann equation; electrostatics; finite difference technique.

Publication types

Research Support, N.I.H., Extramural
Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

Algorithms*
Reproducibility of Results
Static Electricity

Grants and funding

R01 GM093937/GM/NIGMS NIH HHS/United States