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

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

Special Issues: Recent developments and applications in Computational Biophysics and Bioinformatics

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

Citation: Chuan Li, Mark McGowan, Emil Alexov, Shan Zhao. A Newton-like iterative method implemented in the DelPhi for solving the nonlinear Poisson-Boltzmann equation. Mathematical Biosciences and Engineering, 2020, 17(6): 6259-6277. doi: 10.3934/mbe.2020331


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