A Newton-like iterative method implemented in the DelPhi for solving the nonlinear Poisson-Boltzmann equation
Chuan Li1, Mark McGowan2, Emil Alexov3
1Department of Mathematics, West Chester University of Pennsylvania, West Chester, Pennsylvania 19383, 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.
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