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

  • Received: 29 June 2020 Accepted: 06 September 2020 Published: 21 September 2020
  • 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.

    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[J]. Mathematical Biosciences and Engineering, 2020, 17(6): 6259-6277. doi: 10.3934/mbe.2020331

    Related Papers:

  • 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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