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.

中文翻译：

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DelPhi 中求解非线性 Poisson-Boltzmann 方程的类牛顿迭代法

DelPhi 是一种流行的科学程序，它通过有限差分法对浸入水中的生物分子的静电势和能量的泊松-玻尔兹曼方程 (PBE) 进行数值求解。它以其准确性、可靠性、灵活性和效率而闻名。在这项工作中，除了已经实施的连续过松弛 (SOR) 算法之外，还介绍了新版 DelPhi，它使用一种新颖的类牛顿方法来求解非线性 PBE。我们对各种例子的测试表明，这种新方法在求解非线性 PBE 时在稳定性方面优于 SOR 方法，即使对于涉及非常强非线性的问题也能够收敛。