Abstract
We present a modification on the successive overrelaxation (SOR) method and the iteration of the Green's function integral representation for the solution of the (nonlinear) Poisson-Boltzmann equation between two spheres. In comparison with other attempts, which approximate the geometry or the nonlinearity, the computations here are done for the full problem and compared with those done by the finite element method as a typical method for such problems. For the parameters of general interest, while the SOR method does not work, and the iteration of the integral representation is limited in its convergence, our modification to these iterative schemes converge. The modified SOR surpasses both methods in simplicity and speed; it is about 100 times faster than the modified iteration of the integral representation, with the latter being still simpler and faster than the finite element method. These two examples further illustrate the advantage of our recent modification to iterative methods, which is based on an analytical fixed point argument.
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Jerri, A.J., Herman, R.L. The solution of the poisson-boltzmann equation between two spheres: Modified iterative method. J Sci Comput 11, 127–153 (1996). https://doi.org/10.1007/BF02088820
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DOI: https://doi.org/10.1007/BF02088820