A rapid finite difference algorithm, utilizing successive over‐relaxation to solve the Poisson–Boltzmann equation

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Abstract
An efficient algorithm is presented for the numerical solution of the Poisson–Boltzmann equation by the finite difference method of successive over‐relaxation. Improvements include the rapid estimation of the optimum relaxation parameter, reduction in number of operations per iteration, and vector‐oriented array mapping. The algorithm has been incorporated into the electrostatic program DelPhi, reducing the required computing time by between one and two orders of magnitude. As a result the estimation of electrostatic effects such as solvent screening, ion distributions, and solvation energies of small solutes and biological macromolecules in solution, can be performed rapidly, and with minimal computing facilities.