  Discretization of non-linear Poisson-Boltzmann Equation equations results in
a system of non-linear equations with symmetric Jacobian. The Newton algorithm
is the most useful tool for solving non-linear equations. It consists of
solving a series of linear system of equations (Jacobian system). In this
article, we adaptively define the tolerance of the Jacobian systems. Numerical
experiment shows that compared to the traditional method our approach can save
a substantial amount of computational work. The presented algorithm can be
easily incorporated in existing simulators.
