Study of local and nonlocal Poisson-Boltzmann equations for linear and nonlinear models with spherical symmetry

Abstract In this paper, the local and nonlocal Poisson–Boltzmann equations are studied on their linear and nonlinear models with spherical symmetry. In particular, the exact solutions of the linear and nonlinear modes are obtained in either analytical expressions or simplified boundary value problems, whose solutions can be found easily via the Maple procedure dsolve for example. Numerical results confirm the derived solution properties, and show that the two new linear models proposed in this paper can have higher accuracy than the two conventional linear models in approximation to the local and nonlocal nonlinear models, respectively.