Solving Stochastic Nonlinear Poisson-Boltzmann Equations Using a Collocation Method Based on RBFs

In this paper, we present a numerical scheme based on collocation method to solve stochastic non-linear Poisson–Boltzmann equations (PBE). This equation is generalized version of the arising from form biomolecular modeling case. Applying radial basis functions (RBFs) allows us deal with difficulties complexity domain. To indicate accuracy RBF method, results for two-dimensional models, also study stability numerically. We examine our RBF-reference value and Chebyshev Spectral Collocation (CSC) method. Furthermore, discuss finding appropriate shape parameter obtain an accurate solution besides greatest stability. have exerted Newton–Raphson approach solving system resulting discretization by technique.