This paper reviews the application of the modified iterative method to solving chemical reaction problems and the recent solution of the Poisson-Boltzmann equation between two spheres. The chemical reaction problems include the study of non-linear chemical concentration in catalyst pellets of planar, cylindrical and spherical shapes. We will discuss in full detail the success of the modified iterative methods in solving the Poisson-Boltzmann equation, where our results compared very favourably with other typical methods used for solving these problems, such as the finite element method.