This book offers an application of Sobolev gradient approach to Poisson Boltzmann system. A detailed description of Sobolev gradient method is given and its application is demonstrated on the Poisson Boltzmann system when there are large non-linearities and discontinuities in the coefficient functions. Poisson Boltzmann is a physical model that governs the electrostatic potential of macromolecules when immersed in solvent. It is shown that in some cases Sobolev gradient performs better in terms of efficiency than other existing fast methods such as multigrid and Newton's methods. The...