The Finite Difference Method

Illustrate the concept of the finite difference method for the simple one dimensional case of solute diffusion, with and without advective transport, for both stationary and non stationary cases. Generalize the concept of the finite difference method for two and three dimensional geometries. Show how the boundary and initial conditions are applied. Establish a link between the finite difference method and the similar finite volume and direct finite difference methods. Give an idea of the extension of the method to more complicated cases (non-Cartesian coordinate systems, alternating direction implicit method).