Finite differencing methods

Today analytical techniques, numerical algorithms, and computation facilities have made it possible to solve many hydrologic problems. The emphasis on numerical solutions requires that the hydrologist have some basic knowledge of numerical methods, i.e., the calculus of finite differences. Flow of water in its various phases comprises a large part of hydrologic studies. These processes described by partial differential equations (generally nonlinear) require finite difference approximations for tractable computations. Considerations of convergence, order of approximation, and stability of these difference quotients again require some background in finite difference methods. Through brief discussions, several examples, and a list of references, this paper attempts to introduce some of the above considerations.