ABSTRACT
Various schemes are available for finite difference approximation of nonlinear diffusion problems as a system of linear algebraic equations. They include, among others, the lagging of temperature or concentration-dependent properties by one time step, the use of three-time-level finite differencing, and linearization procedures. This chapter examines the application of such approaches. It also describes the solution of nonlinear, steady-state diffusion problems by the false transient method. In this approach, the steady-state problem is replaced by the relevant time-dependent parabolic system, which is solved by any one of the standard finite difference methods until the solution ceases to change with time; that is, the steady-state condition is reached. The method readily yields the steady-state solution if the steady state exists and is unique. The basic idea in the false transient technique is simple, the algorithm is straightforward, and for sufficiently large times the transients die out and the steady-state condition is approached.
