Finite difference techniques numerical experiments

Finite-Difference Methods. The numerical analysis literature abounds with finite difference methods for the numerical solution of partial differential equations. While these methods have been successfully applied in the solution of two-dimensional problems in fluid mechanics and diffusion (24, 25), there is little reported experience in the solution of three-dimensional, time-dependent, nonlinear problems. Application of these techniques, then, must proceed by extending methods successfully applied in two-dimensional formulations to the more complex problem of solving (7). The various types of finite-difference methods applicable in the solution of partial differential equations and their advantages and disadvantages are discussed by von Rosenberg (26), Forsythe and Wasow (27), and Ames (2S). 

In this chapter we introduce techniques that modify the batch experiment, in order to allow one to assimilate information regarding a finite reflux column. Numerous papers from the COMPS group have been published on this topic for both rectifying and stripping CSs, and have been shown to be extremely useful in validating the theoretical node-shifting predicted through CPMs, as well as to compare different thermodynamic models at finite reflux [1 6]. 

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