Critical case problems nonlinear problem

Adsorption problems are generally indicated by the calibration curve not psssing through the origin, and in some cases by nonlinearity of the curve. A change of the column may be the answer. Perhaps increased temperature will reduce the problem to a workable level. Even though it is not desirable, some adsorption can be tolerated and still give quantitative results but frequent recalibration is critical. 

In the previous three chapters, we described various analytical techniques to produce practical solutions for linear partial differential equations. Analytical solutions are most attractive because they show explicit parameter dependences. In design and simulation, the system behavior as parameters change is quite critical. When the partial differential equations become nonlinear, numerical solution is the necessary last resort. Approximate methods are often applied, even when an analytical solution is at hand, owing to the complexity of the exact solution. For example, when an eigenvalue expression requires trial-error solutions in terms of a parameter (which also may vary), then the numerical work required to successfully use the analytical solution may become more intractable than a full numerical solution would have been. If this is the case, solving the problem directly by numerical techniques is attractive since it may be less prone to human error than the analytical counterpart. 

In practice, it often turns out that the system (4.28) has a family of solutions that depends on one or more arbitrary parameters. Thus, the problem for the singularly perturbed equation (4.27) is the nonlinear critical case. 

Since the complexity of the physiologic system identification problem rivals its importance, we begin by demarcating those areas where effective methods and tools currently exist. The selection among candidate models is made on the basis of the following key functional characteristics (1) static or dynamic (2) linear or nonlinear (3) stationary or nonstationary (4) deterministic or stochastic (5) single or multiple inputs and/or outputs (6) lumped or distributed. These classification criteria do not constitute an exhaustive list but cover most cases of current interest. Furthermore, it is critical to remember that contaminating noise (be it systemic or measurement-related) is always present in an actual study, and... 

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