By N.V. Krylov
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Extra resources for Nonlinear elliptic and parabolic equations of the second order
The desired range of process variables will be between a lower value x^ and an upper • • • value x^ with a desired accuracy of 10%. 2. MATHEMATICAL MODELS In Chapter 1, we discussed briefly some key aspects of models and, in particular, mathematical models. We saw that models of various sorts are constructed and used in engineering especially where undertaking experiments would not be possible, feasible or desirable for economic, safety or environmental reasons. A model can be used to help design experiments which are costly or considered difficult or dangerous.
He continued, ... the use of computers and the development of mathematical process simulation techniques may result in completely new methods and approaches which will justify themselves by economic and technological improvements. It is interesting to note that Williams' application of systems engineering covered all activities from process development through plant design to control and operations. Much of the work at Monsanto centred on the use of advanced control techniques aided by the development of computers capable of performing online control.
Efficiency and robustness of solution were often poor and diagnostics as to what had happened were virtually non-existent. Some things have not changed! The development of mini-computers in the 1970s and the emergence of UNIXbased computers followed by the personal computer (PC) in the early 1980s gave a boost to the development of modelling and simulation tools. It became a reality that every engineer could have a simulation tool on the desk which could address a wide range of steady state and dynamic simulation problems.
Nonlinear elliptic and parabolic equations of the second order by N.V. Krylov