Chemical Engineering 142
Numerical Methods
Spring 2008
Note that both of the equations that begin, “X = …” were entered into Polymath as implicit equations
(i.e. by clicking “Add NLE” and then entering the equations rearranged to be in the form “0 = f(variable)
= …”). This is the method used in example 8-5 from the text. When you define a variable implicitly
(with an NLE), Polymath requires you to make an initial guess at the value of this variable. It’s best to
guess reasonably, to increase the chances of the program converging on a solution.
It would also have been possible to enter one of these equations explicitly (i.e. by clicking “Add EE”)
and one of them implicitly. For example :
In this case, we have an explicit definition of X and an implicit definition of T. When doing this,
Polymath requires a Lower and Upper Limit to be set on the implicit variable (T). It would not have
been possible to enter both of these two equations as explicit equations in X (i.e. “X=…” and “X=…”),
because Polymath would perceive this as over-defining X. Note that it would have also worked to use
the first equation as an explicit definition of X and to use the second equation as the implicit definition
of T (remember that k is a function of T).
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