Having argued that fast-solving models have an important role to play, it is worthwhile to make some comments about the solution of such models. Note that this book does not address or teach methods for solution of mathematical models based on differential equations. Suffice to say that readers without the appropriate training in mathematics and computing should seek help from engineers or mathematicians with the appropriate skills.
The models may contain either ordinary differential equations (in the case of well-mixed systems) or partial differential equations (in situations where the system cannot be treated as well-mixed):
• Typically for ordinary differential equations it is possible to find software packages that only require the user to input: (1) equations; (2) parameter values; and (3) the initial values of each of the state variables. The writing of computer programs is typically not necessary. Such software packages typically operate on the basis of numerical integration according to the method of Runge-Kutta, although other integrating algorithms are also available.
• Techniques are available for the numerical solution of partial differential equations, such as "orthogonal collocation" and "finite differences". Readers with mathematical abilities interested in these methods can find more information elsewhere (see the further reading section at the end of this chapter). Unlike the case with ordinary differential equations, unless a highly sophisticated software package is available, it is not a simple matter of inserting the equations into the appropriate place within a program. Typically various lines of code need to be written.
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