xnuke is right- the problem is first simplified, an ODE is associated with the process, the initial conditions and boundary conditions are defined, and the solution is normally solved numerically. Bright colorful charts of the solution are then presented to management/customer, and there is a tendency to think these charts represent the "truth" , and decisions are then made.
There are several faults to this approach that the decison maker needs to be made aware of, including:
a) The initial simplification of the process , as well as the initial conditions and boundary conditions are assumptions and often do not capture the intricacies of reality. For example , 3D CFD solution of fluid flow assumes continuity of processes and ignores the possibility of fractal or chaos effects.
b) The knowledge or accuracy of assumed physical properties is sometimes poor, yet the assumed accuracy of the used properties is never evaluated. For example, for thermal radiation heat transfer of participating media, the complex index of refraction of the entrained particles is usually poorly known, likewise isotropic properties of metals is nearly always assumed yet non-isotropic properties dominate weld interfaces and crystalline differences throughout thick objects that were heated and cooled quickly.
c) The computer program used by most users is normally a commercial program, and the details of that program are deliberately made unknowable to the end user. The numerical solution of differential equations is affected by the chosen integration method, the stability of the solution is a function of the discrete spacial and time steps utilized as well as the details of the programming method. For example , numerical round off errors can propagate, and instabilities can go unnoticed. The fact that the program ended without error messages and the colorful charts are impressive to all can hide the fact that the numerical solution is wrong.
d) In the worst case, if the analyst has a financial interest in the final solution, it can affect their chosen assumptions, so as to affect the indicated "solution". The current 30 yr effort to predict "climate change" stands out as a notable instance of this problem.
"...when logic, and proportion, have fallen, sloppy dead..." Grace Slick