It is useful to begin by discussing where we are methodologically and, more generally, where we are in the overall problem-solving process. At this point, we are ready to begin Step 5 of our overall methodology. Thus, we have completed at least an initial pass of Steps 1–4:

  • Step 1: Decide on the central questions of interest;
  • Step 2: Define key phenomena underlying these questions;
  • Step 3: Develop one or more visualizations of relationships among phenomena;
  • Step 4: Determine key trade-offs that appear to warrant deeper exploration.

Steps 5–7 are the focus of this chapter. Progress on these steps is likely to result in revisiting Steps 1–4 as, for example, digging deeper results in identifying one or more important phenomena not previously considered. In general, however, we are ready to consider how we might address the trade-offs resulting from Step 4 using mathematical and computational methods and tools.

Table 9.1 summarizes the phenomena associated with the six archetypal problems discussed throughout this book and addressed in detail in Chapters 47. For each instance of a phenomenon, potentially useful modeling paradigms are listed. This chapter elaborates these paradigms, while also providing a brief overview of software tools available to support use of these approaches.

Table 9.1 Archetypal Phenomena and Modeling Paradigms

Category Phenomenon Modeling Paradigm
Physical, natural Flow of water Dynamic systems ...

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