Module 1 2 The Modeling Process Angela B

Modeling • Application of methods to analyze complex, real-world problems in order to predict what might happen with some course of action

Model Classifications • Probabilistic or stochastic behavior - element of chance • Deterministic behavior v Dynamic model changes with time v Static model § Continuous model – times changes continuously § Discrete model – time changes in incremental steps

Steps of Modeling Process - Cyclic • Analyze problem: problem identification and classification; determine the problem’s objective; translate the problem into mathematical symbols • Formulate a model – Gather data – Make simplifying assumptions and document them – Determine variables (independent and dependent) and units – Establish relationships among variables and sub-models (draw a diagram) – Determine equations and functions

Steps of Modeling Process • Solve model: exact answer or numerical solution • Verify and interpret model's solution – verification determines if solution works correctly (solving the problem right) – validation establishes if system satisfies problem's requirements (solving the right problem) – If the solution shows weakness, return step 1 or 2 for problem refinement and/or simplification.

Steps of Modeling Process • Report on model – Analysis of problem (explain the problem and objectives of the study) – Model design (state assumptions and rationale for employing them; show relationships among variables and sub-models) – Model solution (describe the techniques for solving the problem and the solution) – Results and conclusions (include results, interpretations, implications, recommendations, conclusions and suggestions for future work). • Maintain model (make corrections and improvements).

Exercise • Compare and contrast the modeling process with the scientific method – make observations; formulate a hypothesis; develop a testing method for the hypothesis; collect data for the test; using the data, test the hypothesis; accept or reject the hypothesis • Compare and contrast the modeling process with the software life cycle – analysis, design, implementation, testing, documentation, maintenance.

Other Resource • SIAM Mathematical Modeling Process Video Series (7 parts)