# Mathematical model and computer simulation

1. What are mathematical models and computer simulations?

2. What are stochastic models and deterministic models?

3. What is convergence and numerical instability?

4. What are sensitivity analyses and uncertainty analyses?

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#### Solution Preview

1. A mathematical model is an equation, or set of equations, that describes a system by taking into account inputs, outputs, and internal states (possibly friction, heat generation, etc). A good example of this is saying that a spring-mass system (or KM system) could have a mathematical model that describes the natural frequency as omega=(spring stiffness/mass)^(1/2).

A computer simulation on the other hand is a program (either commercial or hand coded such as MATLAB) that is used to simulate a system. This could be useful if you need an estimate of a model that can not be solved in closed form. You could use iterations that will close in on the solution ...

#### Solution Summary

This solution provides the definitions of a series of concepts involving mathematical models and computer simulation. The included topics are, stochastic models and deterministic models, convergence and numerical instability, sensitivity analysis and uncertainty analysis, and a general discussion of mathematical models and computer simulations.