MATHEMATICAL MODELINGPHYSICAL

By: Fabián Flor A.

Definition Is a mathematical procedure that identifies a set of values consisting of: state variables, constants and parameters; which aims at presenting the state of a physical phenomenon being studied allowing you to see how a model works when there are changes in the variables.

1. Analyze the problem.The goal is to create our mental model through data system, which we obtain and study to identify their behavior.

Then we must endeavor to simplify the phenomenon as possible to obtain a feasible adequate mathematical formulation to solve.

If possible it is convenient to divide the model into sub models coupled replace the original model.

2. Formulate the model• We find the variables input, state and output which

characterize the system and determine the units that will work, so that the calculation result between compatible magnitudes. For example for a simple pendulum problem are:

• Establishing relationships between variables through equations, functions and algorithms that allow us to calculate the value of the dependent variables or output when input change.

3. Solving the model1. This is best done analytically because it helps the

understanding of the model.2. When you can not do is come numerically through a

simulation on a computer.3. When the model is mathematically intractable proceed to

simplify thanks to a rethink.

4. Validate and interpret1. Must be validated to determine if the model allows us to

better understand the system.

2. We check whether the model can predict, meaning contrast their ability to produce previously unknown and which conform to the experiences in the future can be performed values.

5. Report on the model• It is necessary to document the work done as a training

tool and can help to improve the model through a detailed report. This should include:

System AnalysisDesign chosen modelModel solution obtained by analytical or

numerical means

• Results and conclusions

6. Keeping the model1. Check it occasionally to2. Adapt to new circumstances or uses and 3. Correct

Credits1. Course notes Modelling Laboratory of the University of

Murcia, given by:Francisco Esquembre Martínez

Rafael Chicón Romero

2. Free Graphics from page :www.pixabay.com