1-015-Text-S-DimensionlessVariables

By Kurt Bryan

Mathematics, Rose-Hulman Institute of Technology, Terre Haute IN USA

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Abstract

This material introduces the idea of ``rescaling'' for ordinary differential equations (ODE's) by the introduction of dimensionless variables. In practice this is an extremely common and useful prelude to the analysis and solution of ODE's, and yet is not often taught in an introductory course. Most ODE texts do not cover the material, but the benefits of understanding these techniques are myriad: rescaling indicates the appropriate physical scale on which the relevant independent and dependent variables exist, and can help determine conditions under which certain terms in an ODE model can be safely ignored, sometimes leading to great simplification. Proper scaling is also a useful prelude to the numerical solution of ODE's, and can improve the stability and efficiency of numerical methods.

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Researchers should cite this work as follows:

  • Kurt Bryan (2018), "1-015-Text-S-DimensionlessVariables," https://simiode.org/resources/5125.

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