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1-015-DimensionlessVariables-TechniqueNarrative

Author(s): Kurt Bryan

Keywords: linearization dimensional analysis time scale scaling dimensionless variables spatial scale

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Abstract

Resource Image This material introduces the idea of ``rescaling'' for ordinary differential equations (ODE's) by the use of dimensionless variables. In practice this is an extremely common and useful prelude to the analysis and solution of ODE's.

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Article Context

Resource Type
Differential Equation Type
Technique
Qualitative Analysis
Application Area
Course
Course Level
Lesson Length
Technology
Approach
Skills
Key Scientific Process Skills
Assessment Type
Pedagogical Approaches
Vision and Change Core Competencies - Ability
Principles of How People Learn
Bloom's Cognitive Level

Description

However, the use of dimensionless variables 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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Authors

Author(s): Kurt Bryan

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