$$ \newcommand{\half}{\frac{1}{2}} \newcommand{\tp}{\thinspace .} \newcommand{\uex}{{u_{\small\mbox{e}}}} \newcommand{\normalvec}{\boldsymbol{n}} \newcommand{\x}{\boldsymbol{x}} \renewcommand{\u}{\boldsymbol{u}} \renewcommand{\v}{\boldsymbol{v}} \newcommand{\w}{\boldsymbol{w}} \newcommand{\rpos}{\boldsymbol{r}} \newcommand{\f}{\boldsymbol{f}} \newcommand{\F}{\boldsymbol{F}} \newcommand{\stress}{\boldsymbol{\sigma}} \newcommand{\I}{\boldsymbol{I}} \newcommand{\U}{\boldsymbol{U}} \newcommand{\dfc}{\alpha} % diffusion coefficient \newcommand{\ii}{\boldsymbol{i}} \newcommand{\jj}{\boldsymbol{j}} \newcommand{\kk}{\boldsymbol{k}} \newcommand{\ir}{\boldsymbol{i}_r} \newcommand{\ith}{\boldsymbol{i}_{\theta}} $$

Scaling of Differential Equations

Hans Petter Langtangen [1, 2] Geir K. Pedersen [3]

[1] Center for Biomedical Computing, Simula Research Laboratory [2] Department of Informatics, University of Oslo [3] Department of Mathematics, University of Oslo

This book explains the mathematical details of making differential equation models dimensionless. A key feature of the text is the reasoning about the right choice of scales. A large number of worked examples demonstrate the scaling technique for ordinary and partial differential equations from physics and biology. How to utilize scaled models in simulation software is also addressed.

Scaling of Differential Equations

Jun 20, 2016