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

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.