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5.2 Initial Value Problems II: Conservative-parabolic DE

Diffusion:
$\displaystyle \frac{\partial u}{\partial t} = \frac{\partial}{\partial x}
(\lambda \frac{\partial u}{\partial x})
\;\;\;\;$ $\textstyle {\rm or}$ $\displaystyle \;\;\;
\frac{\partial u}{\partial t} = \lambda \frac{\partial^{2} u}{\partial x^{2}}$  



Best: 2 second-order schemes

- Crank-Nicholson
- Dufort-Frankel

But: first-order algorithms perform well, too

- FTCS (one up for old Leonhard E.!)
- Implicit (even better - good enough for many purposes!)



Subsections

Franz J. Vesely Oct 2005
See also:
"Computational Physics - An Introduction," Kluwer-Plenum 2001