Franz J. Vesely > CompPhys Textbook > Errata

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 Franz J. Vesely: Computational Physics - An Introduction Second Edition Kluwer Academic / Plenum Publishers, New York-London 2001. ISBN 0-306-46631-7

Here are a few errata I have detected since publication

 Es irrt der Mensch, solang er strebt [Goethe] If anything can go wrong, it will [Murphy]
Status: Sep-08

Page 34: Equation 2.53 should read

$\begin{eqnarray} a_{ii} \, x_{i}^{(k+1)} &=& b_{i} - \sum_{j > i} a_{ij} \, x_{j}^{(k)} - \sum_{j < i} a_{ij} \, x_{j}^{(k+1)} \; ; \;\;\; i=1,\dots,N \end{eqnarray}$

[May 02; thanks to Steve Knudsen]
Page 34: Equation 2.58 should read

$\begin{eqnarray} \left[ D + L \right] \cdot x_{k+1} &=& \omega \, b - \left[ \omega \, R - (1-\omega) \, A \right] \cdot x_{k} \end{eqnarray}$

[and in 2.59, the last $(k)$ should be a superscipt]

[May 02; thanks to Steve Knudsen]
Page 39: Equation 2.72 should read
$\vec{h}_{1}= \vec{g}_{1} -\frac{\textstyle (A \cdot \vec{g}_{1}) \cdot (A \cdot \vec{g}_{0})}{\textstyle \left| A \cdot \vec{g}_{0} \right|^{2}}$

(Note that $\vec{h}_{0} \equiv \vec{g}_{0}$).

Accordingly, eq. 2.75 should be
$\vec{h}_{2} = \vec{g}_{2} - \frac{\textstyle (A \cdot \vec{g}_{2}) \cdot (A \cdot \vec{h}_{1})}{\textstyle \left| A \cdot \vec{h}_{1} \right|^{2}}$

With these corrections the example calculation following eq. 2.77 converges faster - as it should.

[Sep 04; thanks to Greg Hammett]
Page 82: The last five lines should read:

In our simple example the fitness is bound to the value $f_{i} \equiv f(x_{i}^{0})$: the lower $f_{i}$, the higher the fitness of $x_{i}^{0}$. It is always possible, and convenient, to assign the fitness $g_{i} \equiv g(x_{i}^{0})$ such that it is positive definite.

A relative fitness, or probability of reproduction, is defined as $p_{i} \equiv g_{i}/\sum_{i=1}^{N}g_{i}$. It has all the markings of a probability density, and accordingly we may also ...

[Dec 03]

Page 117: Equ. 4.153 should read:

$q_{n+1}=q_{n}+P(p_{n})\Delta t \, , \;\;\;\; p_{n+1}= p_{n}+ F( q_{n+1})\Delta t$

- Somewhat later, the sentence beginning "Incidentally, .." should read:

A very similar first-order symplectic scheme, also known as the Euler-Cromer algorithm,

$p_{n+1}= p_{n}+ F( q_{n})\Delta t \, , \;\;\;\; q_{n+1}= q_{n}+ P(p_{n+1})\Delta t$

exactly conserves the perturbed Hamiltonian
$\tilde{H}=H_{ho}-\frac{\textstyle \omega^{2} \Delta t}{\textstyle 2}pq$

When applied to oscillator-like equations of motion it is a definite improvement over the (unstable) Euler-Cauchy method ...

[Dec 03, thanks to Denis Donnelly]
Page 154: Equ. 5.137 is printed as

$\beta_{l}= 2 \cos\left[ \frac{\textstyle 2(l-1)\pi}{\textstyle 2^{p+1}}\right]$

$\beta_{l}= 2 \cos\left[ \frac{\textstyle (2l-1)\pi}{\textstyle 2^{p+1}}\right]$

Note: the same error appears in Hockney's book.

[Jan 04, thanks to the class of 03/04]
Page 168: The text following equ. 6.8 should read

... where $u^{*} \equiv u_{LJ}/\epsilon$ and ...

[Oct 03]
Page 187: Eq. 6.60: the second term in the brackets should read

$\sum_{\vec{n}} \frac{\textstyle L^{3}}{\textstyle |\vec{r}_{i,j,\vec{n}}|} F(\eta |\vec{r}_{i,j,\vec{n}}|)$

[Apr 06]

Page 217: Eq. 8.12: should be

$\begin{eqnarray} \frac{\textstyle d e}{\textstyle dt} &=& - (e+p) \nabla \cdot v - (v \cdot \nabla)\, p \\ &=& -e (\nabla \cdot v) - \nabla \cdot (p v) \end{eqnarray}$

[May 06]
Page 218: Eq. 8.18: first line should be

$\begin{eqnarray} e_{j}^{n+1}&=&\frac{1}{2}\left(e_{j+1}^{n}+e_{j-1}^{n} \right) \\ &&- \dots \end{eqnarray}$

[May 06]

Pages 223-225: The energy equ. of motion (eqs. 8.52, 8.62 and 8.66) should have a factor $1/2$ on the r.h.s., thus:

$\frac{\textstyle d \epsilon_{i}}{\textstyle dt} = - \frac{\textstyle 1}{\textstyle 2} \sum \limits_{k=1}^{N}m_{k}\, \left( \frac{\textstyle p_{k}}{\textstyle \rho_{k}^{2}} + \frac{\textstyle p_{i}}{\textstyle \rho_{i}^{2}} \right) \, \vec{v}_{ik} \cdot \nabla_{i}w_{ik}$

[Aug 08]
Page 232: In Figure 8.6 the shading of some cells is barely visible.

MAC method: the 4 types of surface cells and the appropriate boundary conditions for $v_{x}, v_{y}$ (see POTTER).

[May 02]
F. J. Vesely / University of Vienna