--- trunk/doc/user/diffusion.tex 2006/03/01 04:40:10 572
+++ trunk/doc/user/diffusion.tex 2006/03/02 00:42:53 573
@@ -78,8 +78,8 @@
scheme is based
on the Taylor expansion of $T$ at time $t^{(n)}$:
\begin{equation}
-T^{(n-1)}\approx T^{(n)}+T\hackscore{,t}^{(n)}(t^{(n-1)}-t^{(n)})
-=T^{(n-1)} - h \cdot T\hackscore{,t}^{(n)}
+T^{(n)}\approx T^{(n-1)}+T\hackscore{,t}^{(n)}(t^{(n)}-t^{(n-1)})
+=T^{(n-1)} + h \cdot T\hackscore{,t}^{(n)}
\label{DIFFUSION TEMP EQ 6}
\end{equation}
This is inserted into \eqn{DIFFUSION TEMP EQ 1}. By separating the terms at
@@ -159,7 +159,7 @@
$\delta\hackscore{ij}$ is the Kronecker symbol \index{Kronecker symbol} defined by $\delta\hackscore{ij}=1$ for
$i=j$ and $0$ otherwise. Undefined coefficients are assumed to be not present\footnote{There is a difference
in \escript of being not present and set to zero. As not present coefficients are not processed,
-it is more efficient to leave a coefficient undefined insted assigning zero to it.}
+it is more efficient to leave a coefficient undefined instead of assigning zero to it.}
Defining and solving the Helmholtz equation is very easy now:
\begin{python}
@@ -177,7 +177,7 @@
returning the Kronecker symbol.
The coefficients can set by several calls of \method{setValue} where the order can be chosen arbitrarily.
-If a value is assigned to a coefficint several times, the last assigned value is used when
+If a value is assigned to a coefficient several times, the last assigned value is used when
the solution is calculated:
\begin{python}
mypde=LinearPDE(mydomain)
@@ -245,7 +245,7 @@
\end{python}
The script is similar to the script \file{poisson.py} dicussed in \Chap{FirstSteps}.
\code{mydomain.getNormal()} returns the outer normal field on the surface of the domain. The function \function{Lsup}
-imported by the \code{from esys.escript import *} statement and returns the maximum absulute value of its argument.
+imported by the \code{from esys.escript import *} statement and returns the maximum absolute value of its argument.
The error shown by the print statement should be in the order of $10^{-7}$. As piecewise bi-linear interpolation is
used by \finley approximate the solution and our solution is a linear function of the spatial coordinates one might
expect that the error would be zero or in the order of machine precision (typically $\approx 10^{-15}$).
@@ -283,7 +283,7 @@
in an area defined as a circle of radius \var{r} and center \var{xc} and zero outside this circle.
\var{q0} is a fixed constant. The following script defines \var{q} as desired:
\begin{python}
-from esys.escript import length
+from esys.escript import length,whereNegative
xc=[0.02,0.002]
r=0.001
x=mydomain.getX()