--- 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 $t^{(n)}$: $$-T^{(n-1)}\approx T^{(n)}+T\hackscore{,t}^{(n)}(t^{(n-1)}-t^{(n)}) -=T^{(n-1)} - h \cdot T\hackscore{,t}^{(n)} +T^{(n)}\approx T^{(n-1)}+T\hackscore{,t}^{(n)}(t^{(n)}-t^{(n-1)}) +=T^{(n-1)} + h \cdot T\hackscore{,t}^{(n)} \label{DIFFUSION TEMP EQ 6}$$ 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()