 # Diff of /trunk/doc/cookbook/example01.tex

revision 2911 by jfenwick, Wed Feb 3 03:30:40 2010 UTC revision 2931 by gross, Mon Feb 8 06:45:41 2010 UTC
# Line 248  This is simplifying PDE coefficient and Line 248  This is simplifying PDE coefficient and
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250  \subsection{A Clarification for the 1D Case}  \subsection{A Clarification for the 1D Case}
251    \label{SEC: 1D CLARIFICATION}
252  It is necessary for clarification that we revisit the general PDE from \refeq{eqn:commonform nabla} under the light of a two dimensional domain. \esc is inherently designed to solve problems that are greater than one dimension and so \refEq{eqn:commonform nabla} needs to be read as a higher dimensional problem. In the case of two spatial dimensions the \textit{Nabla operator} has in fact two components $\nabla = (\frac{\partial}{\partial x}, \frac{\partial}{\partial y})$. In full, \refEq{eqn:commonform nabla} assuming a constant coefficient $A$, takes the form;  It is necessary for clarification that we revisit the general PDE from \refeq{eqn:commonform nabla} under the light of a two dimensional domain. \esc is inherently designed to solve problems that are greater than one dimension and so \refEq{eqn:commonform nabla} needs to be read as a higher dimensional problem. In the case of two spatial dimensions the \textit{Nabla operator} has in fact two components $\nabla = (\frac{\partial}{\partial x}, \frac{\partial}{\partial y})$. In full, \refEq{eqn:commonform nabla} assuming a constant coefficient $A$, takes the form;
253  \begin{equation}\label{eqn:commonform2D}  \begin{equation}\label{eqn:commonform2D}
254  -A\hackscore{00}\frac{\partial^{2}u}{\partial x^{2}}  -A\hackscore{00}\frac{\partial^{2}u}{\partial x^{2}}
# Line 453  result into the file \verb|totE.png| whi Line 454  result into the file \verb|totE.png| whi
454  As expected the total energy is constant over time, see \reffig{fig:onedheatout1}.  As expected the total energy is constant over time, see \reffig{fig:onedheatout1}.
455
456  \subsection{Plotting the Temperature Distribution}  \subsection{Plotting the Temperature Distribution}
457    \label{sec: plot T}
458  \sslist{onedheatdiff001b.py}  \sslist{onedheatdiff001b.py}
459  For plotting the spatial distribution of the temperature we need to modify the strategy we have used  For plotting the spatial distribution of the temperature we need to modify the strategy we have used
460  for the total energy. Instead of producing a final plot at the end we will generate a  for the total energy. Instead of producing a final plot at the end we will generate a

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