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\subsection{A Clarification for the 1D Case} 
\subsection{A Clarification for the 1D Case} 
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\label{SEC: 1D CLARIFICATION} 
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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; 
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\begin{equation}\label{eqn:commonform2D} 
\begin{equation}\label{eqn:commonform2D} 
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A\hackscore{00}\frac{\partial^{2}u}{\partial x^{2}} 
A\hackscore{00}\frac{\partial^{2}u}{\partial x^{2}} 
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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}. 
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\subsection{Plotting the Temperature Distribution} 
\subsection{Plotting the Temperature Distribution} 
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\label{sec: plot T} 
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\sslist{onedheatdiff001b.py} 
\sslist{onedheatdiff001b.py} 
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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 
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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 