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In the following the upper index ${(n)}$ refers to a value at time $t^{(n)}$. The simplest |
In the following the upper index ${(n)}$ refers to a value at time $t^{(n)}$. The simplest |
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and most robust scheme to approximate the time derivative of the the temperature is |
and most robust scheme to approximate the time derivative of the the temperature is |
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the backward Euler |
the backward Euler |
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\index{backward Euler} scheme, see~\cite{XXX} for alternatives. The backward Euler |
\index{backward Euler} scheme. The backward Euler |
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scheme is based |
scheme is based |
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on the Taylor expansion of $T$ at time $t^{(n)}$: |
on the Taylor expansion of $T$ at time $t^{(n)}$: |
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\begin{equation} |
\begin{equation} |