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\@writefile{toc}{\contentsline {section}{\numberline {1}Vocabulary: {\it  {explicit}} versus {\it  {implicit}} }{1}}
\@writefile{toc}{\contentsline {section}{\numberline {2}{\it  {stiff\_deriv.m}} defines a surprisingly difficult ODE}{2}}
\@writefile{toc}{\contentsline {section}{\numberline {3}{\it  {stiff\_solution.m}} evaluates the exact solution}{2}}
\@writefile{toc}{\contentsline {section}{\numberline {4}{\it  {stiff\_euler.m}} tries to approximate the solution}{2}}
\@writefile{lol}{\contentsline {lstlisting}{\numberline {1}stiff\_euler.m Euler method for the stiff ODE.}{3}}
\@writefile{toc}{\contentsline {section}{\numberline {5}{\it  {stiff\_rk2.m}} tries a more accurate approach}{4}}
\@writefile{toc}{\contentsline {section}{\numberline {6}Implicit ODE methods reference data we don't know yet}{4}}
\@writefile{toc}{\contentsline {section}{\numberline {7}Applying the backward Euler method to our stiff ODE }{5}}
\@writefile{lol}{\contentsline {lstlisting}{\numberline {2}Explicit Euler update step.}{5}}
\@writefile{lol}{\contentsline {lstlisting}{\numberline {3}Implicit Euler update step.}{5}}
\@writefile{lol}{\contentsline {lstlisting}{\numberline {4}stiff\_backward\_euler\_explicit.m computes a backward Euler solution.}{5}}
\@writefile{toc}{\contentsline {section}{\numberline {8}Exercise: Find explicit form of a backward Euler step}{6}}
\@writefile{toc}{\contentsline {section}{\numberline {9}Solving an implicit equation}{7}}
\@writefile{lol}{\contentsline {lstlisting}{\numberline {5}Solving an implicit equation using fsolve().}{7}}
\@writefile{lol}{\contentsline {lstlisting}{\numberline {6}Example of using fsolve().}{7}}
\@writefile{toc}{\contentsline {section}{\numberline {10}A backward Euler solver using {\it  {fsolve()}} }{8}}
\@writefile{lol}{\contentsline {lstlisting}{\numberline {7}Signature for backward Euler code.}{8}}
\@writefile{lol}{\contentsline {lstlisting}{\numberline {8}backward\_euler.m}{8}}
\@writefile{lol}{\contentsline {lstlisting}{\numberline {9}Code to evaluate the backward Euler relation.}{9}}
\@writefile{toc}{\contentsline {section}{\numberline {11}{\it  {stiff\_backward\_euler()}} repeats our computation}{9}}
\@writefile{toc}{\contentsline {section}{\numberline {12}The QUADEX ODE}{9}}
\@writefile{toc}{\contentsline {section}{\numberline {13}Homework \#7}{10}}
\@writefile{toc}{\contentsline {section}{\numberline {14}Extra credit}{10}}