\relax \providecommand\tcolorbox@label[2]{} \@writefile{toc}{\contentsline {section}{\numberline {1}Sometimes, if it looks wrong, it is wrong!}{1}} \@writefile{lol}{\contentsline {lstlisting}{\numberline {1}The incorrect backward Euler code for the flame ODE.}{1}} \@writefile{toc}{\contentsline {section}{\numberline {2}The forward Euler code}{2}} \@writefile{lol}{\contentsline {lstlisting}{\numberline {2}flame\_euler.m the (correct) forward Euler code for the flame ODE.}{2}} \@writefile{toc}{\contentsline {section}{\numberline {3}Convergence of the forward Euler method for the flame}{2}} \@writefile{toc}{\contentsline {section}{\numberline {4}Making a stab at a backward Euler solver for the flame ODE}{4}} \@writefile{toc}{\contentsline {section}{\numberline {5}Heun's method: a second order ODE solver}{4}} \@writefile{lol}{\contentsline {lstlisting}{\numberline {3}Pseudocode for rk2.m}{4}} \@writefile{toc}{\contentsline {section}{\numberline {6}Error estimation}{5}} \@writefile{toc}{\contentsline {section}{\numberline {7}Adaptive stepsizes}{5}} \@writefile{toc}{\contentsline {section}{\numberline {8}Report:}{7}}