\relax \providecommand\tcolorbox@label[2]{} \@writefile{toc}{\contentsline {section}{\numberline {1}The system}{1}} \@writefile{toc}{\contentsline {section}{\numberline {2}Modifying the Euler code}{2}} \@writefile{lol}{\contentsline {lstlisting}{\numberline {1}euler.m: Euler code modifed to handle systems of ODEs.}{2}} \@writefile{toc}{\contentsline {section}{\numberline {3}Solution with the Euler code}{2}} \@writefile{lol}{\contentsline {lstlisting}{\numberline {2}predator\_deriv evaluates the predator ODE right hand side.}{2}} \@writefile{lol}{\contentsline {lstlisting}{\numberline {3}predator\_phase\_euler.m makes plot and phase plane.}{3}} \@writefile{toc}{\contentsline {section}{\numberline {4}A conserved quantity}{3}} \@writefile{lol}{\contentsline {lstlisting}{\numberline {4}Printing the conserved quantity.}{4}} \@writefile{lol}{\contentsline {lstlisting}{\numberline {5}Disastrous output from a 100 step Euler calculation}{4}} \@writefile{toc}{\contentsline {section}{\numberline {5}Higher order methods}{4}} \@writefile{lol}{\contentsline {lstlisting}{\numberline {6}rk4 ODE algorithm.}{4}} \@writefile{toc}{\contentsline {section}{\numberline {6}Report}{5}}