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% Inherit from the specified cell style.




    
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    % Document parameters
    \title{ArenstorfRefSol}
    
    
    

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% for compatibility with earlier versions
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    % Prevent overflowing lines due to hard-to-break entities
    \sloppy 
    % Setup hyperref package
    \hypersetup{
      breaklinks=true,  % so long urls are correctly broken across lines
      colorlinks=true,
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    \geometry{verbose,tmargin=1in,bmargin=1in,lmargin=1in,rmargin=1in}
    
    

    \begin{document}
    \begin{Verbatim}[commandchars=\\\{\}]
	\PY{c}{\PYZsh{} Load the required packages}
        \PY{k}{using} \PY{n}{ODE}
        \PY{k}{using} \PY{n}{JLD}
        
        \PY{c}{\PYZsh{} Set precision to quadruple precision (QP)}
        \PY{c}{\PYZsh{} QP has 113 bits}
        \PY{n}{set\PYZus{}bigfloat\PYZus{}precision}\PY{p}{(}\PY{l+m+mi}{113}\PY{p}{)}\PY{p}{;}
        
        \PY{c}{\PYZsh{} Define the right\PYZhy{}hand function}
        \PY{k}{function}\PY{n+nf}{ }\PY{n+nf}{arenstorf}\PY{p}{(}\PY{n}{t}\PY{p}{,}\PY{n}{x}\PY{p}{)}
            
            \PY{n}{mu} \PY{o}{=} \PY{n}{parse}\PY{p}{(}\PY{n}{BigFloat}\PY{p}{,}\PY{l+s}{\PYZdq{}}\PY{l+s}{0.012277471}\PY{l+s}{\PYZdq{}}\PY{p}{)}\PY{p}{;} \PY{n}{ms} \PY{o}{=} \PY{l+m+mi}{1} \PY{o}{\PYZhy{}} \PY{n}{mu}\PY{p}{;}
            \PY{n}{r1} \PY{o}{=} \PY{n}{vecnorm}\PY{p}{(}\PY{n}{x}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{:}\PY{l+m+mi}{2}\PY{p}{]}\PY{o}{\PYZhy{}}\PY{p}{[}\PY{o}{\PYZhy{}}\PY{n}{mu}\PY{p}{,}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{)}\PY{p}{;}
            \PY{n}{r2} \PY{o}{=} \PY{n}{vecnorm}\PY{p}{(}\PY{n}{x}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{:}\PY{l+m+mi}{2}\PY{p}{]}\PY{o}{\PYZhy{}}\PY{p}{[} \PY{n}{ms}\PY{p}{,}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{)}\PY{p}{;}
            
            \PY{n}{dx} \PY{o}{=} \PY{n}{Vector}\PY{p}{\PYZob{}}\PY{n}{BigFloat}\PY{p}{\PYZcb{}}\PY{p}{(}\PY{l+m+mi}{4}\PY{p}{)}\PY{p}{;}
            \PY{n}{dx}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]} \PY{o}{=} \PY{n}{x}\PY{p}{[}\PY{l+m+mi}{3}\PY{p}{]}\PY{p}{;}
            \PY{n}{dx}\PY{p}{[}\PY{l+m+mi}{2}\PY{p}{]} \PY{o}{=} \PY{n}{x}\PY{p}{[}\PY{l+m+mi}{4}\PY{p}{]}\PY{p}{;}
            \PY{n}{dx}\PY{p}{[}\PY{l+m+mi}{3}\PY{p}{]} \PY{o}{=} \PY{n}{x}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]} \PY{o}{+} \PY{l+m+mi}{2}\PY{o}{*}\PY{n}{x}\PY{p}{[}\PY{l+m+mi}{4}\PY{p}{]} \PY{o}{\PYZhy{}} \PY{n}{ms}\PY{o}{*}\PY{p}{(}\PY{n}{x}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]}\PY{o}{+}\PY{n}{mu}\PY{p}{)}\PY{o}{/}\PY{n}{r1}\PY{o}{\PYZca{}}\PY{l+m+mi}{3} \PY{o}{\PYZhy{}} \PY{n}{mu}\PY{o}{*}\PY{p}{(}\PY{n}{x}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]}\PY{o}{\PYZhy{}}\PY{n}{ms}\PY{p}{)}\PY{o}{/}\PY{n}{r2}\PY{o}{\PYZca{}}\PY{l+m+mi}{3}\PY{p}{;}
            \PY{n}{dx}\PY{p}{[}\PY{l+m+mi}{4}\PY{p}{]} \PY{o}{=} \PY{n}{x}\PY{p}{[}\PY{l+m+mi}{2}\PY{p}{]} \PY{o}{\PYZhy{}} \PY{l+m+mi}{2}\PY{o}{*}\PY{n}{x}\PY{p}{[}\PY{l+m+mi}{3}\PY{p}{]} \PY{o}{\PYZhy{}} \PY{n}{ms}\PY{o}{*}     \PY{n}{x}\PY{p}{[}\PY{l+m+mi}{2}\PY{p}{]}\PY{o}{/}\PY{n}{r1}\PY{o}{\PYZca{}}\PY{l+m+mi}{3} \PY{o}{\PYZhy{}} \PY{n}{mu}\PY{o}{*}     \PY{n}{x}\PY{p}{[}\PY{l+m+mi}{2}\PY{p}{]}\PY{o}{/}\PY{n}{r2}\PY{o}{\PYZca{}}\PY{l+m+mi}{3}\PY{p}{;}
            \PY{k}{return} \PY{n}{dx}\PY{p}{;}
        \PY{k}{end}
        
        \PY{c}{\PYZsh{} Set up the initial conditions}
        \PY{n}{t0} \PY{o}{=} \PY{n}{parse}\PY{p}{(}\PY{n}{BigFloat}\PY{p}{,}\PY{l+s}{\PYZdq{}}\PY{l+s}{0.0}\PY{l+s}{\PYZdq{}}\PY{p}{)}\PY{p}{;}
        \PY{n}{T} \PY{o}{=} \PY{n}{parse}\PY{p}{(}\PY{n}{BigFloat}\PY{p}{,}\PY{l+s}{\PYZdq{}}\PY{l+s}{17.0652165601579625588917206249}\PY{l+s}{\PYZdq{}}\PY{p}{)}\PY{p}{;}
        \PY{n}{x0}\PY{o}{=}\PY{p}{[}\PY{n}{parse}\PY{p}{(}\PY{n}{BigFloat}\PY{p}{,}\PY{l+s}{\PYZdq{}}\PY{l+s}{0.994}\PY{l+s}{\PYZdq{}}\PY{p}{)}\PY{p}{,}
            \PY{n}{parse}\PY{p}{(}\PY{n}{BigFloat}\PY{p}{,}\PY{l+s}{\PYZdq{}}\PY{l+s}{0.0}\PY{l+s}{\PYZdq{}}\PY{p}{)}\PY{p}{,}\PY{n}{parse}\PY{p}{(}\PY{n}{BigFloat}\PY{p}{,}\PY{l+s}{\PYZdq{}}\PY{l+s}{0.0}\PY{l+s}{\PYZdq{}}\PY{p}{)}\PY{p}{,}
            \PY{n}{parse}\PY{p}{(}\PY{n}{BigFloat}\PY{p}{,}\PY{l+s}{\PYZdq{}}\PY{l+s}{\PYZhy{}2.00158510637908252240537862224}\PY{l+s}{\PYZdq{}}\PY{p}{)}\PY{p}{]}\PY{p}{;}
        
        \PY{c}{\PYZsh{} Set the tolerance as machine epsilon }
        \PY{n}{Tol} \PY{o}{=} \PY{n}{parse}\PY{p}{(}\PY{n}{BigFloat}\PY{p}{,}\PY{l+s}{\PYZdq{}}\PY{l+s}{1e\PYZhy{}33}\PY{l+s}{\PYZdq{}}\PY{p}{)}\PY{p}{;}
        
        \PY{c}{\PYZsh{} Solve and get the solution at T = tEnd}
        \PY{p}{(}\PY{n}{t}\PY{p}{,}\PY{n}{x\PYZus{}ref}\PY{p}{)} \PY{o}{=} \PY{n}{ode78}\PY{p}{(}\PY{n}{arenstorf}\PY{p}{,}\PY{n}{x0}\PY{p}{,}\PY{p}{[}\PY{n}{t0}\PY{p}{,}\PY{n}{T}\PY{p}{]}\PY{p}{;}
        \PY{n}{reltol}\PY{o}{=}\PY{n}{Tol}\PY{p}{,}\PY{n}{abstol}\PY{o}{=}\PY{n}{Tol}\PY{p}{,}\PY{n}{points}\PY{o}{=}\PY{p}{:}\PY{n}{specified}\PY{p}{)}\PY{p}{;}
        
        \PY{c}{\PYZsh{} Save the solution to a file}
        \PY{n}{save}\PY{p}{(}\PY{l+s}{\PYZdq{}}\PY{l+s}{refSolAren.jld}\PY{l+s}{\PYZdq{}}\PY{p}{,}\PY{l+s}{\PYZdq{}}\PY{l+s}{x\PYZus{}ref}\PY{l+s}{\PYZdq{}}\PY{p}{,}\PY{n}{x\PYZus{}ref}\PY{p}{[}\PY{l+m+mi}{2}\PY{p}{]}\PY{p}{)}\PY{p}{;}
\end{Verbatim}


    % Add a bibliography block to the postdoc
    
    
    
    \end{document}
