I would like to plot the following differential equation :
on LaTeX, I have trouble to understand what I need to do for it to work (I know that there have been posts on it but I don't get it). Can someone please tell me which package(s) to use and give me a simple example to do so please?
It is to study the speed of a projectile in the gravitational field with air friction. I know all the initial conditions.
This example uses PSTricks package pst-ode to solve the differential equation numerically with the RKF45 method.
PSTricks requires the latex-->dvips-->ps2pdf workflow for typesetting. Since we use pgfplots here, solving the ODE with command \pstODEsolve is outsourced into an auxiliary document and the solution is written to file table.dat. Therefore, in order to typeset the code listed below, run pdflatex or lualatex with option --shell-escape.
Note that with RKF45, precision of the result does not depend on the chosen number of output points. The method uses adaptive step size control. For comparison, the solution with only 4 output points (t_0, t_1, t_2, t_e) is plotted against the fine-grained solution with 250 output points.
Typeset with pdflatex --shell-escape example.tex.
example.tex:
\documentclass{standalone}
%%%%%%%%%%%%%%%%%%%%%%% solve ODE in auxiliary document %%%%%%%%%%%%%%%%%%%%%%%%
\begin{filecontents}[overwrite]{solve.tex}
\documentclass{article}
\usepackage{pst-ode}
\begin{document}
% arguments:
% algebraicAll --> all arguments in algebraic notation
% saveData --> also write result into file `table.dat'
% `table' --> PostScript variable that takes result
% t | x[0] --> output format in `table' and `table.dat'
% 0, 10 --> integration interval t_0, t_e
% 250 --> number of saved output points t_0, t_1, ..., t_e
% 10 --> initial value
% 9.81 - ... --> right-hand side of ODE
\pstODEsolve[algebraicAll,saveData]{table}{ t | y[0] }{ 0 }{ 10 }{ 250 }{ 10 }{
9.81 - 1.15*10^-3 / (58*10^-3) * y[0]^2
}
% for comparison: 4 output points
\pstODEsolve[algebraicAll,saveData]{table2}{ t | y[0] }{ 0 }{ 10 }{ 4 }{ 10 }{
9.81 - 1.15*10^-3 / (58*10^-3) * y[0]^2
}
dummy text
\end{document}
\end{filecontents}
\immediate\write18{latex solve}
\immediate\write18{dvips solve}
\immediate\write18{ps2pdf -dNOSAFER solve.ps}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage{pgfplots}
\pgfplotsset{compat=1.17}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
xlabel=$t$,
ylabel=$v$,
ylabel style={rotate=-90}
]
\addplot [thin,black] table {table2.dat}; % solution with 4 output points
\addplot [blue] table {table.dat};
\end{axis}
\end{tikzpicture}
\end{document}
Alternatively, without --shell-escape, the auxiliary document solve.tex can by typeset manually before typesetting the main document example.tex:
latex solve
dvips solve
ps2pdf -dNOSAFER solve.ps
pdflatex example
pdflatex example
ps2pdf must be run with option -dNOSAFER in order to allow it to write files (table.dat).
--shell-escape please? I am using MikTeX so I can choose between PdfLaTex or LuaLaTeX as you told me but I am not sure about how to set this option.
– Axel
May 01 '20 at 05:30
--shell-escape. Where to do this is editor-specific. Look into the editor manual. In MiKTeX, you can also open a terminal and run pdflatex --shell-escape myfile.tex on the command line.
– AlexG
May 01 '20 at 05:43
--shell-escape with the terminal, but it tells me that: `! LaTeX Error: Missing \begin{document}.
See the LaTeX manual or LaTeX Companion for explanation.
Type H
l.4 \begin{filecontents}[o verwrite]{solve.tex}`
– Axel May 01 '20 at 05:53[.tex, is that normal?
– Axel
May 01 '20 at 06:18
pst-odepackage. It is simple to use, perhaps a bit less simple to compile. – Apr 30 '20 at 20:09pdflatexorxelatex. You can compile it withlatex, convert thedvitopdf, or usexelatex. However, sadly the results of both methods may not be the same. – Apr 30 '20 at 20:15tikz-pgfandasymptoteto get more attention – Black Mild Sep 02 '22 at 16:05