% !TEX TS-program = LuaLaTeX
% !TEX encoding = UTF-8 Unicode
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
%% This file is an example of using asmeconf with lualatex to solve and plot an ode in a landscape figure.
%%
%% Author: John H. Lienhard V
%% Department of Mechanical Engineering
%% Massachusetts Institute of Technology
%% Cambridge, MA 02139-4307 USA
%%
%=========================================================
%%
%% LICENSE:
%%
%% Copyright (c) 2021 John H. Lienhard
%% Offered under the MIT license: https://ctan.org/license/mit
%%
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\documentclass[varvw,colorlinks,nofoot]{asmeconf}
\hypersetup{%
pdftitle={Example of asmconf with LuaLaTeX to solve an ODE},
pdfkeywords={asmeconf, LuaLaTeX, ODE, pgfplots, landscape figure},
pdfauthor={John H. Lienhard},
}
\usepackage[figuresright]{rotating}% to use a landscape figure
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Now use lua code
%% Runge-Kutta for simple first-order ODE
\begin{luacode*}
-- Differential equation y’(t) = f(t,y)
-- with f(t,y) = A * y * cos(t+sqrt(1+y)).
-- Initial condition: y(0) = 1
function f(t,y,A)
return A * y * math.cos(t+math.sqrt(1+y))
end
-- Code to write PGFplots data as coordinates
function print_RKfour(tMax,npoints,A,option)
local t0 = 0.0
local y0 = 1.0
local A = A
local h = (tMax-t0)/(npoints-1)
local t = t0
local y = y0
if option~=[[]] then
tex.sprint("\\addplot["..option.."] coordinates{")
else
tex.sprint("\\addplot coordinates{")
end
tex.sprint("("..t0..","..y0..")")
for i=1, npoints do
k1 = h * f(t,y,A)
k2 = h * f(t+h/2,y+k1/2,A)
k3 = h * f(t+h/2,y+k2/2,A)
k4 = h * f(t+h,y+k3,A)
y = y + (k1+2*k2+2*k3+k4)/6
t = t + h
tex.sprint("("..t..","..y..")")
end
tex.sprint("}")
end
\end{luacode*}
%% Define a latex macro to call the case to be plotted
\newcommand\addLUADEDplot[4][]{%
\directlua{print_RKfour(#2,#3,#4,[[#1]])}%
}
% SYNTAX: Solution of the initial value problem
% Code assumed t = 0 at start and y(0) = 1
% #2 is the final time
% #3 is the number of points
% #4 is an amplitude parameter
% #1 are options passed to the pgfplots \addplot function.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% For plotting the results, call pgfplots package
\usepackage{pgfplots}% load AFTER xcolor, which was already called by asmeconf.cls
\pgfplotsset{compat=newest}% to activate latest features
\pgfplotsset{%
width=\textwidth,%
height=0.6\textwidth,%
/tikz/font={\sffamily},%
% every axis plot/.style={line width=2pt},
every axis/.append style={very thick},% see manual page 189
every minor tick/.append style={very thin,black},% modifies the style `every tick'
every minor grid/.append style={very thin, color=Snow4},
every major tick/.append style={thin, black},% modifies the style `every minor tick'
every major grid/.append style={thin, color=Snow4},
major tick length={1.2em},
minor tick length={0.5em},
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% This environment will generate the .bib file the first time you run the code
% if the .bib file already exists, it will not be overwritten
\begin{filecontents}{asmeconf-lualatex-ode-example.bib}
@online{fairbairns,
author = {Robin Fairbairns and Sebastian Rahtz and Leonor Barroca},
title = {A Package for Rotated Objects in \LaTeX},
version = {2.16d},
organization = {Comprehensive \TeX\ Archive Network},
year = {2016},
url = {https://www.ctan.org/pkg/rotating},
urldate = {October 2, 2019},
}
@article{montijano2014,
title = {Numerical methods with {\LuaLaTeX}},
author = {Juan I. Montijano and Mario P{\'{e}}rez and Luis R{\'{a}}ndez and Juan Luis Varona},
year = 2014,
volume = 35,
month = {January},
number = 1,
pages = {51--56},
journal = {TUGboat},
url = {https://tug.org/TUGboat/tb35-1/tb109montijano.pdf},
note = {Open access.}
}
@manual{pgfplots,
title = {Manual for Package \textsc{PGFPLOTS}},
url = {https://ctan.org/pkg/pgfplots},
author = {Christian Feuers{\"{a}}nger},
version = {1.17},
year = {2020},
organization = {Comprehensive \TeX\ Archive Network},
month = feb,
urldate = {January 4, 2021},
}
@manual{lua,
author = {Roberto {l}erusalimschy and Luiz Henrique {de Figueiredo} and Waldemar Celes},
title = {{L}ua 5.3 Reference Manual},
url = {https://www.lua.org/manual/5.3/},
organization = {Pontifical Catholic University},
address = {Rio de Janeiro, Brazil},
year = {2017},
}
\end{filecontents}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}
\ConfName{Proceedings of the \texttt{asmeconf} \linebreak International Examples Congress and Exposition}
\ConfAcronym{AIECE21}
\ConfDate{January 20, 2021}
\ConfCity{Cambridge, MA}
\PaperNo{AIECE2021-0001}
\title{Example of \NoCaseChange{{\upshape\hologo{LuaLaTeX}}} with asmeconf.cls for ODE Integration}
\SetAuthors{John H.\ Lienhard V\affil{1}\CorrespondingAuthor{lienhard@mit.edu}}
\SetAffiliation{1}{Massachusetts Institute of Technology, Cambridge, MA}
\maketitle
\versionfootnote{Version~1.0, \today}
\keywords{asmeconf, \hologo{LuaLaTeX}, ODE, pgfplots, landscape}
%%%%%%%%% ABSTRACT %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{abstract}
This paper is an example of using \texttt{asmeconf} with {\upshape\hologo{LuaLaTeX}} to solve an ODE initial value problem using a fourth-order Runge-Kutta method and to plot the result using \texttt{PGFPLOTS}. The use of a landscape figure is also illustrated. References are given for further reading.
\end{abstract}
%%%%%%%%% NOMENCLATURE (OPTIONAL) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{nomenclature}
\entry{$A$}{Constant parameter [--]}
\entry{$t$}{Time [s]}
\entry{$y(t)$}{Position [m]}
\end{nomenclature}
%%%%%%%%% BODY OF PAPER %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Introduction}
\hologo{LuaLaTeX} is built upon the Lua programming language~\cite{lua}. By directly using Lua code in a \LaTeX\ file, we can accomplish a wide range of tasks, as illustrated in the open-access paper by Montijano et al.~\cite{montijano2014}. In the present example, we follow Montijano et al.\ in solving a nonlinear first-order ordinary differential equation and plotting the result---all within a single \LaTeX\ file!
\section{Solution to an initial value problem}
We consider an initial value problem like that of Montijano et al.:
\begin{equation}\label{eqn:1}
y'(t) = A\cdot y(t) \cos\Big(t + \sqrt{1 + y(t)}\,\Big) \text{ with }y(0)=1
\end{equation}
Here, $A$ is a constant. We may adopt a fourth-order Runge-Kutta algorithm for the integration, which we shall perform to $t = 30$~s using a 400 point discretization. The details of the Runge-Kutta algorithm and a listing of the code are given in Montijano et al. (You can also read the code in the present \texttt{.tex} file.)
The algorithm is implemented directly in the preamble of this file, and the results are plotted in Fig.~\ref{fig:1} for $A = \{0.25, 0.5, 0.75, 1.0\}$. Plotting is done using the \texttt{PGFPLOTS} package~\cite{pgfplots}.
Landscape figures, such as Fig.~\ref{fig:1}, may be produced at full-page size by putting \verb|\usepackage[figuresright]{rotating}| in your \texttt{.tex} file's preamble and using the \texttt{sidewaysfigure*} environment~\cite{fairbairns}.
\begin{sidewaysfigure*}
\begin{tikzpicture}
\begin{axis}[%
xmin=0.,
xmax=30.,
ymin=0.0,
ymax=1.1,
xtick={0,5,...,30},
ytick={0,0.2,...,1.0},
minor x tick num=4,
minor y tick num=3,
xlabel={Time, $\mathsf{t}$ [s]},
ylabel={Position, $\mathsf{y}$ [m]},
xticklabel={$\mathsf{\pgfmathprintnumber{\tick}}$},
yticklabel={$\mathsf{\pgfmathprintnumber{\tick}}$},
legend style={
at={(0.7,0.85)},
anchor=west,
fill=none,
cells={anchor=west},
},
]
% tMax = 30, npoints = 400, A is the last argument
\addLUADEDplot[color=Purple4,densely dashed,,very thick]{30}{400}{0.25};% color names are from xcolor package
\addlegendentry[fill=white]{$\mathsf{A = 0.25}$};
\addLUADEDplot[color=Chartreuse4,dashdotted,very thick]{30}{400}{0.5};
\addlegendentry[fill=white]{$\mathsf{A = 0.5}$};
\addLUADEDplot[color=Red3,densely dotted,very thick]{30}{400}{0.75};
\addlegendentry[fill=white]{$\mathsf{A = 0.75}$};
\addLUADEDplot[color=Blue3,smooth,very thick]{30}{400}{1};
\addlegendentry[fill=white]{$\mathsf{A = 1}$};
\end{axis}
\end{tikzpicture}
\caption{A trial of pgfplot with Luacode Runge-Kutta integration\label{fig:1}}
\end{sidewaysfigure*}
%%% CONCLUSIONS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Conclusion}
\hologo{LuaLaTeX} enables numerical computations within a \LaTeX\ environment. By combining this capability with
\texttt{PGFPlots}, the need for separate numerical and/or graphics packages can be reduced.
%%% ACKNOWLEDGMENTS %%%%%%%%%%%%%%%%%%%%%%%%%%%
\section*{Acknowledgments}
The example shown in this paper is directly based on an example given by Montijano et al.~\cite{montijano2014}. Additional examples, such as the
Lorenz attractor, are contained in that paper.
%%% REFERENCES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\bibliographystyle{asmeconf}%% .bst file following ASME conference format. Do not change.
\bibliography{asmeconf-lualatex-ode-example}%% this bib file will be generated from the filecontents environment upon first run of this .tex file.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\end{document}