From 292ac684b5385c7e79680b1addcd47b994d4341b Mon Sep 17 00:00:00 2001
From: Karl Berry <karl@freefriends.org>
Date: Sat, 5 Jan 2008 17:03:21 +0000
Subject: new metapost/(la)tex package mfpic4ode (3jan08)

git-svn-id: svn://tug.org/texlive/trunk@6041 c570f23f-e606-0410-a88d-b1316a301751
---
 .../texmf-dist/doc/latex/mfpic4ode/mfpic4ode.tex   | 192 +++++++++++++++++++++
 1 file changed, 192 insertions(+)
 create mode 100644 Master/texmf-dist/doc/latex/mfpic4ode/mfpic4ode.tex

(limited to 'Master/texmf-dist/doc/latex/mfpic4ode/mfpic4ode.tex')

diff --git a/Master/texmf-dist/doc/latex/mfpic4ode/mfpic4ode.tex b/Master/texmf-dist/doc/latex/mfpic4ode/mfpic4ode.tex
new file mode 100644
index 00000000000..a20ce6c6131
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/mfpic4ode/mfpic4ode.tex
@@ -0,0 +1,192 @@
+%%
+%% This is file `mfpic4ode.tex',
+%% generated with the docstrip utility.
+%%
+%% The original source files were:
+%%
+%% mfpic4ode.dtx  (with options: `tex')
+%% 
+%% This is a generated file.
+%% 
+%% Copyright (C) 2007 by Robert Marik <marik@mendelu.cz>
+%% 
+%% This file may be distributed and/or modified under the conditions of
+%% the LaTeX Project Public License, either version 1.2 of this license
+%% or (at your option) any later version.  The latest version of this
+%% license is in:
+%% 
+%%    http://www.latex-project.org/lppl.txt
+%% 
+%% and version 1.2 or later is part of all distributions of LaTeX version
+%% 1999/12/01 or later.
+%% 
+\catcode`\@=11
+
+\newif\ifcolorODEarrow
+%%%\colorODEarrowfalse
+\colorODEarrowtrue
+
+%%% The line from one point to another
+\def\ODEline#1#2{\lines{#1,#2}}
+
+%%% The variable ODErhs is used to store the function from the right
+%%% hand side of ODE in the form y'=f(x,y). We use command
+%%% ODEdefineequation to set up this variable.
+\def\ODEdefineequation#1{\fdef{ODErhs}{x,y}{#1}}
+
+%%% Integral curve using Euler method. The step of this method is
+%%% ODEstep and the number of steps is ODEstepcount. The points are
+%%% stored in metapost variables x1,y1.
+\def\trajectory#1#2{
+  \mfsrc{x1:=#1;y1:=#2;
+    for i=1 upto ODEstepcount:
+    x2:=x1+ODEstep;
+    y2:=y1+ODEstep*ODErhs(x1,y1);}
+  \ODEline{z1}{z2}
+  \mfsrc{
+    if ((y2>yneg) and (y2<ypos)): x1:=x2; y1:=y2 fi;
+    endfor
+  }}
+
+%%% Integral curve using Runge--Kutta method.
+\def\trajectoryRK#1#2{
+  \mfsrc{x1:=#1;y1:=#2;
+    for i=1 upto ODEstepcount:
+    k1:=ODErhs(x1,y1);
+    x3:=x1+(ODEstep/2);
+    y3:=y1+k1*(ODEstep/2);
+    k2:=ODErhs(x3,y3);
+    x2:=x1+ODEstep;
+    y2:=y1+ODEstep*k2;}
+  \ODEline{z1}{z2}
+  \mfsrc{
+    if ((y2>yneg) and (y2<ypos)): x1:=x2; y1:=y2 fi;
+    endfor
+  }}
+%%% Integral curve using fourth order Runge--Kutta method.
+\def\trajectoryRKF#1#2{
+  \mfsrc{x1:=#1;y1:=#2;
+    for i=1 upto ODEstepcount:
+    k1:=ODErhs(x1,y1);
+    x3:=x1+(ODEstep/2);
+    y3:=y1+k1*(ODEstep/2);
+    k2:=ODErhs(x3,y3);
+    y4:=y1+k2*(ODEstep/2);
+    k3:=ODErhs(x3,y4);
+    y5:=y1+k3*(ODEstep/2);
+    k4:=ODErhs(x3,y5);
+    kk:=(k1+2*k2+2*k3+k4)/6;
+    x2:=x1+ODEstep;
+    y2:=y1+ODEstep*kk;}
+  \ODEline{z1}{z2}
+  \mfsrc{
+    if ((y2>yneg) and (y2<ypos)): x1:=x2; y1:=y2 fi;
+    endfor
+  }}
+\def\ODEarrow#1#2{
+  \mfsrc{x1:=#1; y1:=#2;
+    x3:=x1+(ODEarrowlength)/((xscale)++(ODErhs(#1,#2)*yscale));
+    y3:=y1+(ODEarrowlength*ODErhs(#1,#2))/((xscale)++(ODErhs(#1,#2)*yscale));
+    if y3>y1:ODEcolorarrow:=blue else: ODEcolorarrow:=red fi;
+  }
+  \ifcolorODEarrow
+    \drawcolor{ODEcolorarrow} \headcolor{ODEcolorarrow}
+  \fi
+  \draw\arrow\lines{z1,z3}
+}
+
+\def\ODEarrows#1{\ODE@cycle@points#1;,;}
+\def\trajectories#1{\ODE@cycle@IC#1;,;}
+\def\ODE@last@point{}
+\def\ODE@cycle@points#1,#2;{\def\temp{#1}\ifx\temp\ODE@last@point\let\next\relax
+  \else\ODEarrow{#1}{#2}\relax\let\next\ODE@cycle@points\fi\next}
+\def\ODE@cycle@IC#1,#2;{\def\temp{#1}\ifx\temp\ODE@last@point\let\next\relax
+  \else
+  \trajectoryRKF{#1}{#2}\relax\let\next\ODE@cycle@IC\fi\next}
+\mfsrc{path p,q;color ODEcolorarrow;}
+
+%%% Onedimensional autonomous systems y'=f(y) where  '=d/dx
+\def\ODEharrow#1{
+  \mfsrc{x1:=#1;
+    if ODErhs(0,x1)>0: x3:=x1+ODEarrowlength else: x3:=x1-ODEarrowlength fi;
+    if ODErhs(0,x1)*ODErhs(0,x3)<0: x1:=-100;x3:=-100 fi;
+    if x3>x1:ODEcolorarrow:=blue else: ODEcolorarrow:=red fi;
+  }
+  \ifcolorODEarrow \drawcolor{ODEcolorarrow}
+  \headcolor{ODEcolorarrow} \fi
+  \pen{1.5pt}
+  \draw\arrow\lines{(x1,0),(x3,0)}
+}
+
+\def\ODEvarrow#1{
+  \mfsrc{x1:=#1;
+    if ODErhs(0,#1)>0:
+    x3:=x1+(ODEarrowlength/yscale) else: x3:=x1-(ODEarrowlength/yscale) fi;
+    if ODErhs(0,x1)*ODErhs(0,x3)<0: x1:=-100;x3:=-100 fi;
+    if x3>x1:ODEcolorarrow:=blue else: ODEcolorarrow:=red fi;
+  }
+  \ifcolorODEarrow \drawcolor{ODEcolorarrow}
+  \headcolor{ODEcolorarrow} \fi
+  \pen{1.5pt}
+  \draw\arrow\lines{(0,x1),(0,x3)}
+}
+
+%%% Twodimensional autonomous systems  x'=f(x,y), y'=g(x,y) where '=d/dt
+\def\ASdefineequations#1#2{\fdef{ASf}{x,y}{#1}\fdef{ASg}{x,y}{#2}}
+
+\def\AStrajectory#1#2{
+  \mfsrc{x1:=#1;y1:=#2;
+    for i=1 upto ODEstepcount:
+    x2:=x1+ODEstep*ASf(x1,y1);
+    y2:=y1+ODEstep*ASg(x1,y1);}
+  \ODEline{z1}{z2}
+  \mfsrc{
+    if ((y2>yneg) and (y2<ypos)): x1:=x2; y1:=y2 fi;
+    endfor
+  }}
+\def\ASarrow#1#2{
+  \mfsrc{x1:=#1; y1:=#2;
+    x3:=x1+(ODEarrowlength*ASf(#1,#2))/((ASf(#1,#2)*xscale)++(ASg(#1,#2)*yscale    ));
+    y3:=y1+(ODEarrowlength*ASg(#1,#2))/((ASf(#1,#2)*xscale)++(ASg(#1,#2)*yscale    ));
+    if y3>y1:ODEcolorarrow:=blue else: ODEcolorarrow:=red fi;
+  }
+  \ifcolorODEarrow
+  \drawcolor{ODEcolorarrow} \headcolor{ODEcolorarrow}
+  \fi
+  \draw\arrow\lines{z1,z3}
+}
+
+\def\ASarrows#1{\AS@cycle@points#1;,;}
+\def\AS@cycle@points#1,#2;{\def\temp{#1}\ifx\temp\ODE@last@point\let\next\relax
+  \else\ASarrow{#1}{#2}\relax\let\next\AS@cycle@points\fi\next}
+\def\AStrajectories#1{\AS@cycle@IC#1;,;}
+\def\AS@cycle@IC#1,#2;{\def\temp{#1}\ifx\temp\ODE@last@point\let\next\relax
+  \else
+  \AStrajectoryRKF{#1}{#2}\relax\let\next\AS@cycle@IC\fi\next}
+\def\AStrajectoryRKF#1#2{
+  \mfsrc{x1:=#1;y1:=#2;
+    TIMEsteps:=abs(TIMEend/TIMEstep);
+    TIME:=0;
+    for i=1 upto TIMEsteps:
+    k1:=ASf(x1,y1);
+    l1:=ASg(x1,y1);
+    k2:=ASf(x1+(TIMEstep*k1/2),y1+(TIMEstep*l1/2));
+    l2:=ASg(x1+(TIMEstep*k1/2),y1+(TIMEstep*l1/2));
+    k3:=ASf(x1+(TIMEstep*k2/2),y1+(TIMEstep*l2/2));
+    l3:=ASg(x1+(TIMEstep*k2/2),y1+(TIMEstep*l2/2));
+    k4:=ASf(x1+(TIMEstep*k3),y1+(TIMEstep*l3));
+    l4:=ASg(x1+(TIMEstep*k3),y1+(TIMEstep*l3));
+    k5:=((k1)/6)+((k2)/3)+((k3)/3)+((k4)/6);
+    l5:=(l1/6)+(l2/3)+(l3/3)+(l4/6);
+    x2:=x1+(TIMEstep*k5);
+    y2:=y1+(TIMEstep*l5);}
+  \ODEline{z1}{z2}
+  \mfsrc{
+    if ((y2>yneg) and (y2<ypos) and (x2<xpos) and (x2>xneg)): x1:=x2; y1:=y2 fi;
+    endfor
+  }}
+
+\catcode`\@12\relax
+\endinput
+%%
+%% End of file `mfpic4ode.tex'.
-- 
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