From 9da8ac113f97e68e91e3a1ef26467f9814eb4312 Mon Sep 17 00:00:00 2001
From: Karl Berry <karl@freefriends.org>
Date: Mon, 8 Apr 2019 17:23:59 +0000
Subject: pgf revert to previous release (r49607, committed 5jan19)

git-svn-id: svn://tug.org/texlive/trunk@50867 c570f23f-e606-0410-a88d-b1316a301751
---
 .../tex/generic/pgf/math/pgfmathode.code.tex         | 20 ++++++++++----------
 1 file changed, 10 insertions(+), 10 deletions(-)

(limited to 'Master/texmf-dist/tex/generic/pgf/math/pgfmathode.code.tex')

diff --git a/Master/texmf-dist/tex/generic/pgf/math/pgfmathode.code.tex b/Master/texmf-dist/tex/generic/pgf/math/pgfmathode.code.tex
index cb3d0d26ca8..d8837897558 100644
--- a/Master/texmf-dist/tex/generic/pgf/math/pgfmathode.code.tex
+++ b/Master/texmf-dist/tex/generic/pgf/math/pgfmathode.code.tex
@@ -36,12 +36,12 @@
 %**********************************************************************
 
 % Numerically solve a differential system with 1st order Runge-Kutta
-% (Euler method)
+% (Euler method) 
 % dq1/dt = f1(t,q1,q2,...,qN)
 % dq2/dt = f2(t,q1,q2,...,qN)
 % ...
 % dqN/dt = fN(t,q1,q2,...,qN)
-%
+% 
 % #1: A pgf array where the solution will be stored.
 % At the end:
 % #1 -> {{t(0),q1(t(0)),q2(t(0)),...,qN(t(0))},
@@ -58,7 +58,7 @@
 % * First order example: dq/dt = -q + 5 with IC=(t=0,q(0)=0)
 % \pgfmathodeRKI{\Sol}{{-\Sol[1]+5}}{{0,0}}{3.5}{100}
 % * Second order example: {dq1/dt=q2, dq2/dt=-q2/2-sin(q1)} (damped
-%   pendulum)
+%   pendulum) 
 % \pgfmathodeRKI{\Sol}{{\Sol[2],-\Sol[2]/2-sin(deg(\Sol[1]))}}%
 %   {{0,-1,5}}{15}{50}
 
@@ -71,8 +71,8 @@
     % The set of rhs {f1(t,q1,q2,...,qN),...,fN(t,q1,q2,...,qN)} is
     % given in terms of #1[0],#1[1],...,#1[N]. We need to transform to
     % #1[\pgfmathode@timeindex][0],...,#1[\pgfmathode@timeindex][N], that is
-    % add [\pgfmathode@timeindex] after every occurrence of #1 in #2.
-    % No need to brace #2 since it is already surrounded by braces. The
+    % add [\pgfmathode@timeindex] after every occurence of #1 in #2.
+    % No need to brace #2 since it is already surounded by braces. The
     % result is stored in \pgfmathode@func
     \pgfmathode@addindextofunc[#1]#2%
     % Set time step. Actually the number of time steps is #5-1, so we
@@ -93,9 +93,9 @@
       \foreach \pgfmathode@funcindex in {1,...,\pgfmathode@dimfunc} {%
         % The RKI algorithm
         % qk[t(i)] = Deltat*fk(t(i-1),q1(t(i-1)),...qN(t(i-1))) +
-        %            qk[t(i-1)]
-        % Note: this part can be really slow due to array management in
-        % pgfmath.
+        %            qk[t(i-1)] 
+        % Note: this part can be really slow due to array managment in
+        % pgfmath. 
         % TODO: find a better way (at least inside this loop)
         \pgfmathparse{%
           \pgfmathode@Deltat*(\pgfmathode@func[\pgfmathode@funcindex-1])+
@@ -132,7 +132,7 @@
       % Start the function loop
       \foreach \pgfmathode@funcindex in {1,...,\pgfmathode@dimfunc} {%
         % The RKIV algorithm
-        % qk[t(i)] = qk[t(i-1)] +
+        % qk[t(i)] = qk[t(i-1)] + 
         %            (1/6) * (j1k + 2j2k + 2j3k + j4k)
         % where j1k = fk(t(i-1),q1(t(i-1)),...qN(t(i-1))) * Deltat
         %       j2k = fk(t(i-1)+.5*Deltat,
@@ -175,4 +175,4 @@
   \endgroup}
 
 
-\endinput
+\endinput
\ No newline at end of file
-- 
cgit v1.2.3

