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-rw-r--r--Master/texmf-dist/tex/generic/pgf/math/pgfmathode.code.tex20
1 files changed, 10 insertions, 10 deletions
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