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authorKarl Berry <karl@freefriends.org>2019-03-05 22:33:03 +0000
committerKarl Berry <karl@freefriends.org>2019-03-05 22:33:03 +0000
commit2471723425925c57b3e9e7e421a86e64b16a49bb (patch)
tree955b121458c4dbd9afb78279a194232e35398024 /Master/texmf-dist/doc/generic/pst-ode/pst-ode-doc.tex
parentdc89c467e680b069a8f6d50a46024e38dc595d7b (diff)
pst-ode (5mar19)
git-svn-id: svn://tug.org/texlive/trunk@50243 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/doc/generic/pst-ode/pst-ode-doc.tex')
-rw-r--r--Master/texmf-dist/doc/generic/pst-ode/pst-ode-doc.tex32
1 files changed, 19 insertions, 13 deletions
diff --git a/Master/texmf-dist/doc/generic/pst-ode/pst-ode-doc.tex b/Master/texmf-dist/doc/generic/pst-ode/pst-ode-doc.tex
index bbb001b2ea0..33cb6433b4a 100644
--- a/Master/texmf-dist/doc/generic/pst-ode/pst-ode-doc.tex
+++ b/Master/texmf-dist/doc/generic/pst-ode/pst-ode-doc.tex
@@ -1,5 +1,16 @@
-\documentclass[11pt,english,BCOR10mm,DIV12,bibliography=totoc,parskip=false,smallheadings,
- headexclude,footexclude,oneside,dvips,UKenglish]{pst-doc}
+\documentclass[
+ fontsize=11pt,
+ english,
+ BCOR=10mm,DIV=12,
+ bibliography=totoc,
+ parskip=false,
+ headings=small,
+ headinclude=false,
+ footinclude=false,
+ twoside=false,
+% dvips,
+ UKenglish
+]{pst-doc}
\usepackage[T1]{fontenc}
%\usepackage{lmodern}
\usepackage[tt=false]{libertine} %override beramono (doesn't look like tt font)
@@ -17,11 +28,6 @@
\let\pstFV\fileversion
\let\belowcaptionskip\abovecaptionskip
-\makeatletter
-\renewcommand*\l@subsection{\bprot@dottedtocline{2}{1.5em}{3.6em}}
-\renewcommand*\l@subsubsection{\bprot@dottedtocline{3}{3.8em}{4.5em}}
-\makeatother
-
\def\bgImage{%
\pstVerb{
/alpha 10 def
@@ -74,7 +80,6 @@
}
\begin{document}
-%\author{Alexander Grahn}
\author{Alexander Grahn}
\expandafter\parsedate\filedate\relax %set current date to package date
\title{pst-ode\\[4ex]}
@@ -97,22 +102,23 @@ An initial value problem involves finding the solution $\mathbf{x}(t)$ of a set
\begin{equation}
\frac{\mathrm{d}\mathbf{x}}{\mathrm{d}t}=\mathbf{f}(t,\mathbf{x})
\end{equation}
-by integrating them with respect to the independent variable $t$ starting at $t_0$ up to $t_\mathrm{e}$. If the set consists of $n$ differential equations,
+by integrating them with respect to the independent variable $t$. If the set consists of $n$ differential equations,
a vector of initial conditions
\begin{equation}
\mathbf{x}(t_0)=\mathbf{x}_0
\end{equation}
of the same length $n$ is required. For $n=1$ the initial value problem is one-dimensional:
\begin{gather}
- \frac{\mathrm{d}x}{\mathrm{d}t}=f(t,x)\quad\text{for}\ t \in [t_0, t_\mathrm{e}]\text{, where}\label{eq:1dode}\\
+% \frac{\mathrm{d}x}{\mathrm{d}t}=f(t,x)\quad\text{for}\ t \in [t_0, t_\mathrm{e}]\text{, where}\label{eq:1dode}\\
+ \frac{\mathrm{d}x}{\mathrm{d}t}=f(t,x),\label{eq:1dode}\\
x(t_0) = x_0.\label{eq:1ini}
\end{gather}
-Instead of producing analytical expressions of the solution functions $\mathbf{x}(t)$, the numerical method gives only approximate values $\mathbf{x}_i$ at $N$ discrete points $t_i$ of the integration interval $I=[t_0, t_\mathrm{e}]$:
+Instead of producing analytical expressions of the solution functions $\mathbf{x}(t)$, the numerical method gives only approximate values $\mathbf{x}_i$ at $N$ discrete points $t_i$ in the interval $I=[t_0, t_\mathrm{e}]$ of the independent variable $t$:
\begin{equation}
\mathbf{x}_i\approx\mathbf{x}(t_i).
\end{equation}
-The computed approximations $\mathbf{x}_i$ of the solution as well as the initial condition vector $\mathbf{x}_0$ are called `state vectors'. In the case of a single equation problem, Eqs.~\eqref{eq:1dode}, \eqref{eq:1ini}, the state vectors have only one component.
+The computed approximations $\mathbf{x}_i$ of the solution as well as the initial condition vector $\mathbf{x}_0$ are called `state vectors'. In the case of a single equation problem, Eqs.~\eqref{eq:1dode}, \eqref{eq:1ini}, state vectors have only one component.
\section{Commands}
\begin{BDef}
@@ -129,7 +135,7 @@ Arguments $t_0$ and $t_\mathrm{e}$ define the interval of integration $I=[t_0, t
$N$ is the number of \emph{equally} spaced output points, including $t_0$ and $t_\mathrm{e}$; it must be $\ge 2$. In order to divide the interval of integration into $K$ output steps, $N$ must be set to $K+1$. Note that the precision of the solution does \emph{not} depend on $N$; internal integration steps are automatically inserted and resized according to the changes in the solution.
-$\mathbf{x}_0$ is a list of $n$ space separated initial values, one for each differential equation. Alternatively, $\mathbf{x}_0$ can be given as a \PS{} procedure pushing the initial values on the stack, or as an algebraic expression in infix notation where the elements are separated by `\Lkeyword{|}'. Infix notation requires option \Lkeyword{algebraicIC}. This argument can be left empty. In that case, the last computed state vector of a preceding \Lcs{pstODEsolve} call. Of course, the number of equations $n$ must be the same as in the preceding calculation.
+$\mathbf{x}_0$ is a list of $n$ space separated initial values, one for each differential equation. Alternatively, $\mathbf{x}_0$ can be given as a \PS{} procedure pushing the initial values on the stack, or as an algebraic expression in infix notation where the elements are separated by `\Lkeyword{|}'. Infix notation requires option \Lkeyword{algebraicIC}. This argument can be left empty. In that case, the last computed state vector of a preceding \Lcs{pstODEsolve} call serves as initial condition. Of course, the number of equations $n$ must be the same as in the preceding calculation.
$\mathbf{f}(t,\mathbf{x})$ is the right-hand side of the differential equations. Equations can be entered in either infix or \PS{} (postfix, reverse polish) notation. Infix notation requires option \Lkeyword{algebraic}, and equations have to be separated by `\Lkeyword{|}'. The $n$ current state vector components can be referred to as \Lkeyword{x[0]}, \Lkeyword{x[1]}, \dots, \Lkeyword{x[}$n-1$\Lkeyword{]} or \Lkeyword{y[0]}, \Lkeyword{y[1]}, \dots, \Lkeyword{y[}$n-1$\Lkeyword{]}, and the current independent variable value as `\Lkeyword{t}'. If given in \PS{} notation, the provided procedure must first pop the current state vector components in reverse order(!) from the operand stack and then push the first derivatives in regular order back to it. Again, the independent variable value can be accessed using `\Lkeyword{t}'.%\\