diff options
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.tex | 16 |
1 files changed, 10 insertions, 6 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 a5c57a07f45..b87607545a6 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 @@ -10,7 +10,7 @@ twoside=false, % dvips, UKenglish -]{pst-doc} +]{pst-doc-new} \usepackage[T1]{fontenc} %\usepackage{lmodern} \usepackage[tt=false]{libertine} %override beramono (doesn't look like tt font) @@ -18,7 +18,7 @@ %\usepackage[scaled=0.83]{luximono} %override beramono (doesn't look like tt font) \usepackage{attachfile2} \attachfilesetup{date={},color=1 0 0} -\usepackage[utf8]{inputenc} +%\usepackage[utf8]{inputenc} \usepackage{amsmath} \usepackage{pst-3dplot} \usepackage{pst-plot} @@ -79,12 +79,13 @@ \def\day{#3} } -\begin{document} \author{Alexander Grahn} \expandafter\parsedate\filedate\relax %set current date to package date \title{pst-ode\\[4ex]} \subtitle{A PSTricks package for solving initial value problems for sets of Ordinary Differential Equations (ODE), v\pstFV\\[2ex]\url{https://gitlab.com/agrahn/pst-ode}} -\maketitle + +\begin{document} +\settitle %\clearpage \begin{abstract} @@ -140,7 +141,7 @@ $\mathbf{x}_0$ is a list of $n$ space separated initial values, one for each dif $\mathbf{f}(t,\mathbf{x})$ 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}'.%\\ \newpage -\noindent\Lcs{pstODEsolve} accepts a few \OptArgs:\\% \Lkeyword{dt0}, \Lkeyword{append}, \Lkeyword{saveData}, \Lkeyword{algebraicOutputFormat}, \Lkeyword{algebraicT}, \Lkeyword{algebraicN}, \Lkeyword{algebraicIC}, \Lkeyword{algebraic}, \Lkeyword{algebraicAll}, \Lkeyword{silent} and \Lkeyword{varsteptol}.\\ +\noindent\Lcs{pstODEsolve} accepts a few \OptArgs:\\% \Lkeyword{dt0}, \Lkeyword{append}, \Lkeyword{saveData}, \Lkeyword{algebraicOutputFormat}, \Lkeyword{algebraicT}, \Lkeyword{algebraicN}, \Lkeyword{algebraicIC}, \Lkeyword{algebraic}, \Lkeyword{algebraicAll}, \Lkeyword{silent}, \Lkeyword{varsteptol} and \Lkeyword{rk4}.\\ \noindent\OptArg*{dt0=<number>}\\ \noindent By default, the output step $(t_\mathrm{e}-t_\mathrm{0})/(N-1)$ is used as the intitial, tentative integration step size. A large initial step may cause the integration to crash early by numerical overflow, in particular if the right-hand side evaluates to large values. With option \Lkeyword{dt0}, an arbitrary value of the initial step size can be specified.\\ @@ -173,7 +174,10 @@ Option \Lkeyword{algebraicAll} is equivalent to setting all of \Lkeyword{algebra Option \Lkeyword{silent} suppresses the terminal output of stepping information.\\ \noindent\OptArg*{varsteptol=<number>}\\ -The tolerance for automatic calculation of the integration step size can be set with \Lkeyword{varsteptol}. The default value is \Lkeyword{1e-6}. Sometimes, it may be helpful to relax this value in order to cope with situations where integration stops with step size underflow. The occurence of step size underflow is indicated by writing `\Lkeyword{!}' to the terminal and integration stops prematurely before reaching $t_\mathrm{e}$. The current value of $t$ and the current state vector $\mathbf{x}$ are written to the terminal. Step size underflow may happen for stiff ODEs at some point along the integration interval $[t_0, t_\mathrm{e}]$.\\[1ex] +The tolerance for automatic calculation of the integration step size can be set with \Lkeyword{varsteptol}. The default value is \Lkeyword{1e-6}. Sometimes, it may be helpful to relax this value in order to cope with situations where integration stops with step size underflow. The occurence of step size underflow is indicated by writing `\Lkeyword{!}' to the terminal and integration stops prematurely before reaching $t_\mathrm{e}$. The current value of $t$ and the current state vector $\mathbf{x}$ are written to the terminal. Step size underflow may happen for stiff ODEs at some point along the integration interval $[t_0, t_\mathrm{e}]$.\\ + +\noindent\OptArg*{rk4}\\ +With this option, the classical 4th-order Runge-Kutta method is used to integrate the ODE between output points. No automatic step size control is performed in this case. This option is provided mainly for comparison purposes.\\[1ex] \begin{BDef} \Lcs{pstODEsaveState}\Largb{state} |