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Boost-Commit : |
Subject: [Boost-commit] svn:boost r82742 - in website/public_html/live/doc: fixes/1_53_0 fixes/1_53_0/libs fixes/1_53_0/libs/numeric fixes/1_53_0/libs/numeric/odeint fixes/1_53_0/libs/numeric/odeint/doc fixes/1_53_0/libs/numeric/odeint/doc/html fixes/1_53_0/libs/numeric/odeint/doc/html/boost_numeric_odeint fixes/1_53_0/libs/numeric/odeint/doc/html/boost_numeric_odeint/getting_started libs/1_53_0
From: dnljms_at_[hidden]
Date: 2013-02-06 20:26:07
Author: danieljames
Date: 2013-02-04 14:31:19 EST (Mon, 04 Feb 2013)
New Revision: 82742
URL: http://svn.boost.org/trac/boost/changeset/82742
Log:
Website: Put the odeint fix in the right place.
Added:
website/public_html/live/doc/fixes/1_53_0/
website/public_html/live/doc/fixes/1_53_0/libs/
website/public_html/live/doc/fixes/1_53_0/libs/numeric/
website/public_html/live/doc/fixes/1_53_0/libs/numeric/odeint/
website/public_html/live/doc/fixes/1_53_0/libs/numeric/odeint/doc/
website/public_html/live/doc/fixes/1_53_0/libs/numeric/odeint/doc/html/
website/public_html/live/doc/fixes/1_53_0/libs/numeric/odeint/doc/html/boost_numeric_odeint/
website/public_html/live/doc/fixes/1_53_0/libs/numeric/odeint/doc/html/boost_numeric_odeint/getting_started/
website/public_html/live/doc/fixes/1_53_0/libs/numeric/odeint/doc/html/boost_numeric_odeint/getting_started/overview.html (contents, props changed)
Removed:
website/public_html/live/doc/libs/1_53_0/
Added: website/public_html/live/doc/fixes/1_53_0/libs/numeric/odeint/doc/html/boost_numeric_odeint/getting_started/overview.html
==============================================================================
--- (empty file)
+++ website/public_html/live/doc/fixes/1_53_0/libs/numeric/odeint/doc/html/boost_numeric_odeint/getting_started/overview.html 2013-02-04 14:31:19 EST (Mon, 04 Feb 2013)
@@ -0,0 +1,1168 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
+<title>Overview</title>
+<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets V1.76.1">
+<link rel="home" href="../../index.html" title="Chapter 1. Boost.Numeric.Odeint">
+<link rel="up" href="../getting_started.html" title="Getting started">
+<link rel="prev" href="../getting_started.html" title="Getting started">
+<link rel="next" href="usage__compilation__headers.html" title="Usage, Compilation, Headers">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../logo.jpg"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../getting_started.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../getting_started.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="usage__compilation__headers.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
+</div>
+<div class="section">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="boost_numeric_odeint.getting_started.overview"></a><a class="link" href="overview.html" title="Overview">Overview</a>
+</h3></div></div></div>
+<p>
+ odeint is a library for solving initial value problems (IVP) of ordinary
+ differential equations. Mathematically, these problems are formulated as
+ follows:
+ </p>
+<p>
+ <span class="emphasis"><em>x'(t) = f(x,t)</em></span>, <span class="emphasis"><em>x(0) = x0</em></span>.
+ </p>
+<p>
+ <span class="emphasis"><em>x</em></span> and <span class="emphasis"><em>f</em></span> can be vectors and the
+ solution is some function <span class="emphasis"><em>x(t)</em></span> fulfilling both equations
+ above. In the following we will refer to <span class="emphasis"><em>x'(t)</em></span> also
+ <code class="computeroutput"><span class="identifier">dxdt</span></code> which is also our notation
+ for the derivative in the source code.
+ </p>
+<p>
+ Ordinary differential equations occur nearly everywhere in natural sciences.
+ For example, the whole Newtonian mechanics are described by second order
+ differential equations. Be sure, you will find them in every discipline.
+ They also occur if partial differential equations (PDEs) are discretized.
+ Then, a system of coupled ordinary differential occurs, sometimes also referred
+ as lattices ODEs.
+ </p>
+<p>
+ Numerical approximations for the solution <span class="emphasis"><em>x(t)</em></span> are calculated
+ iteratively. The easiest algorithm is the Euler scheme, where starting at
+ <span class="emphasis"><em>x(0)</em></span> one finds <span class="emphasis"><em>x(dt) = x(0) + dt f(x(0),0)</em></span>.
+ Now one can use <span class="emphasis"><em>x(dt)</em></span> and obtain <span class="emphasis"><em>x(2dt)</em></span>
+ in a similar way and so on. The Euler method is of order 1, that means the
+ error at each step is <span class="emphasis"><em>~ dt<sup>2</sup></em></span>. This is, of course, not
+ very satisfying, which is why the Euler method is rarely used for real life
+ problems and serves just as illustrative example.
+ </p>
+<p>
+ The main focus of odeint is to provide numerical methods implemented in a
+ way where the algorithm is completely independent on the data structure used
+ to represent the state <span class="emphasis"><em>x</em></span>. In doing so, odeint is applicable
+ for a broad variety of situations and it can be used with many other libraries.
+ Besides the usual case where the state is defined as a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span></code>
+ or a <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">array</span></code>, we provide native support for the
+ following libraries:
+ </p>
+<div class="itemizedlist"><ul class="itemizedlist" type="disc">
+<li class="listitem">
+ Boost.uBLAS
+ </li>
+<li class="listitem">
+ Thrust, making
+ odeint naturally running on CUDA devices
+ </li>
+<li class="listitem">
+ gsl_vector for compatibility with the many numerical function in the
+ GSL
+ </li>
+<li class="listitem">
+ Boost.Range
+ </li>
+<li class="listitem">
+ Boost.Fusion
+ (the state type can be a fusion vector)
+ </li>
+<li class="listitem">
+ Boost.Units
+ </li>
+<li class="listitem">
+ <a href="http://software.intel.com/en-us/articles/intel-mkl/" target="_top">Intel
+ Math Kernel Library</a> for maximum performance
+ </li>
+<li class="listitem">
+ VexCL for OpenCL
+ </li>
+<li class="listitem">
+ Boost.Graph
+ (still experimentally)
+ </li>
+</ul></div>
+<p>
+ In odeint, the following algorithms are implemented:
+ </p>
+<div class="table">
+<a name="boost_numeric_odeint.getting_started.overview.stepper_algorithms"></a><p class="title"><b>Table 1.1. Stepper Algorithms</b></p>
+<div class="table-contents"><table class="table" summary="Stepper Algorithms">
+<colgroup>
+<col>
+<col>
+<col>
+<col>
+<col>
+<col>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+ <p>
+ Algorithm
+ </p>
+ </th>
+<th>
+ <p>
+ Class
+ </p>
+ </th>
+<th>
+ <p>
+ Concept
+ </p>
+ </th>
+<th>
+ <p>
+ System Concept
+ </p>
+ </th>
+<th>
+ <p>
+ Order
+ </p>
+ </th>
+<th>
+ <p>
+ Error Estimation
+ </p>
+ </th>
+<th>
+ <p>
+ Dense Output
+ </p>
+ </th>
+<th>
+ <p>
+ Internal state
+ </p>
+ </th>
+<th>
+ <p>
+ Remarks
+ </p>
+ </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+ <p>
+ Explicit Euler
+ </p>
+ </td>
+<td>
+ <p>
+ <code class="computeroutput"><span class="identifier">euler</span></code>
+ </p>
+ </td>
+<td>
+ <p>
+ <a class="link" href="../concepts/dense_output_stepper.html" title="Dense Output Stepper">Dense
+ Output Stepper</a>
+ </p>
+ </td>
+<td>
+ <p>
+ <a class="link" href="../concepts/system.html" title="System">System</a>
+ </p>
+ </td>
+<td>
+ <p>
+ 1
+ </p>
+ </td>
+<td>
+ <p>
+ No
+ </p>
+ </td>
+<td>
+ <p>
+ Yes
+ </p>
+ </td>
+<td>
+ <p>
+ No
+ </p>
+ </td>
+<td>
+ <p>
+ Very simple, only for demonstrating purpose
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ Modified Midpoint
+ </p>
+ </td>
+<td>
+ <p>
+ <code class="computeroutput"><span class="identifier">modified_midpoint</span></code>
+ </p>
+ </td>
+<td>
+ <p>
+ <a class="link" href="../concepts/stepper.html" title="Stepper">Stepper</a>
+ </p>
+ </td>
+<td>
+ <p>
+ <a class="link" href="../concepts/system.html" title="System">System</a>
+ </p>
+ </td>
+<td>
+ <p>
+ configurable (2)
+ </p>
+ </td>
+<td>
+ <p>
+ No
+ </p>
+ </td>
+<td>
+ <p>
+ No
+ </p>
+ </td>
+<td>
+ <p>
+ No
+ </p>
+ </td>
+<td>
+ <p>
+ Used in Bulirsch-Stoer implementation
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ Runge-Kutta 4
+ </p>
+ </td>
+<td>
+ <p>
+ <code class="computeroutput"><span class="identifier">runge_kutta4</span></code>
+ </p>
+ </td>
+<td>
+ <p>
+ <a class="link" href="../concepts/stepper.html" title="Stepper">Stepper</a>
+ </p>
+ </td>
+<td>
+ <p>
+ <a class="link" href="../concepts/system.html" title="System">System</a>
+ </p>
+ </td>
+<td>
+ <p>
+ 4
+ </p>
+ </td>
+<td>
+ <p>
+ No
+ </p>
+ </td>
+<td>
+ <p>
+ No
+ </p>
+ </td>
+<td>
+ <p>
+ No
+ </p>
+ </td>
+<td>
+ <p>
+ The classical Runge-Kutta scheme, good general scheme without error
+ control
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ Cash-Karp
+ </p>
+ </td>
+<td>
+ <p>
+ <code class="computeroutput"><span class="identifier">runge_kutta_cash_karp54</span></code>
+ </p>
+ </td>
+<td>
+ <p>
+ <a class="link" href="../concepts/error_stepper.html" title="Error Stepper">Error
+ Stepper</a>
+ </p>
+ </td>
+<td>
+ <p>
+ <a class="link" href="../concepts/system.html" title="System">System</a>
+ </p>
+ </td>
+<td>
+ <p>
+ 5
+ </p>
+ </td>
+<td>
+ <p>
+ Yes (4)
+ </p>
+ </td>
+<td>
+ <p>
+ No
+ </p>
+ </td>
+<td>
+ <p>
+ No
+ </p>
+ </td>
+<td>
+ <p>
+ Good general scheme with error estimation, to be used in controlled_error_stepper
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ Dormand-Prince 5
+ </p>
+ </td>
+<td>
+ <p>
+ <code class="computeroutput"><span class="identifier">runge_kutta_dopri5</span></code>
+ </p>
+ </td>
+<td>
+ <p>
+ <a class="link" href="../concepts/error_stepper.html" title="Error Stepper">Error
+ Stepper</a>
+ </p>
+ </td>
+<td>
+ <p>
+ <a class="link" href="../concepts/system.html" title="System">System</a>
+ </p>
+ </td>
+<td>
+ <p>
+ 5
+ </p>
+ </td>
+<td>
+ <p>
+ Yes (4)
+ </p>
+ </td>
+<td>
+ <p>
+ Yes
+ </p>
+ </td>
+<td>
+ <p>
+ Yes
+ </p>
+ </td>
+<td>
+ <p>
+ Standard method with error control and dense output, to be used
+ in controlled_error_stepper and in dense_output_controlled_explicit_fsal.
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ Fehlberg 78
+ </p>
+ </td>
+<td>
+ <p>
+ <code class="computeroutput"><span class="identifier">runge_kutta_fehlberg78</span></code>
+ </p>
+ </td>
+<td>
+ <p>
+ <a class="link" href="../concepts/error_stepper.html" title="Error Stepper">Error
+ Stepper</a>
+ </p>
+ </td>
+<td>
+ <p>
+ <a class="link" href="../concepts/system.html" title="System">System</a>
+ </p>
+ </td>
+<td>
+ <p>
+ 8
+ </p>
+ </td>
+<td>
+ <p>
+ Yes (7)
+ </p>
+ </td>
+<td>
+ <p>
+ No
+ </p>
+ </td>
+<td>
+ <p>
+ No
+ </p>
+ </td>
+<td>
+ <p>
+ Good high order method with error estimation, to be used in controlled_error_stepper.
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ Adams Bashforth
+ </p>
+ </td>
+<td>
+ <p>
+ <code class="computeroutput"><span class="identifier">adams_bashforth</span></code>
+ </p>
+ </td>
+<td>
+ <p>
+ <a class="link" href="../concepts/stepper.html" title="Stepper">Stepper</a>
+ </p>
+ </td>
+<td>
+ <p>
+ <a class="link" href="../concepts/system.html" title="System">System</a>
+ </p>
+ </td>
+<td>
+ <p>
+ configurable
+ </p>
+ </td>
+<td>
+ <p>
+ No
+ </p>
+ </td>
+<td>
+ <p>
+ No
+ </p>
+ </td>
+<td>
+ <p>
+ Yes
+ </p>
+ </td>
+<td>
+ <p>
+ Multistep method
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ Adams Moulton
+ </p>
+ </td>
+<td>
+ <p>
+ <code class="computeroutput"><span class="identifier">adams_moulton</span></code>
+ </p>
+ </td>
+<td>
+ <p>
+ <a class="link" href="../concepts/stepper.html" title="Stepper">Stepper</a>
+ </p>
+ </td>
+<td>
+ <p>
+ <a class="link" href="../concepts/system.html" title="System">System</a>
+ </p>
+ </td>
+<td>
+ <p>
+ configurable
+ </p>
+ </td>
+<td>
+ <p>
+ No
+ </p>
+ </td>
+<td>
+ <p>
+ No
+ </p>
+ </td>
+<td>
+ <p>
+ Yes
+ </p>
+ </td>
+<td>
+ <p>
+ Multistep method
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ Adams Bashforth Moulton
+ </p>
+ </td>
+<td>
+ <p>
+ <code class="computeroutput"><span class="identifier">adams_bashforth_moulton</span></code>
+ </p>
+ </td>
+<td>
+ <p>
+ <a class="link" href="../concepts/stepper.html" title="Stepper">Stepper</a>
+ </p>
+ </td>
+<td>
+ <p>
+ <a class="link" href="../concepts/system.html" title="System">System</a>
+ </p>
+ </td>
+<td>
+ <p>
+ configurable
+ </p>
+ </td>
+<td>
+ <p>
+ No
+ </p>
+ </td>
+<td>
+ <p>
+ No
+ </p>
+ </td>
+<td>
+ <p>
+ Yes
+ </p>
+ </td>
+<td>
+ <p>
+ Combined multistep method
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ Controlled Runge-Kutta
+ </p>
+ </td>
+<td>
+ <p>
+ <code class="computeroutput"><span class="identifier">controlled_runge_kutta</span></code>
+ </p>
+ </td>
+<td>
+ <p>
+ <a class="link" href="../concepts/controlled_stepper.html" title="Controlled Stepper">Controlled
+ Stepper</a>
+ </p>
+ </td>
+<td>
+ <p>
+ <a class="link" href="../concepts/system.html" title="System">System</a>
+ </p>
+ </td>
+<td>
+ <p>
+ depends
+ </p>
+ </td>
+<td>
+ <p>
+ Yes
+ </p>
+ </td>
+<td>
+ <p>
+ No
+ </p>
+ </td>
+<td>
+ <p>
+ depends
+ </p>
+ </td>
+<td>
+ <p>
+ Error control for <a class="link" href="../concepts/error_stepper.html" title="Error Stepper">Error
+ Stepper</a>. Requires an <a class="link" href="../concepts/error_stepper.html" title="Error Stepper">Error
+ Stepper</a> from above. Order depends on the given ErrorStepper
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ Dense Output Runge-Kutta
+ </p>
+ </td>
+<td>
+ <p>
+ <code class="computeroutput"><span class="identifier">dense_output_runge_kutta</span></code>
+ </p>
+ </td>
+<td>
+ <p>
+ <a class="link" href="../concepts/dense_output_stepper.html" title="Dense Output Stepper">Dense
+ Output Stepper</a>
+ </p>
+ </td>
+<td>
+ <p>
+ <a class="link" href="../concepts/system.html" title="System">System</a>
+ </p>
+ </td>
+<td>
+ <p>
+ depends
+ </p>
+ </td>
+<td>
+ <p>
+ No
+ </p>
+ </td>
+<td>
+ <p>
+ Yes
+ </p>
+ </td>
+<td>
+ <p>
+ Yes
+ </p>
+ </td>
+<td>
+ <p>
+ Dense output for <a class="link" href="../concepts/stepper.html" title="Stepper">Stepper</a>
+ and <a class="link" href="../concepts/error_stepper.html" title="Error Stepper">Error
+ Stepper</a> from above if they provide dense output functionality
+ (like <code class="computeroutput"><span class="identifier">euler</span></code> and
+ <code class="computeroutput"><span class="identifier">runge_kutta_dopri5</span></code>).
+ Order depends on the given stepper.
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ Bulirsch-Stoer
+ </p>
+ </td>
+<td>
+ <p>
+ <code class="computeroutput"><span class="identifier">bulirsch_stoer</span></code>
+ </p>
+ </td>
+<td>
+ <p>
+ <a class="link" href="../concepts/controlled_stepper.html" title="Controlled Stepper">Controlled
+ Stepper</a>
+ </p>
+ </td>
+<td>
+ <p>
+ <a class="link" href="../concepts/system.html" title="System">System</a>
+ </p>
+ </td>
+<td>
+ <p>
+ variable
+ </p>
+ </td>
+<td>
+ <p>
+ Yes
+ </p>
+ </td>
+<td>
+ <p>
+ No
+ </p>
+ </td>
+<td>
+ <p>
+ No
+ </p>
+ </td>
+<td>
+ <p>
+ Stepper with step size and order control. Very good if high precision
+ is required.
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ Bulirsch-Stoer Dense Output
+ </p>
+ </td>
+<td>
+ <p>
+ <code class="computeroutput"><span class="identifier">bulirsch_stoer_dense_out</span></code>
+ </p>
+ </td>
+<td>
+ <p>
+ <a class="link" href="../concepts/dense_output_stepper.html" title="Dense Output Stepper">Dense
+ Output Stepper</a>
+ </p>
+ </td>
+<td>
+ <p>
+ <a class="link" href="../concepts/system.html" title="System">System</a>
+ </p>
+ </td>
+<td>
+ <p>
+ variable
+ </p>
+ </td>
+<td>
+ <p>
+ Yes
+ </p>
+ </td>
+<td>
+ <p>
+ Yes
+ </p>
+ </td>
+<td>
+ <p>
+ No
+ </p>
+ </td>
+<td>
+ <p>
+ Stepper with step size and order control as well as dense output.
+ Very good if high precision and dense output is required.
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ Implicit Euler
+ </p>
+ </td>
+<td>
+ <p>
+ <code class="computeroutput"><span class="identifier">implicit_euler</span></code>
+ </p>
+ </td>
+<td>
+ <p>
+ <a class="link" href="../concepts/stepper.html" title="Stepper">Stepper</a>
+ </p>
+ </td>
+<td>
+ <p>
+ <a class="link" href="../concepts/implicit_system.html" title="Implicit System">Implicit
+ System</a>
+ </p>
+ </td>
+<td>
+ <p>
+ 1
+ </p>
+ </td>
+<td>
+ <p>
+ No
+ </p>
+ </td>
+<td>
+ <p>
+ No
+ </p>
+ </td>
+<td>
+ <p>
+ No
+ </p>
+ </td>
+<td>
+ <p>
+ Basic implicit routine. Requires the Jacobian. Works only with
+ Boost.uBLAS
+ vectors as state types.
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ Rosenbrock 4
+ </p>
+ </td>
+<td>
+ <p>
+ <code class="computeroutput"><span class="identifier">rosenbrock4</span></code>
+ </p>
+ </td>
+<td>
+ <p>
+ <a class="link" href="../concepts/error_stepper.html" title="Error Stepper">Error
+ Stepper</a>
+ </p>
+ </td>
+<td>
+ <p>
+ <a class="link" href="../concepts/implicit_system.html" title="Implicit System">Implicit
+ System</a>
+ </p>
+ </td>
+<td>
+ <p>
+ 4
+ </p>
+ </td>
+<td>
+ <p>
+ Yes
+ </p>
+ </td>
+<td>
+ <p>
+ Yes
+ </p>
+ </td>
+<td>
+ <p>
+ No
+ </p>
+ </td>
+<td>
+ <p>
+ Good for stiff systems. Works only with Boost.uBLAS
+ vectors as state types.
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ Controlled Rosenbrock 4
+ </p>
+ </td>
+<td>
+ <p>
+ <code class="computeroutput"><span class="identifier">rosenbrock4_controller</span></code>
+ </p>
+ </td>
+<td>
+ <p>
+ <a class="link" href="../concepts/controlled_stepper.html" title="Controlled Stepper">Controlled
+ Stepper</a>
+ </p>
+ </td>
+<td>
+ <p>
+ <a class="link" href="../concepts/implicit_system.html" title="Implicit System">Implicit
+ System</a>
+ </p>
+ </td>
+<td>
+ <p>
+ 4
+ </p>
+ </td>
+<td>
+ <p>
+ Yes
+ </p>
+ </td>
+<td>
+ <p>
+ Yes
+ </p>
+ </td>
+<td>
+ <p>
+ No
+ </p>
+ </td>
+<td>
+ <p>
+ Rosenbrock 4 with error control. Works only with Boost.uBLAS
+ vectors as state types.
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ Dense Output Rosenbrock 4
+ </p>
+ </td>
+<td>
+ <p>
+ <code class="computeroutput"><span class="identifier">rosenbrock4_dense_output</span></code>
+ </p>
+ </td>
+<td>
+ <p>
+ <a class="link" href="../concepts/dense_output_stepper.html" title="Dense Output Stepper">Dense
+ Output Stepper</a>
+ </p>
+ </td>
+<td>
+ <p>
+ <a class="link" href="../concepts/implicit_system.html" title="Implicit System">Implicit
+ System</a>
+ </p>
+ </td>
+<td>
+ <p>
+ 4
+ </p>
+ </td>
+<td>
+ <p>
+ Yes
+ </p>
+ </td>
+<td>
+ <p>
+ Yes
+ </p>
+ </td>
+<td>
+ <p>
+ No
+ </p>
+ </td>
+<td>
+ <p>
+ Controlled Rosenbrock 4 with dense output. Works only with Boost.uBLAS
+ vectors as state types.
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ Symplectic Euler
+ </p>
+ </td>
+<td>
+ <p>
+ <code class="computeroutput"><span class="identifier">symplectic_euler</span></code>
+ </p>
+ </td>
+<td>
+ <p>
+ <a class="link" href="../concepts/stepper.html" title="Stepper">Stepper</a>
+ </p>
+ </td>
+<td>
+ <p>
+ <a class="link" href="../concepts/symplectic_system.html" title="Symplectic System">Symplectic
+ System</a> <a class="link" href="../concepts/simple_symplectic_system.html" title="Simple Symplectic System">Simple
+ Symplectic System</a>
+ </p>
+ </td>
+<td>
+ <p>
+ 1
+ </p>
+ </td>
+<td>
+ <p>
+ No
+ </p>
+ </td>
+<td>
+ <p>
+ No
+ </p>
+ </td>
+<td>
+ <p>
+ No
+ </p>
+ </td>
+<td>
+ <p>
+ Basic symplectic solver for separable Hamiltonian system
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ Symplectic RKN McLachlan
+ </p>
+ </td>
+<td>
+ <p>
+ <code class="computeroutput"><span class="identifier">symplectic_rkn_sb3a_mclachlan</span></code>
+ </p>
+ </td>
+<td>
+ <p>
+ <a class="link" href="../concepts/stepper.html" title="Stepper">Stepper</a>
+ </p>
+ </td>
+<td>
+ <p>
+ <a class="link" href="../concepts/symplectic_system.html" title="Symplectic System">Symplectic
+ System</a> <a class="link" href="../concepts/simple_symplectic_system.html" title="Simple Symplectic System">Simple
+ Symplectic System</a>
+ </p>
+ </td>
+<td>
+ <p>
+ 4
+ </p>
+ </td>
+<td>
+ <p>
+ No
+ </p>
+ </td>
+<td>
+ <p>
+ No
+ </p>
+ </td>
+<td>
+ <p>
+ No
+ </p>
+ </td>
+<td>
+ <p>
+ Symplectic solver for separable Hamiltonian system with 6 stages
+ and order 4.
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ Symplectic RKN McLachlan
+ </p>
+ </td>
+<td>
+ <p>
+ <code class="computeroutput"><span class="identifier">symplectic_rkn_sb3a_m4_mclachlan</span></code>
+ </p>
+ </td>
+<td>
+ <p>
+ <a class="link" href="../concepts/stepper.html" title="Stepper">Stepper</a>
+ </p>
+ </td>
+<td>
+ <p>
+ <a class="link" href="../concepts/symplectic_system.html" title="Symplectic System">Symplectic
+ System</a> <a class="link" href="../concepts/simple_symplectic_system.html" title="Simple Symplectic System">Simple
+ Symplectic System</a>
+ </p>
+ </td>
+<td>
+ <p>
+ 4
+ </p>
+ </td>
+<td>
+ <p>
+ No
+ </p>
+ </td>
+<td>
+ <p>
+ No
+ </p>
+ </td>
+<td>
+ <p>
+ No
+ </p>
+ </td>
+<td>
+ <p>
+ Symplectic solver with 5 stages and order 4, can be used with arbitrary
+ precision types.
+ </p>
+ </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break">
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2009-2012 Karsten
+ Ahnert and Mario Mulansky<p>
+ Distributed under the Boost Software License, Version 1.0. (See accompanying
+ file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+ </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../getting_started.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../getting_started.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="usage__compilation__headers.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
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+</html>
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