| <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 V1.78.1"> |
| <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"><a href="../../../../../../../index.html">Home</a></td> |
| <td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td> |
| <td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> |
| <td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> |
| <td align="center"><a href="../../../../../../../more/index.htm">More</a></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" style="list-style-type: disc; "> |
| <li class="listitem"> |
| <a href="http://www.boost.org/doc/libs/release/libs/numeric/ublas/index.html" target="_top">Boost.uBLAS</a> |
| </li> |
| <li class="listitem"> |
| <a href="http://code.google.com/p/thrust/" target="_top">Thrust</a>, 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"> |
| <a href="http://www.boost.org/doc/libs/release/libs/range/" target="_top">Boost.Range</a> |
| </li> |
| <li class="listitem"> |
| <a href="http://www.boost.org/doc/libs/release/libs/fusion/" target="_top">Boost.Fusion</a> |
| (the state type can be a fusion vector) |
| </li> |
| <li class="listitem"> |
| <a href="http://www.boost.org/doc/libs/release/libs/units/" target="_top">Boost.Units</a> |
| </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"> |
| <a href="https://github.com/ddemidov/vexcl" target="_top">VexCL</a> for OpenCL |
| </li> |
| <li class="listitem"> |
| <a href="http://www.boost.org/doc/libs/release/libs/graph/" target="_top">Boost.Graph</a> |
| (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 |
| <a href="http://www.boost.org/doc/libs/release/libs/numeric/ublas/index.html" target="_top">Boost.uBLAS</a> |
| 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 <a href="http://www.boost.org/doc/libs/release/libs/numeric/ublas/index.html" target="_top">Boost.uBLAS</a> |
| 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 <a href="http://www.boost.org/doc/libs/release/libs/numeric/ublas/index.html" target="_top">Boost.uBLAS</a> |
| 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 <a href="http://www.boost.org/doc/libs/release/libs/numeric/ublas/index.html" target="_top">Boost.uBLAS</a> |
| 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> |
| <tr> |
| <td> |
| <p> |
| Velocity Verlet |
| </p> |
| </td> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">velocity_verlet</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/second_order_system.html" title="Second Order System">Second |
| Order System</a> |
| </p> |
| </td> |
| <td> |
| <p> |
| 1 |
| </p> |
| </td> |
| <td> |
| <p> |
| No |
| </p> |
| </td> |
| <td> |
| <p> |
| No |
| </p> |
| </td> |
| <td> |
| <p> |
| Yes |
| </p> |
| </td> |
| <td> |
| <p> |
| Velocity verlet method suitable for molecular dynamics simulation. |
| </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 <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) |
| </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> |
| </div> |
| </body> |
| </html> |
