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odeint v2 - Solving ordinary differential equations in C++

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19 Oct 2011CPOL19 min read 128.7K   2.8K   34  
odeint v2 - Solving ordinary differential equations in C++
 
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<title>Controlled Stepper</title>
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<div class="titlepage"><div><div><h3 class="title">
<a name="boost_sandbox_numeric_odeint.concepts.controlled_stepper"></a><a class="link" href="controlled_stepper.html" title="Controlled Stepper">Controlled
      Stepper</a>
</h3></div></div></div>
<p>
        This concept specifies the interface a controlled stepper has to fulfill
        to be used within <a class="link" href="../odeint_in_detail/integrate_functions.html" title="Integrate functions">integrate
        functions</a>.
      </p>
<a name="boost_sandbox_numeric_odeint.concepts.controlled_stepper.description"></a><h5>
<a name="id614015"></a>
        <a class="link" href="controlled_stepper.html#boost_sandbox_numeric_odeint.concepts.controlled_stepper.description">Description</a>
      </h5>
<p>
        A controlled stepper following this Controlled Stepper concept provides the
        possibilty to perform one step of the solution <span class="emphasis"><em>x(t)</em></span>
        of an ODE with step-size <span class="emphasis"><em>dt</em></span> to obtain <span class="emphasis"><em>x(t+dt)</em></span>
        with a given step-size <span class="emphasis"><em>dt</em></span>. Depending on an error estimate
        of the solution the step might be rejected and a smaller step-size is suggested.
      </p>
<a name="boost_sandbox_numeric_odeint.concepts.controlled_stepper.notation"></a><h5>
<a name="id614055"></a>
        <a class="link" href="controlled_stepper.html#boost_sandbox_numeric_odeint.concepts.controlled_stepper.notation">Notation</a>
      </h5>
<div class="variablelist">
<p class="title"><b></b></p>
<dl>
<dt><span class="term"><code class="computeroutput"><span class="identifier">ControlledStepper</span></code></span></dt>
<dd><p>
              A type that is a model of Controlled Stepper
            </p></dd>
<dt><span class="term"><code class="computeroutput"><span class="identifier">State</span></code></span></dt>
<dd><p>
              A type representing the state <span class="emphasis"><em>x</em></span> of the ODE
            </p></dd>
<dt><span class="term"><code class="computeroutput"><span class="identifier">Time</span></code></span></dt>
<dd><p>
              A type representing the time <span class="emphasis"><em>t</em></span> of the ODE
            </p></dd>
<dt><span class="term"><code class="computeroutput"><span class="identifier">stepper</span></code></span></dt>
<dd><p>
              An object of type <code class="computeroutput"><span class="identifier">ControlledStepper</span></code>
            </p></dd>
<dt><span class="term"><code class="computeroutput"><span class="identifier">x</span></code></span></dt>
<dd><p>
              Object of type <code class="computeroutput"><span class="identifier">State</span></code>
            </p></dd>
<dt><span class="term"><code class="computeroutput"><span class="identifier">t</span></code>, <code class="computeroutput"><span class="identifier">dt</span></code></span></dt>
<dd><p>
              Objects of type <code class="computeroutput"><span class="identifier">Time</span></code>
            </p></dd>
<dt><span class="term"><code class="computeroutput"><span class="identifier">sys</span></code></span></dt>
<dd><p>
              An object defining the ODE, should be a model of <a class="link" href="system.html" title="System">System</a>,
              <a class="link" href="symplectic_system.html" title="Symplectic_System">Symplectic_System</a>,
              <a class="link" href="simple_symplectic_system.html" title="Simple_Symplectic_System">Simple_Symplectic_System</a>
              or <a class="link" href="implicit_system.html" title="Implicit_System">Implicit_System</a>.
            </p></dd>
</dl>
</div>
<a name="boost_sandbox_numeric_odeint.concepts.controlled_stepper.valid_expressions"></a><h5>
<a name="id614308"></a>
        <a class="link" href="controlled_stepper.html#boost_sandbox_numeric_odeint.concepts.controlled_stepper.valid_expressions">Valid
        Expressions</a>
      </h5>
<div class="informaltable"><table class="table">
<colgroup>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
                <p>
                  Name
                </p>
              </th>
<th>
                <p>
                  Expression
                </p>
              </th>
<th>
                <p>
                  Type
                </p>
              </th>
<th>
                <p>
                  Semantics
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Do step
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput"><span class="identifier">stepper</span><span class="special">.</span><span class="identifier">try_step</span><span class="special">(</span>
                  <span class="identifier">sys</span> <span class="special">,</span>
                  <span class="identifier">x</span> <span class="special">,</span>
                  <span class="identifier">t</span> <span class="special">,</span>
                  <span class="identifier">dt</span> <span class="special">)</span></code>
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput"><span class="identifier">controlled_step_result</span></code>
                </p>
              </td>
<td>
                <p>
                  Tries one step of step size <code class="computeroutput"><span class="identifier">dt</span></code>.
                  If the step was succesfull, <code class="computeroutput"><span class="identifier">success</span></code>
                  is returned, the resulting state is written to <code class="computeroutput"><span class="identifier">x</span></code>,
                  the new time is stored in <code class="computeroutput"><span class="identifier">t</span></code>
                  and <code class="computeroutput"><span class="identifier">dt</span></code> now contains
                  a new (possibly larger) step-size for the next step. If the error
                  was too big, <code class="computeroutput"><span class="identifier">rejected</span></code>
                  is returned and the results are neglected - <code class="computeroutput"><span class="identifier">x</span></code>
                  and <code class="computeroutput"><span class="identifier">t</span></code> are unchanged
                  and <code class="computeroutput"><span class="identifier">dt</span></code> now contains
                  a reduced step-size to be used for the next try.
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Do step with reference
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput"><span class="identifier">stepper</span><span class="special">.</span><span class="identifier">try_step</span><span class="special">(</span>
                  <span class="identifier">boost</span><span class="special">::</span><span class="identifier">ref</span><span class="special">(</span><span class="identifier">sys</span><span class="special">)</span>
                  <span class="special">,</span> <span class="identifier">x</span>
                  <span class="special">,</span> <span class="identifier">t</span>
                  <span class="special">,</span> <span class="identifier">dt</span>
                  <span class="special">)</span></code>
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput"><span class="keyword">void</span></code>
                </p>
              </td>
<td>
                <p>
                  Same as above with <code class="computeroutput"><span class="identifier">System</span></code>
                  as reference
                </p>
              </td>
</tr>
</tbody>
</table></div>
<a name="boost_sandbox_numeric_odeint.concepts.controlled_stepper.models"></a><h5>
<a name="id614721"></a>
        <a class="link" href="controlled_stepper.html#boost_sandbox_numeric_odeint.concepts.controlled_stepper.models">Models</a>
      </h5>
<div class="itemizedlist"><ul type="disc">
<li>
            controlled_error_stepper&lt; runge_kutta_cash_karp54 &gt;
          </li>
<li>
            controlled_error_stepper_fsal&lt; runge_kutta_dopri5 &gt;
          </li>
<li>
            controlled_error_stepper&lt; runge_kutta_fehlberg78 &gt;
          </li>
<li>
            rosenbrock4_controller
          </li>
<li>
            bulirsch_stoer
          </li>
</ul></div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<td align="right"><div class="copyright-footer">Copyright &#169; 2009 -2011 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>
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