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<title>Basic stepper</title>
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<div class="titlepage"><div><div><h3 class="title">
<a name="boost_sandbox_numeric_odeint.old_concepts.basic_stepper"></a><a class="link" href="basic_stepper.html" title="Basic stepper">Basic
stepper</a>
</h3></div></div></div>
<p>
Basic steppers execute one timestep of a specific order with a given stepsize.
They usually allocate internal memory to store intermediate function call
results. If state types with variable size are used (e.g. <code class="computeroutput"><span class="identifier">vector</span></code>),
it has to be assured that the stepper gets informed about any change of the
state size by calling its <code class="computeroutput"><span class="identifier">adjust_size</span></code>
method.
</p>
<p>
<span class="bold"><strong>Associated Types</strong></span>
</p>
<div class="informaltable"><table class="table">
<colgroup>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
</th>
<th>
</th>
<th>
<p>
Description
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
Time
</p>
</td>
<td>
<p>
Stepper::time_type
</p>
</td>
<td>
<p>
Type of the time variable, e.g. <code class="computeroutput"><span class="keyword">double</span></code>
</p>
</td>
</tr>
<tr>
<td>
<p>
Container
</p>
</td>
<td>
<p>
Stepper::container_type
</p>
</td>
<td>
<p>
Type of the system state, e.g. <code class="computeroutput"><span class="identifier">vector</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span></code>
</p>
</td>
</tr>
<tr>
<td>
<p>
Value
</p>
</td>
<td>
<p>
Stepper::value_type
</p>
</td>
<td>
<p>
Value type of the state, e.g. <code class="computeroutput"><span class="keyword">double</span></code>
</p>
</td>
</tr>
<tr>
<td>
<p>
Order Type
</p>
</td>
<td>
<p>
Stepper::order_type
</p>
</td>
<td>
<p>
Type of the order parameter, usually <code class="computeroutput"><span class="keyword">unsigned</span>
<span class="keyword">short</span></code>
</p>
</td>
</tr>
</tbody>
</table></div>
<p>
<span class="bold"><strong>Methods</strong></span>
</p>
<div class="itemizedlist"><ul type="disc">
<li>
<code class="computeroutput"><span class="identifier">Stepper</span><span class="special">()</span></code>
Constructor.
</li>
<li>
<code class="computeroutput"><span class="identifier">Stepper</span><span class="special">(</span>
<span class="identifier">container_type</span> <span class="special">&</span><span class="identifier">x</span> <span class="special">)</span></code>
Constructor that allocates internal memory to store intermediate results
of the same size as <code class="computeroutput"><span class="identifier">x</span></code>.
</li>
<li>
<code class="computeroutput"><span class="keyword">void</span> <span class="identifier">do_step</span><span class="special">(</span> <span class="identifier">DynamicalSystem</span>
<span class="special">&</span><span class="identifier">system</span>
<span class="special">,</span> <span class="identifier">container_type</span>
<span class="special">&</span><span class="identifier">x</span>
<span class="special">,</span> <span class="identifier">time_type</span>
<span class="identifier">t</span> <span class="special">,</span>
<span class="identifier">time_type</span> <span class="identifier">dt</span>
<span class="special">)</span></code>
</li>
</ul></div>
<p>
Executes one timestep with the given parameters:
</p>
<div class="informaltable"><table class="table">
<colgroup>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
<p>
Parameter
</p>
</th>
<th>
<p>
Type
</p>
</th>
<th>
<p>
Description
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
system
</p>
</td>
<td>
<p>
DynamicalSystem
</p>
</td>
<td>
<p>
Function (callable object) that computes the rhs of the ode
</p>
</td>
</tr>
<tr>
<td>
<p>
x
</p>
</td>
<td>
<p>
container_type
</p>
</td>
<td>
<p>
The current state of the system <span class="bold"><strong>x(t)</strong></span>
</p>
</td>
</tr>
<tr>
<td>
<p>
t
</p>
</td>
<td>
<p>
time_type
</p>
</td>
<td>
<p>
The current time <span class="bold"><strong>t</strong></span>
</p>
</td>
</tr>
<tr>
<td>
<p>
dt
</p>
</td>
<td>
<p>
time_type
</p>
</td>
<td>
<p>
Length of the timestep to be executed
</p>
</td>
</tr>
</tbody>
</table></div>
<p>
The result of this method is the (approximate) state of the system <span class="bold"><strong>x(t+dt)</strong></span> and is stored in the variable <code class="computeroutput"><span class="identifier">x</span></code> (in-place). Note, that the time <code class="computeroutput"><span class="identifier">t</span></code> is not automatically increased by this
method.
</p>
<div class="itemizedlist"><ul type="disc"><li>
<code class="computeroutput"><span class="keyword">void</span> <span class="identifier">do_step</span><span class="special">(</span> <span class="identifier">DynamicalSystem</span>
<span class="special">&</span><span class="identifier">system</span>
<span class="special">,</span> <span class="identifier">container_type</span>
<span class="special">&</span><span class="identifier">x</span>
<span class="special">,</span> <span class="keyword">const</span>
<span class="identifier">container_type</span> <span class="special">&</span><span class="identifier">dxdt</span> <span class="special">,</span> <span class="identifier">time_type</span> <span class="identifier">t</span>
<span class="special">,</span> <span class="identifier">time_type</span>
<span class="identifier">dt</span> <span class="special">)</span></code>
</li></ul></div>
<p>
The same as above but with the additional parameter <code class="computeroutput"><span class="identifier">dxdt</span></code>
that represents the derivative <span class="bold"><strong>x'(t) = f(x,t)</strong></span>
at the time <span class="bold"><strong>t</strong></span>.
</p>
<div class="itemizedlist"><ul type="disc">
<li>
<code class="computeroutput"><span class="keyword">void</span> <span class="identifier">adjust_size</span><span class="special">(</span> <span class="keyword">const</span> <span class="identifier">container_type</span> <span class="special">&</span><span class="identifier">x</span> <span class="special">)</span></code>
Adjusts the internal memory to store intermediate results of the same
size as <code class="computeroutput"><span class="identifier">x</span></code>. This function
<span class="emphasis"><em>must</em></span> be called whenever the system size changes
during the integration.
</li>
<li>
<code class="computeroutput"><span class="identifier">order_type</span> <span class="identifier">order_step</span><span class="special">()</span></code> Returns the order of the algorithm.
If <span class="bold"><strong>n</strong></span> is the order of a method, then
the result of one iteration with the timestep <span class="bold"><strong>dt</strong></span>
is accurate up to <span class="bold"><strong>dt^n</strong></span>. That means the
error made by the time discretization is of order <span class="bold"><strong>dt^(n+1)</strong></span>.
</li>
</ul></div>
<p>
<span class="bold"><strong>Stepper that model this concept</strong></span>
</p>
<div class="itemizedlist"><ul type="disc">
<li>
<code class="computeroutput"><span class="identifier">stepper_euler</span></code>
</li>
<li>
<code class="computeroutput"><span class="identifier">stepper_rk4</span></code>
</li>
<li>
<code class="computeroutput"><span class="identifier">stepper_rk78_fehlberg</span></code>
</li>
</ul></div>
</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 -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>
</tr></table>
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