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<title>Controlled Stepper</title>
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<link rel="home" href="../../index.html" title="Chapter 1. Boost.Numeric.Odeint">
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<link rel="up" href="../concepts.html" title="Concepts">
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<link rel="prev" href="error_stepper.html" title="Error Stepper">
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<div class="section">
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<div class="titlepage"><div><div><h3 class="title">
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<a name="boost_numeric_odeint.concepts.controlled_stepper"></a><a class="link" href="controlled_stepper.html" title="Controlled Stepper">Controlled
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Stepper</a>
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</h3></div></div></div>
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<p>
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This concept specifies the interface a controlled stepper has to fulfill
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to be used within <a class="link" href="../odeint_in_detail/integrate_functions.html" title="Integrate functions">integrate
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functions</a>.
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</p>
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<h5>
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<a name="boost_numeric_odeint.concepts.controlled_stepper.h0"></a>
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<span><a name="boost_numeric_odeint.concepts.controlled_stepper.description"></a></span><a class="link" href="controlled_stepper.html#boost_numeric_odeint.concepts.controlled_stepper.description">Description</a>
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</h5>
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<p>
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A controlled stepper following this Controlled Stepper concept provides the
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possibility to perform one step of the solution <span class="emphasis"><em>x(t)</em></span>
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of an ODE with step-size <span class="emphasis"><em>dt</em></span> to obtain <span class="emphasis"><em>x(t+dt)</em></span>
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with a given step-size <span class="emphasis"><em>dt</em></span>. Depending on an error estimate
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of the solution the step might be rejected and a smaller step-size is suggested.
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</p>
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<h5>
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<a name="boost_numeric_odeint.concepts.controlled_stepper.h1"></a>
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<span><a name="boost_numeric_odeint.concepts.controlled_stepper.associated_types"></a></span><a class="link" href="controlled_stepper.html#boost_numeric_odeint.concepts.controlled_stepper.associated_types">Associated
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types</a>
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</h5>
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<div class="itemizedlist"><ul class="itemizedlist" type="disc">
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<li class="listitem">
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<p><span class="bold"><strong>state_type</strong></span></p>
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<p><code class="computeroutput"><span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">state_type</span></code></p>
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<p>The
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type characterizing the state of the ODE, hence <span class="emphasis"><em>x</em></span>.</p>
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</li>
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<li class="listitem">
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<p><span class="bold"><strong>deriv_type</strong></span></p>
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<p><code class="computeroutput"><span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">deriv_type</span></code></p>
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<p>The
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type characterizing the derivative of the ODE, hence <span class="emphasis"><em>d x/dt</em></span>.</p>
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</li>
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<li class="listitem">
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<p><span class="bold"><strong>time_type</strong></span></p>
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<p><code class="computeroutput"><span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">time_type</span></code></p>
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<p>The
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type characterizing the dependent variable of the ODE, hence the time
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<span class="emphasis"><em>t</em></span>.</p>
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</li>
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<li class="listitem">
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<p><span class="bold"><strong>value_type</strong></span></p>
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<p><code class="computeroutput"><span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">value_type</span></code></p>
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<p>The
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numerical data type which is used within the stepper, something like
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<code class="computeroutput"><span class="keyword">float</span></code>, <code class="computeroutput"><span class="keyword">double</span></code>,
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<code class="computeroutput"><span class="identifier">complex</span><span class="special">&</span><span class="identifier">lt</span><span class="special">;</span> <span class="keyword">double</span> <span class="special">&</span><span class="identifier">gt</span><span class="special">;</span></code>.</p>
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</li>
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</ul></div>
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<h5>
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<a name="boost_numeric_odeint.concepts.controlled_stepper.h2"></a>
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<span><a name="boost_numeric_odeint.concepts.controlled_stepper.notation"></a></span><a class="link" href="controlled_stepper.html#boost_numeric_odeint.concepts.controlled_stepper.notation">Notation</a>
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</h5>
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<div class="variablelist">
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<p class="title"><b></b></p>
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<dl>
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<dt><span class="term"><code class="computeroutput"><span class="identifier">ControlledStepper</span></code></span></dt>
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<dd><p>
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A type that is a model of Controlled Stepper
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</p></dd>
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<dt><span class="term"><code class="computeroutput"><span class="identifier">State</span></code></span></dt>
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<dd><p>
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A type representing the state <span class="emphasis"><em>x</em></span> of the ODE
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</p></dd>
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<dt><span class="term"><code class="computeroutput"><span class="identifier">Time</span></code></span></dt>
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<dd><p>
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A type representing the time <span class="emphasis"><em>t</em></span> of the ODE
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</p></dd>
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<dt><span class="term"><code class="computeroutput"><span class="identifier">stepper</span></code></span></dt>
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<dd><p>
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An object of type <code class="computeroutput"><span class="identifier">ControlledStepper</span></code>
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</p></dd>
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<dt><span class="term"><code class="computeroutput"><span class="identifier">x</span></code></span></dt>
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<dd><p>
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Object of type <code class="computeroutput"><span class="identifier">State</span></code>
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</p></dd>
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<dt><span class="term"><code class="computeroutput"><span class="identifier">t</span></code>, <code class="computeroutput"><span class="identifier">dt</span></code></span></dt>
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<dd><p>
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Objects of type <code class="computeroutput"><span class="identifier">Time</span></code>
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</p></dd>
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<dt><span class="term"><code class="computeroutput"><span class="identifier">sys</span></code></span></dt>
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<dd><p>
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An object defining the ODE, should be a model of <a class="link" href="system.html" title="System">System</a>,
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<a class="link" href="symplectic_system.html" title="Symplectic System">Symplectic
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System</a>, <a class="link" href="simple_symplectic_system.html" title="Simple Symplectic System">Simple
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Symplectic System</a> or <a class="link" href="implicit_system.html" title="Implicit System">Implicit
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System</a>.
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</p></dd>
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</dl>
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</div>
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<h5>
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<a name="boost_numeric_odeint.concepts.controlled_stepper.h3"></a>
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<span><a name="boost_numeric_odeint.concepts.controlled_stepper.valid_expressions"></a></span><a class="link" href="controlled_stepper.html#boost_numeric_odeint.concepts.controlled_stepper.valid_expressions">Valid
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Expressions</a>
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</h5>
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<div class="informaltable"><table class="table">
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<colgroup>
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<col>
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<col>
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<col>
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<col>
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</colgroup>
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<thead><tr>
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<th>
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<p>
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Name
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</p>
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</th>
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<th>
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<p>
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Expression
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</p>
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</th>
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<th>
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<p>
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Type
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</p>
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</th>
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<th>
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<p>
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Semantics
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</p>
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</th>
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</tr></thead>
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<tbody><tr>
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<td>
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<p>
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Do step
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</p>
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</td>
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<td>
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<p>
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</p>
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<pre xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" class="table-programlisting"><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></pre>
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<p>
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</p>
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</td>
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<td>
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<p>
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<code class="computeroutput"><span class="identifier">controlled_step_result</span></code>
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</p>
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</td>
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<td>
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<p>
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Tries one step of step size <code class="computeroutput"><span class="identifier">dt</span></code>.
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If the step was successful, <code class="computeroutput"><span class="identifier">success</span></code>
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is returned, the resulting state is written to <code class="computeroutput"><span class="identifier">x</span></code>,
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the new time is stored in <code class="computeroutput"><span class="identifier">t</span></code>
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and <code class="computeroutput"><span class="identifier">dt</span></code> now contains
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a new (possibly larger) step-size for the next step. If the error
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was too big, <code class="computeroutput"><span class="identifier">rejected</span></code>
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is returned and the results are neglected - <code class="computeroutput"><span class="identifier">x</span></code>
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and <code class="computeroutput"><span class="identifier">t</span></code> are unchanged
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and <code class="computeroutput"><span class="identifier">dt</span></code> now contains
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a reduced step-size to be used for the next try.
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</p>
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</td>
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</tr></tbody>
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</table></div>
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<h5>
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<a name="boost_numeric_odeint.concepts.controlled_stepper.h4"></a>
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<span><a name="boost_numeric_odeint.concepts.controlled_stepper.models"></a></span><a class="link" href="controlled_stepper.html#boost_numeric_odeint.concepts.controlled_stepper.models">Models</a>
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</h5>
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<div class="itemizedlist"><ul class="itemizedlist" type="disc">
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<li class="listitem">
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<code class="computeroutput"><span class="identifier">controlled_error_stepper</span><span class="special"><</span> <span class="identifier">runge_kutta_cash_karp54</span>
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<span class="special">></span></code>
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</li>
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<li class="listitem">
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<code class="computeroutput"><span class="identifier">controlled_error_stepper_fsal</span><span class="special"><</span> <span class="identifier">runge_kutta_dopri5</span>
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<span class="special">></span></code>
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</li>
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<li class="listitem">
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<code class="computeroutput"><span class="identifier">controlled_error_stepper</span><span class="special"><</span> <span class="identifier">runge_kutta_fehlberg78</span>
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<span class="special">></span></code>
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</li>
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<li class="listitem">
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<code class="computeroutput"><span class="identifier">rosenbrock4_controller</span></code>
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</li>
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<li class="listitem">
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<code class="computeroutput"><span class="identifier">bulirsch_stoer</span></code>
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</li>
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</ul></div>
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</div>
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<td align="left"></td>
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<td align="right"><div class="copyright-footer">Copyright © 2009-2011 Karsten Ahnert
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and Mario Mulansky<p>
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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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>)
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</p>
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</div></td>
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</tr></table>
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<hr>
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