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<div class="subTitle">org.apache.commons.math3.ode.nonstiff</div>
<h2 title="Class RungeKuttaIntegrator" class="title">Class RungeKuttaIntegrator</h2>
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<li><a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html" title="class in org.apache.commons.math3.ode">org.apache.commons.math3.ode.AbstractIntegrator</a></li>
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<li>org.apache.commons.math3.ode.nonstiff.RungeKuttaIntegrator</li>
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<dt>All Implemented Interfaces:</dt>
<dd><a href="../../../../../../org/apache/commons/math3/ode/FirstOrderIntegrator.html" title="interface in org.apache.commons.math3.ode">FirstOrderIntegrator</a>, <a href="../../../../../../org/apache/commons/math3/ode/ODEIntegrator.html" title="interface in org.apache.commons.math3.ode">ODEIntegrator</a></dd>
</dl>
<dl>
<dt>Direct Known Subclasses:</dt>
<dd><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/ClassicalRungeKuttaIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff">ClassicalRungeKuttaIntegrator</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/EulerIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff">EulerIntegrator</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/GillIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff">GillIntegrator</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/LutherIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff">LutherIntegrator</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/MidpointIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff">MidpointIntegrator</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/ThreeEighthesIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff">ThreeEighthesIntegrator</a></dd>
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<pre>public abstract class <span class="strong">RungeKuttaIntegrator</span>
extends <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html" title="class in org.apache.commons.math3.ode">AbstractIntegrator</a></pre>
<div class="block">This class implements the common part of all fixed step Runge-Kutta
integrators for Ordinary Differential Equations.
<p>These methods are explicit Runge-Kutta methods, their Butcher
arrays are as follows :
<pre>
0 |
c2 | a21
c3 | a31 a32
... | ...
cs | as1 as2 ... ass-1
|--------------------------
| b1 b2 ... bs-1 bs
</pre>
</p></div>
<dl><dt><span class="strong">Since:</span></dt>
<dd>1.2</dd>
<dt><span class="strong">Version:</span></dt>
<dd>$Id: RungeKuttaIntegrator.java 1588769 2014-04-20 14:29:42Z luc $</dd>
<dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/EulerIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff"><code>EulerIntegrator</code></a>,
<a href="../../../../../../org/apache/commons/math3/ode/nonstiff/ClassicalRungeKuttaIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff"><code>ClassicalRungeKuttaIntegrator</code></a>,
<a href="../../../../../../org/apache/commons/math3/ode/nonstiff/GillIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff"><code>GillIntegrator</code></a>,
<a href="../../../../../../org/apache/commons/math3/ode/nonstiff/MidpointIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff"><code>MidpointIntegrator</code></a></dd></dl>
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<h3>Fields inherited from class&nbsp;org.apache.commons.math3.ode.<a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html" title="class in org.apache.commons.math3.ode">AbstractIntegrator</a></h3>
<code><a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#isLastStep">isLastStep</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#resetOccurred">resetOccurred</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#stepHandlers">stepHandlers</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#stepSize">stepSize</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#stepStart">stepStart</a></code></li>
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<th class="colFirst" scope="col">Modifier</th>
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<td class="colFirst"><code>protected </code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/RungeKuttaIntegrator.html#RungeKuttaIntegrator(java.lang.String, double[], double[][], double[], org.apache.commons.math3.ode.nonstiff.RungeKuttaStepInterpolator, double)">RungeKuttaIntegrator</a></strong>(<a href="http://docs.oracle.com/javase/6/docs/api/java/lang/String.html?is-external=true" title="class or interface in java.lang">String</a>&nbsp;name,
double[]&nbsp;c,
double[][]&nbsp;a,
double[]&nbsp;b,
org.apache.commons.math3.ode.nonstiff.RungeKuttaStepInterpolator&nbsp;prototype,
double&nbsp;step)</code>
<div class="block">Simple constructor.</div>
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<td class="colFirst"><code>void</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/RungeKuttaIntegrator.html#integrate(org.apache.commons.math3.ode.ExpandableStatefulODE, double)">integrate</a></strong>(<a href="../../../../../../org/apache/commons/math3/ode/ExpandableStatefulODE.html" title="class in org.apache.commons.math3.ode">ExpandableStatefulODE</a>&nbsp;equations,
double&nbsp;t)</code>
<div class="block">Integrate a set of differential equations up to the given time.</div>
</td>
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<tr class="rowColor">
<td class="colFirst"><code>double[]</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/RungeKuttaIntegrator.html#singleStep(org.apache.commons.math3.ode.FirstOrderDifferentialEquations, double, double[], double)">singleStep</a></strong>(<a href="../../../../../../org/apache/commons/math3/ode/FirstOrderDifferentialEquations.html" title="interface in org.apache.commons.math3.ode">FirstOrderDifferentialEquations</a>&nbsp;equations,
double&nbsp;t0,
double[]&nbsp;y0,
double&nbsp;t)</code>
<div class="block">Fast computation of a single step of ODE integration.</div>
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<h3>Methods inherited from class&nbsp;org.apache.commons.math3.ode.<a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html" title="class in org.apache.commons.math3.ode">AbstractIntegrator</a></h3>
<code><a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#acceptStep(org.apache.commons.math3.ode.sampling.AbstractStepInterpolator, double[], double[], double)">acceptStep</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#addEventHandler(org.apache.commons.math3.ode.events.EventHandler, double, double, int)">addEventHandler</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#addEventHandler(org.apache.commons.math3.ode.events.EventHandler, double, double, int, org.apache.commons.math3.analysis.solvers.UnivariateSolver)">addEventHandler</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#addStepHandler(org.apache.commons.math3.ode.sampling.StepHandler)">addStepHandler</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#clearEventHandlers()">clearEventHandlers</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#clearStepHandlers()">clearStepHandlers</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#computeDerivatives(double, double[], double[])">computeDerivatives</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#getCurrentSignedStepsize()">getCurrentSignedStepsize</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#getCurrentStepStart()">getCurrentStepStart</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#getEvaluations()">getEvaluations</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#getEvaluationsCounter()">getEvaluationsCounter</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#getEventHandlers()">getEventHandlers</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#getExpandable()">getExpandable</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#getMaxEvaluations()">getMaxEvaluations</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#getName()">getName</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#getStepHandlers()">getStepHandlers</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#initIntegration(double, double[], double)">initIntegration</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#integrate(org.apache.commons.math3.ode.FirstOrderDifferentialEquations, double, double[], double, double[])">integrate</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#sanityChecks(org.apache.commons.math3.ode.ExpandableStatefulODE, double)">sanityChecks</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#setEquations(org.apache.commons.math3.ode.ExpandableStatefulODE)">setEquations</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#setMaxEvaluations(int)">setMaxEvaluations</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#setStateInitialized(boolean)">setStateInitialized</a></code></li>
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<h3>Methods inherited from class&nbsp;java.lang.<a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></h3>
<code><a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#clone()" title="class or interface in java.lang">clone</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#equals(java.lang.Object)" title="class or interface in java.lang">equals</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#finalize()" title="class or interface in java.lang">finalize</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#getClass()" title="class or interface in java.lang">getClass</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#hashCode()" title="class or interface in java.lang">hashCode</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#notify()" title="class or interface in java.lang">notify</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#notifyAll()" title="class or interface in java.lang">notifyAll</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#toString()" title="class or interface in java.lang">toString</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait()" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait(long)" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait(long, int)" title="class or interface in java.lang">wait</a></code></li>
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<h3>Constructor Detail</h3>
<a name="RungeKuttaIntegrator(java.lang.String, double[], double[][], double[], org.apache.commons.math3.ode.nonstiff.RungeKuttaStepInterpolator, double)">
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<h4>RungeKuttaIntegrator</h4>
<pre>protected&nbsp;RungeKuttaIntegrator(<a href="http://docs.oracle.com/javase/6/docs/api/java/lang/String.html?is-external=true" title="class or interface in java.lang">String</a>&nbsp;name,
double[]&nbsp;c,
double[][]&nbsp;a,
double[]&nbsp;b,
org.apache.commons.math3.ode.nonstiff.RungeKuttaStepInterpolator&nbsp;prototype,
double&nbsp;step)</pre>
<div class="block">Simple constructor.
Build a Runge-Kutta integrator with the given
step. The default step handler does nothing.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>name</code> - name of the method</dd><dd><code>c</code> - time steps from Butcher array (without the first zero)</dd><dd><code>a</code> - internal weights from Butcher array (without the first empty row)</dd><dd><code>b</code> - propagation weights for the high order method from Butcher array</dd><dd><code>prototype</code> - prototype of the step interpolator to use</dd><dd><code>step</code> - integration step</dd></dl>
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<h3>Method Detail</h3>
<a name="integrate(org.apache.commons.math3.ode.ExpandableStatefulODE, double)">
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<h4>integrate</h4>
<pre>public&nbsp;void&nbsp;integrate(<a href="../../../../../../org/apache/commons/math3/ode/ExpandableStatefulODE.html" title="class in org.apache.commons.math3.ode">ExpandableStatefulODE</a>&nbsp;equations,
double&nbsp;t)
throws <a href="../../../../../../org/apache/commons/math3/exception/NumberIsTooSmallException.html" title="class in org.apache.commons.math3.exception">NumberIsTooSmallException</a>,
<a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a>,
<a href="../../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</a>,
<a href="../../../../../../org/apache/commons/math3/exception/NoBracketingException.html" title="class in org.apache.commons.math3.exception">NoBracketingException</a></pre>
<div class="block">Integrate a set of differential equations up to the given time.
<p>This method solves an Initial Value Problem (IVP).</p>
<p>The set of differential equations is composed of a main set, which
can be extended by some sets of secondary equations. The set of
equations must be already set up with initial time and partial states.
At integration completion, the final time and partial states will be
available in the same object.</p>
<p>Since this method stores some internal state variables made
available in its public interface during integration (<a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#getCurrentSignedStepsize()"><code>AbstractIntegrator.getCurrentSignedStepsize()</code></a>), it is <em>not</em> thread-safe.</p></div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#integrate(org.apache.commons.math3.ode.ExpandableStatefulODE, double)">integrate</a></code>&nbsp;in class&nbsp;<code><a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html" title="class in org.apache.commons.math3.ode">AbstractIntegrator</a></code></dd>
<dt><span class="strong">Parameters:</span></dt><dd><code>equations</code> - complete set of differential equations to integrate</dd><dd><code>t</code> - target time for the integration
(can be set to a value smaller than <code>t0</code> for backward integration)</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NumberIsTooSmallException.html" title="class in org.apache.commons.math3.exception">NumberIsTooSmallException</a></code> - if integration step is too small</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if the dimension of the complete state does not
match the complete equations sets dimension</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</a></code> - if the number of functions evaluations is exceeded</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NoBracketingException.html" title="class in org.apache.commons.math3.exception">NoBracketingException</a></code> - if the location of an event cannot be bracketed</dd></dl>
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<h4>singleStep</h4>
<pre>public&nbsp;double[]&nbsp;singleStep(<a href="../../../../../../org/apache/commons/math3/ode/FirstOrderDifferentialEquations.html" title="interface in org.apache.commons.math3.ode">FirstOrderDifferentialEquations</a>&nbsp;equations,
double&nbsp;t0,
double[]&nbsp;y0,
double&nbsp;t)</pre>
<div class="block">Fast computation of a single step of ODE integration.
<p>This method is intended for the limited use case of
very fast computation of only one step without using any of the
rich features of general integrators that may take some time
to set up (i.e. no step handlers, no events handlers, no additional
states, no interpolators, no error control, no evaluations count,
no sanity checks ...). It handles the strict minimum of computation,
so it can be embedded in outer loops.</p>
<p>
This method is <em>not</em> used at all by the <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/RungeKuttaIntegrator.html#integrate(org.apache.commons.math3.ode.ExpandableStatefulODE, double)"><code>integrate(ExpandableStatefulODE, double)</code></a>
method. It also completely ignores the step set at construction time, and
uses only a single step to go from <code>t0</code> to <code>t</code>.
</p>
<p>
As this method does not use any of the state-dependent features of the integrator,
it should be reasonably thread-safe <em>if and only if</em> the provided differential
equations are themselves thread-safe.
</p></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>equations</code> - differential equations to integrate</dd><dd><code>t0</code> - initial time</dd><dd><code>y0</code> - initial value of the state vector at t0</dd><dd><code>t</code> - target time for the integration
(can be set to a value smaller than <code>t0</code> for backward integration)</dd>
<dt><span class="strong">Returns:</span></dt><dd>state vector at <code>t</code></dd></dl>
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