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<div class="subTitle">org.apache.commons.math3.ode.nonstiff</div>
<h2 title="Class DormandPrince54Integrator" class="title">Class DormandPrince54Integrator</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>
<li>
<ul class="inheritance">
<li><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff">org.apache.commons.math3.ode.nonstiff.AdaptiveStepsizeIntegrator</a></li>
<li>
<ul class="inheritance">
<li><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/EmbeddedRungeKuttaIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff">org.apache.commons.math3.ode.nonstiff.EmbeddedRungeKuttaIntegrator</a></li>
<li>
<ul class="inheritance">
<li>org.apache.commons.math3.ode.nonstiff.DormandPrince54Integrator</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>
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<br>
<pre>public class <span class="strong">DormandPrince54Integrator</span>
extends <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/EmbeddedRungeKuttaIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff">EmbeddedRungeKuttaIntegrator</a></pre>
<div class="block">This class implements the 5(4) Dormand-Prince integrator for Ordinary
Differential Equations.
<p>This integrator is an embedded Runge-Kutta integrator
of order 5(4) used in local extrapolation mode (i.e. the solution
is computed using the high order formula) with stepsize control
(and automatic step initialization) and continuous output. This
method uses 7 functions evaluations per step. However, since this
is an <i>fsal</i>, the last evaluation of one step is the same as
the first evaluation of the next step and hence can be avoided. So
the cost is really 6 functions evaluations per step.</p>
<p>This method has been published (whithout the continuous output
that was added by Shampine in 1986) in the following article :
<pre>
A family of embedded Runge-Kutta formulae
J. R. Dormand and P. J. Prince
Journal of Computational and Applied Mathematics
volume 6, no 1, 1980, pp. 19-26
</pre></p></div>
<dl><dt><span class="strong">Since:</span></dt>
<dd>1.2</dd>
<dt><span class="strong">Version:</span></dt>
<dd>$Id: DormandPrince54Integrator.java 1416643 2012-12-03 19:37:14Z tn $</dd></dl>
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<h3>Fields inherited from class&nbsp;org.apache.commons.math3.ode.nonstiff.<a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff">AdaptiveStepsizeIntegrator</a></h3>
<code><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#mainSetDimension">mainSetDimension</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#scalAbsoluteTolerance">scalAbsoluteTolerance</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#scalRelativeTolerance">scalRelativeTolerance</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#vecAbsoluteTolerance">vecAbsoluteTolerance</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#vecRelativeTolerance">vecRelativeTolerance</a></code></li>
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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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<td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/DormandPrince54Integrator.html#DormandPrince54Integrator(double, double, double[], double[])">DormandPrince54Integrator</a></strong>(double&nbsp;minStep,
double&nbsp;maxStep,
double[]&nbsp;vecAbsoluteTolerance,
double[]&nbsp;vecRelativeTolerance)</code>
<div class="block">Simple constructor.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/DormandPrince54Integrator.html#DormandPrince54Integrator(double, double, double, double)">DormandPrince54Integrator</a></strong>(double&nbsp;minStep,
double&nbsp;maxStep,
double&nbsp;scalAbsoluteTolerance,
double&nbsp;scalRelativeTolerance)</code>
<div class="block">Simple constructor.</div>
</td>
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<td class="colFirst"><code>protected double</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/DormandPrince54Integrator.html#estimateError(double[][], double[], double[], double)">estimateError</a></strong>(double[][]&nbsp;yDotK,
double[]&nbsp;y0,
double[]&nbsp;y1,
double&nbsp;h)</code>
<div class="block">Compute the error ratio.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>int</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/DormandPrince54Integrator.html#getOrder()">getOrder</a></strong>()</code>
<div class="block">Get the order of the method.</div>
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<h3>Methods inherited from class&nbsp;org.apache.commons.math3.ode.nonstiff.<a href="../../../../../../org/apache/commons/math3/ode/nonstiff/EmbeddedRungeKuttaIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff">EmbeddedRungeKuttaIntegrator</a></h3>
<code><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/EmbeddedRungeKuttaIntegrator.html#getMaxGrowth()">getMaxGrowth</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/EmbeddedRungeKuttaIntegrator.html#getMinReduction()">getMinReduction</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/EmbeddedRungeKuttaIntegrator.html#getSafety()">getSafety</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/EmbeddedRungeKuttaIntegrator.html#integrate(org.apache.commons.math3.ode.ExpandableStatefulODE, double)">integrate</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/EmbeddedRungeKuttaIntegrator.html#setMaxGrowth(double)">setMaxGrowth</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/EmbeddedRungeKuttaIntegrator.html#setMinReduction(double)">setMinReduction</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/EmbeddedRungeKuttaIntegrator.html#setSafety(double)">setSafety</a></code></li>
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<h3>Methods inherited from class&nbsp;org.apache.commons.math3.ode.nonstiff.<a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff">AdaptiveStepsizeIntegrator</a></h3>
<code><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#filterStep(double, boolean, boolean)">filterStep</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#getCurrentStepStart()">getCurrentStepStart</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#getMaxStep()">getMaxStep</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#getMinStep()">getMinStep</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#initializeStep(boolean, int, double[], double, double[], double[], double[], double[])">initializeStep</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#resetInternalState()">resetInternalState</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#sanityChecks(org.apache.commons.math3.ode.ExpandableStatefulODE, double)">sanityChecks</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#setInitialStepSize(double)">setInitialStepSize</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#setStepSizeControl(double, double, double[], double[])">setStepSizeControl</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#setStepSizeControl(double, double, double, double)">setStepSizeControl</a></code></li>
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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#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#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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<h4>DormandPrince54Integrator</h4>
<pre>public&nbsp;DormandPrince54Integrator(double&nbsp;minStep,
double&nbsp;maxStep,
double&nbsp;scalAbsoluteTolerance,
double&nbsp;scalRelativeTolerance)</pre>
<div class="block">Simple constructor.
Build a fifth order Dormand-Prince integrator with the given step bounds</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>minStep</code> - minimal step (sign is irrelevant, regardless of
integration direction, forward or backward), the last step can
be smaller than this</dd><dd><code>maxStep</code> - maximal step (sign is irrelevant, regardless of
integration direction, forward or backward), the last step can
be smaller than this</dd><dd><code>scalAbsoluteTolerance</code> - allowed absolute error</dd><dd><code>scalRelativeTolerance</code> - allowed relative error</dd></dl>
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<h4>DormandPrince54Integrator</h4>
<pre>public&nbsp;DormandPrince54Integrator(double&nbsp;minStep,
double&nbsp;maxStep,
double[]&nbsp;vecAbsoluteTolerance,
double[]&nbsp;vecRelativeTolerance)</pre>
<div class="block">Simple constructor.
Build a fifth order Dormand-Prince integrator with the given step bounds</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>minStep</code> - minimal step (sign is irrelevant, regardless of
integration direction, forward or backward), the last step can
be smaller than this</dd><dd><code>maxStep</code> - maximal step (sign is irrelevant, regardless of
integration direction, forward or backward), the last step can
be smaller than this</dd><dd><code>vecAbsoluteTolerance</code> - allowed absolute error</dd><dd><code>vecRelativeTolerance</code> - allowed relative error</dd></dl>
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<a name="getOrder()">
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<h4>getOrder</h4>
<pre>public&nbsp;int&nbsp;getOrder()</pre>
<div class="block">Get the order of the method.</div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/EmbeddedRungeKuttaIntegrator.html#getOrder()">getOrder</a></code>&nbsp;in class&nbsp;<code><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/EmbeddedRungeKuttaIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff">EmbeddedRungeKuttaIntegrator</a></code></dd>
<dt><span class="strong">Returns:</span></dt><dd>order of the method</dd></dl>
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<a name="estimateError(double[][], double[], double[], double)">
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<h4>estimateError</h4>
<pre>protected&nbsp;double&nbsp;estimateError(double[][]&nbsp;yDotK,
double[]&nbsp;y0,
double[]&nbsp;y1,
double&nbsp;h)</pre>
<div class="block">Compute the error ratio.</div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/EmbeddedRungeKuttaIntegrator.html#estimateError(double[][], double[], double[], double)">estimateError</a></code>&nbsp;in class&nbsp;<code><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/EmbeddedRungeKuttaIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff">EmbeddedRungeKuttaIntegrator</a></code></dd>
<dt><span class="strong">Parameters:</span></dt><dd><code>yDotK</code> - derivatives computed during the first stages</dd><dd><code>y0</code> - estimate of the step at the start of the step</dd><dd><code>y1</code> - estimate of the step at the end of the step</dd><dd><code>h</code> - current step</dd>
<dt><span class="strong">Returns:</span></dt><dd>error ratio, greater than 1 if step should be rejected</dd></dl>
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