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| <div class="subTitle">org.apache.commons.math3.ode.nonstiff</div> |
| <h2 title="Class DormandPrince853Integrator" class="title">Class DormandPrince853Integrator</h2> |
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| <li> |
| <ul class="inheritance"> |
| <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.DormandPrince853Integrator</li> |
| </ul> |
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| <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">DormandPrince853Integrator</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 8(5,3) Dormand-Prince integrator for Ordinary |
| Differential Equations. |
| |
| <p>This integrator is an embedded Runge-Kutta integrator |
| of order 8(5,3) 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 12 functions evaluations per step for integration and 4 |
| evaluations for interpolation. However, since the first |
| interpolation evaluation is the same as the first integration |
| evaluation of the next step, we have included it in the integrator |
| rather than in the interpolator and specified the method was an |
| <i>fsal</i>. Hence, despite we have 13 stages here, the cost is |
| really 12 evaluations per step even if no interpolation is done, |
| and the overcost of interpolation is only 3 evaluations.</p> |
| |
| <p>This method is based on an 8(6) method by Dormand and Prince |
| (i.e. order 8 for the integration and order 6 for error estimation) |
| modified by Hairer and Wanner to use a 5th order error estimator |
| with 3rd order correction. This modification was introduced because |
| the original method failed in some cases (wrong steps can be |
| accepted when step size is too large, for example in the |
| Brusselator problem) and also had <i>severe difficulties when |
| applied to problems with discontinuities</i>. This modification is |
| explained in the second edition of the first volume (Nonstiff |
| Problems) of the reference book by Hairer, Norsett and Wanner: |
| <i>Solving Ordinary Differential Equations</i> (Springer-Verlag, |
| ISBN 3-540-56670-8).</p></div> |
| <dl><dt><span class="strong">Since:</span></dt> |
| <dd>1.2</dd> |
| <dt><span class="strong">Version:</span></dt> |
| <dd>$Id: DormandPrince853Integrator.java 1416643 2012-12-03 19:37:14Z tn $</dd></dl> |
| </li> |
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| <h3>Fields inherited from class 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 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="colOne" scope="col">Constructor and Description</th> |
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| <td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/DormandPrince853Integrator.html#DormandPrince853Integrator(double, double, double[], double[])">DormandPrince853Integrator</a></strong>(double minStep, |
| double maxStep, |
| double[] vecAbsoluteTolerance, |
| double[] 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/DormandPrince853Integrator.html#DormandPrince853Integrator(double, double, double, double)">DormandPrince853Integrator</a></strong>(double minStep, |
| double maxStep, |
| double scalAbsoluteTolerance, |
| double scalRelativeTolerance)</code> |
| <div class="block">Simple constructor.</div> |
| </td> |
| </tr> |
| </table> |
| </li> |
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| <th class="colFirst" scope="col">Modifier and Type</th> |
| <th class="colLast" scope="col">Method and Description</th> |
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| <tr class="altColor"> |
| <td class="colFirst"><code>protected double</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/DormandPrince853Integrator.html#estimateError(double[][], double[], double[], double)">estimateError</a></strong>(double[][] yDotK, |
| double[] y0, |
| double[] y1, |
| double 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/DormandPrince853Integrator.html#getOrder()">getOrder</a></strong>()</code> |
| <div class="block">Get the order of the method.</div> |
| </td> |
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| <h3>Methods inherited from class 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 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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| </a> |
| <h3>Methods inherited from class 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 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="DormandPrince853Integrator(double, double, double, double)"> |
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| <h4>DormandPrince853Integrator</h4> |
| <pre>public DormandPrince853Integrator(double minStep, |
| double maxStep, |
| double scalAbsoluteTolerance, |
| double scalRelativeTolerance)</pre> |
| <div class="block">Simple constructor. |
| Build an eighth 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> |
| </li> |
| </ul> |
| <a name="DormandPrince853Integrator(double, double, double[], double[])"> |
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| <h4>DormandPrince853Integrator</h4> |
| <pre>public DormandPrince853Integrator(double minStep, |
| double maxStep, |
| double[] vecAbsoluteTolerance, |
| double[] vecRelativeTolerance)</pre> |
| <div class="block">Simple constructor. |
| Build an eighth 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> |
| </li> |
| </ul> |
| </li> |
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| <a name="getOrder()"> |
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| <h4>getOrder</h4> |
| <pre>public int 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> in class <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 double estimateError(double[][] yDotK, |
| double[] y0, |
| double[] y1, |
| double 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> in class <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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