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| <div class="subTitle">org.apache.commons.math3.ode.nonstiff</div> |
| <h2 title="Class AdamsMoultonIntegrator" class="title">Class AdamsMoultonIntegrator</h2> |
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| <li><a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">java.lang.Object</a></li> |
| <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/MultistepIntegrator.html" title="class in org.apache.commons.math3.ode">org.apache.commons.math3.ode.MultistepIntegrator</a></li> |
| <li> |
| <ul class="inheritance"> |
| <li><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdamsIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff">org.apache.commons.math3.ode.nonstiff.AdamsIntegrator</a></li> |
| <li> |
| <ul class="inheritance"> |
| <li>org.apache.commons.math3.ode.nonstiff.AdamsMoultonIntegrator</li> |
| </ul> |
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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> |
| <hr> |
| <br> |
| <pre>public class <span class="strong">AdamsMoultonIntegrator</span> |
| extends <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdamsIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff">AdamsIntegrator</a></pre> |
| <div class="block">This class implements implicit Adams-Moulton integrators for Ordinary |
| Differential Equations. |
| |
| <p>Adams-Moulton methods (in fact due to Adams alone) are implicit |
| multistep ODE solvers. This implementation is a variation of the classical |
| one: it uses adaptive stepsize to implement error control, whereas |
| classical implementations are fixed step size. The value of state vector |
| at step n+1 is a simple combination of the value at step n and of the |
| derivatives at steps n+1, n, n-1 ... Since y'<sub>n+1</sub> is needed to |
| compute y<sub>n+1</sub>, another method must be used to compute a first |
| estimate of y<sub>n+1</sub>, then compute y'<sub>n+1</sub>, then compute |
| a final estimate of y<sub>n+1</sub> using the following formulas. Depending |
| on the number k of previous steps one wants to use for computing the next |
| value, different formulas are available for the final estimate:</p> |
| <ul> |
| <li>k = 1: y<sub>n+1</sub> = y<sub>n</sub> + h y'<sub>n+1</sub></li> |
| <li>k = 2: y<sub>n+1</sub> = y<sub>n</sub> + h (y'<sub>n+1</sub>+y'<sub>n</sub>)/2</li> |
| <li>k = 3: y<sub>n+1</sub> = y<sub>n</sub> + h (5y'<sub>n+1</sub>+8y'<sub>n</sub>-y'<sub>n-1</sub>)/12</li> |
| <li>k = 4: y<sub>n+1</sub> = y<sub>n</sub> + h (9y'<sub>n+1</sub>+19y'<sub>n</sub>-5y'<sub>n-1</sub>+y'<sub>n-2</sub>)/24</li> |
| <li>...</li> |
| </ul> |
| |
| <p>A k-steps Adams-Moulton method is of order k+1.</p> |
| |
| <h3>Implementation details</h3> |
| |
| <p>We define scaled derivatives s<sub>i</sub>(n) at step n as: |
| <pre> |
| s<sub>1</sub>(n) = h y'<sub>n</sub> for first derivative |
| s<sub>2</sub>(n) = h<sup>2</sup>/2 y''<sub>n</sub> for second derivative |
| s<sub>3</sub>(n) = h<sup>3</sup>/6 y'''<sub>n</sub> for third derivative |
| ... |
| s<sub>k</sub>(n) = h<sup>k</sup>/k! y<sup>(k)</sup><sub>n</sub> for k<sup>th</sup> derivative |
| </pre></p> |
| |
| <p>The definitions above use the classical representation with several previous first |
| derivatives. Lets define |
| <pre> |
| q<sub>n</sub> = [ s<sub>1</sub>(n-1) s<sub>1</sub>(n-2) ... s<sub>1</sub>(n-(k-1)) ]<sup>T</sup> |
| </pre> |
| (we omit the k index in the notation for clarity). With these definitions, |
| Adams-Moulton methods can be written: |
| <ul> |
| <li>k = 1: y<sub>n+1</sub> = y<sub>n</sub> + s<sub>1</sub>(n+1)</li> |
| <li>k = 2: y<sub>n+1</sub> = y<sub>n</sub> + 1/2 s<sub>1</sub>(n+1) + [ 1/2 ] q<sub>n+1</sub></li> |
| <li>k = 3: y<sub>n+1</sub> = y<sub>n</sub> + 5/12 s<sub>1</sub>(n+1) + [ 8/12 -1/12 ] q<sub>n+1</sub></li> |
| <li>k = 4: y<sub>n+1</sub> = y<sub>n</sub> + 9/24 s<sub>1</sub>(n+1) + [ 19/24 -5/24 1/24 ] q<sub>n+1</sub></li> |
| <li>...</li> |
| </ul></p> |
| |
| <p>Instead of using the classical representation with first derivatives only (y<sub>n</sub>, |
| s<sub>1</sub>(n+1) and q<sub>n+1</sub>), our implementation uses the Nordsieck vector with |
| higher degrees scaled derivatives all taken at the same step (y<sub>n</sub>, s<sub>1</sub>(n) |
| and r<sub>n</sub>) where r<sub>n</sub> is defined as: |
| <pre> |
| r<sub>n</sub> = [ s<sub>2</sub>(n), s<sub>3</sub>(n) ... s<sub>k</sub>(n) ]<sup>T</sup> |
| </pre> |
| (here again we omit the k index in the notation for clarity) |
| </p> |
| |
| <p>Taylor series formulas show that for any index offset i, s<sub>1</sub>(n-i) can be |
| computed from s<sub>1</sub>(n), s<sub>2</sub>(n) ... s<sub>k</sub>(n), the formula being exact |
| for degree k polynomials. |
| <pre> |
| s<sub>1</sub>(n-i) = s<sub>1</sub>(n) + ∑<sub>j</sub> j (-i)<sup>j-1</sup> s<sub>j</sub>(n) |
| </pre> |
| The previous formula can be used with several values for i to compute the transform between |
| classical representation and Nordsieck vector. The transform between r<sub>n</sub> |
| and q<sub>n</sub> resulting from the Taylor series formulas above is: |
| <pre> |
| q<sub>n</sub> = s<sub>1</sub>(n) u + P r<sub>n</sub> |
| </pre> |
| where u is the [ 1 1 ... 1 ]<sup>T</sup> vector and P is the (k-1)×(k-1) matrix built |
| with the j (-i)<sup>j-1</sup> terms: |
| <pre> |
| [ -2 3 -4 5 ... ] |
| [ -4 12 -32 80 ... ] |
| P = [ -6 27 -108 405 ... ] |
| [ -8 48 -256 1280 ... ] |
| [ ... ] |
| </pre></p> |
| |
| <p>Using the Nordsieck vector has several advantages: |
| <ul> |
| <li>it greatly simplifies step interpolation as the interpolator mainly applies |
| Taylor series formulas,</li> |
| <li>it simplifies step changes that occur when discrete events that truncate |
| the step are triggered,</li> |
| <li>it allows to extend the methods in order to support adaptive stepsize.</li> |
| </ul></p> |
| |
| <p>The predicted Nordsieck vector at step n+1 is computed from the Nordsieck vector at step |
| n as follows: |
| <ul> |
| <li>Y<sub>n+1</sub> = y<sub>n</sub> + s<sub>1</sub>(n) + u<sup>T</sup> r<sub>n</sub></li> |
| <li>S<sub>1</sub>(n+1) = h f(t<sub>n+1</sub>, Y<sub>n+1</sub>)</li> |
| <li>R<sub>n+1</sub> = (s<sub>1</sub>(n) - S<sub>1</sub>(n+1)) P<sup>-1</sup> u + P<sup>-1</sup> A P r<sub>n</sub></li> |
| </ul> |
| where A is a rows shifting matrix (the lower left part is an identity matrix): |
| <pre> |
| [ 0 0 ... 0 0 | 0 ] |
| [ ---------------+---] |
| [ 1 0 ... 0 0 | 0 ] |
| A = [ 0 1 ... 0 0 | 0 ] |
| [ ... | 0 ] |
| [ 0 0 ... 1 0 | 0 ] |
| [ 0 0 ... 0 1 | 0 ] |
| </pre> |
| From this predicted vector, the corrected vector is computed as follows: |
| <ul> |
| <li>y<sub>n+1</sub> = y<sub>n</sub> + S<sub>1</sub>(n+1) + [ -1 +1 -1 +1 ... ±1 ] r<sub>n+1</sub></li> |
| <li>s<sub>1</sub>(n+1) = h f(t<sub>n+1</sub>, y<sub>n+1</sub>)</li> |
| <li>r<sub>n+1</sub> = R<sub>n+1</sub> + (s<sub>1</sub>(n+1) - S<sub>1</sub>(n+1)) P<sup>-1</sup> u</li> |
| </ul> |
| where the upper case Y<sub>n+1</sub>, S<sub>1</sub>(n+1) and R<sub>n+1</sub> represent the |
| predicted states whereas the lower case y<sub>n+1</sub>, s<sub>n+1</sub> and r<sub>n+1</sub> |
| represent the corrected states.</p> |
| |
| <p>The P<sup>-1</sup>u vector and the P<sup>-1</sup> A P matrix do not depend on the state, |
| they only depend on k and therefore are precomputed once for all.</p></div> |
| <dl><dt><span class="strong">Since:</span></dt> |
| <dd>2.0</dd> |
| <dt><span class="strong">Version:</span></dt> |
| <dd>$Id: AdamsMoultonIntegrator.java 1463684 2013-04-02 19:04:13Z luc $</dd></dl> |
| </li> |
| </ul> |
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| <h3>Nested classes/interfaces inherited from class org.apache.commons.math3.ode.<a href="../../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html" title="class in org.apache.commons.math3.ode">MultistepIntegrator</a></h3> |
| <code><a href="../../../../../../org/apache/commons/math3/ode/MultistepIntegrator.NordsieckTransformer.html" title="interface in org.apache.commons.math3.ode">MultistepIntegrator.NordsieckTransformer</a></code></li> |
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| <h3>Fields inherited from class org.apache.commons.math3.ode.<a href="../../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html" title="class in org.apache.commons.math3.ode">MultistepIntegrator</a></h3> |
| <code><a href="../../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#nordsieck">nordsieck</a>, <a href="../../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#scaled">scaled</a></code></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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| <h3>Constructor Summary</h3> |
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| <caption><span>Constructors</span><span class="tabEnd"> </span></caption> |
| <tr> |
| <th class="colOne" scope="col">Constructor and Description</th> |
| </tr> |
| <tr class="altColor"> |
| <td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdamsMoultonIntegrator.html#AdamsMoultonIntegrator(int, double, double, double[], double[])">AdamsMoultonIntegrator</a></strong>(int nSteps, |
| double minStep, |
| double maxStep, |
| double[] vecAbsoluteTolerance, |
| double[] vecRelativeTolerance)</code> |
| <div class="block">Build an Adams-Moulton integrator with the given order and error control parameters.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdamsMoultonIntegrator.html#AdamsMoultonIntegrator(int, double, double, double, double)">AdamsMoultonIntegrator</a></strong>(int nSteps, |
| double minStep, |
| double maxStep, |
| double scalAbsoluteTolerance, |
| double scalRelativeTolerance)</code> |
| <div class="block">Build an Adams-Moulton integrator with the given order and error control parameters.</div> |
| </td> |
| </tr> |
| </table> |
| </li> |
| </ul> |
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| <h3>Method Summary</h3> |
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| <caption><span>Methods</span><span class="tabEnd"> </span></caption> |
| <tr> |
| <th class="colFirst" scope="col">Modifier and Type</th> |
| <th class="colLast" scope="col">Method and Description</th> |
| </tr> |
| <tr class="altColor"> |
| <td class="colFirst"><code>void</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdamsMoultonIntegrator.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> equations, |
| double t)</code> |
| <div class="block">Integrate a set of differential equations up to the given time.</div> |
| </td> |
| </tr> |
| </table> |
| <ul class="blockList"> |
| <li class="blockList"><a name="methods_inherited_from_class_org.apache.commons.math3.ode.nonstiff.AdamsIntegrator"> |
| <!-- --> |
| </a> |
| <h3>Methods inherited from class org.apache.commons.math3.ode.nonstiff.<a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdamsIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff">AdamsIntegrator</a></h3> |
| <code><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdamsIntegrator.html#initializeHighOrderDerivatives(double, double[], double[][], double[][])">initializeHighOrderDerivatives</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdamsIntegrator.html#updateHighOrderDerivativesPhase1(org.apache.commons.math3.linear.Array2DRowRealMatrix)">updateHighOrderDerivativesPhase1</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdamsIntegrator.html#updateHighOrderDerivativesPhase2(double[], double[], org.apache.commons.math3.linear.Array2DRowRealMatrix)">updateHighOrderDerivativesPhase2</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/MultistepIntegrator.html" title="class in org.apache.commons.math3.ode">MultistepIntegrator</a></h3> |
| <code><a href="../../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#computeStepGrowShrinkFactor(double)">computeStepGrowShrinkFactor</a>, <a href="../../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#getMaxGrowth()">getMaxGrowth</a>, <a href="../../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#getMinReduction()">getMinReduction</a>, <a href="../../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#getSafety()">getSafety</a>, <a href="../../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#getStarterIntegrator()">getStarterIntegrator</a>, <a href="../../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#setMaxGrowth(double)">setMaxGrowth</a>, <a href="../../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#setMinReduction(double)">setMinReduction</a>, <a href="../../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#setSafety(double)">setSafety</a>, <a href="../../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#setStarterIntegrator(org.apache.commons.math3.ode.FirstOrderIntegrator)">setStarterIntegrator</a>, <a href="../../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#start(double, double[], double)">start</a></code></li> |
| </ul> |
| <ul class="blockList"> |
| <li class="blockList"><a name="methods_inherited_from_class_org.apache.commons.math3.ode.nonstiff.AdaptiveStepsizeIntegrator"> |
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| </a> |
| <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> |
| </ul> |
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| <li class="blockList"><a name="methods_inherited_from_class_org.apache.commons.math3.ode.AbstractIntegrator"> |
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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> |
| </ul> |
| <ul class="blockList"> |
| <li class="blockList"><a name="methods_inherited_from_class_java.lang.Object"> |
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| </a> |
| <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> |
| </ul> |
| </li> |
| </ul> |
| </li> |
| </ul> |
| </div> |
| <div class="details"> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <!-- ========= CONSTRUCTOR DETAIL ======== --> |
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| <h3>Constructor Detail</h3> |
| <a name="AdamsMoultonIntegrator(int, double, double, double, double)"> |
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| </a> |
| <ul class="blockList"> |
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| <h4>AdamsMoultonIntegrator</h4> |
| <pre>public AdamsMoultonIntegrator(int nSteps, |
| double minStep, |
| double maxStep, |
| double scalAbsoluteTolerance, |
| double scalRelativeTolerance) |
| throws <a href="../../../../../../org/apache/commons/math3/exception/NumberIsTooSmallException.html" title="class in org.apache.commons.math3.exception">NumberIsTooSmallException</a></pre> |
| <div class="block">Build an Adams-Moulton integrator with the given order and error control parameters.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>nSteps</code> - number of steps of the method excluding the one being computed</dd><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> |
| <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 order is 1 or less</dd></dl> |
| </li> |
| </ul> |
| <a name="AdamsMoultonIntegrator(int, double, double, double[], double[])"> |
| <!-- --> |
| </a> |
| <ul class="blockListLast"> |
| <li class="blockList"> |
| <h4>AdamsMoultonIntegrator</h4> |
| <pre>public AdamsMoultonIntegrator(int nSteps, |
| double minStep, |
| double maxStep, |
| double[] vecAbsoluteTolerance, |
| double[] vecRelativeTolerance) |
| throws <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</a></pre> |
| <div class="block">Build an Adams-Moulton integrator with the given order and error control parameters.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>nSteps</code> - number of steps of the method excluding the one being computed</dd><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> |
| <dt><span class="strong">Throws:</span></dt> |
| <dd><code><a href="http://docs.oracle.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</a></code> - if order is 1 or less</dd></dl> |
| </li> |
| </ul> |
| </li> |
| </ul> |
| <!-- ============ METHOD DETAIL ========== --> |
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| <h3>Method Detail</h3> |
| <a name="integrate(org.apache.commons.math3.ode.ExpandableStatefulODE, double)"> |
| <!-- --> |
| </a> |
| <ul class="blockListLast"> |
| <li class="blockList"> |
| <h4>integrate</h4> |
| <pre>public void integrate(<a href="../../../../../../org/apache/commons/math3/ode/ExpandableStatefulODE.html" title="class in org.apache.commons.math3.ode">ExpandableStatefulODE</a> equations, |
| double 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/nonstiff/AdamsIntegrator.html#integrate(org.apache.commons.math3.ode.ExpandableStatefulODE, double)">integrate</a></code> in class <code><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdamsIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff">AdamsIntegrator</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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