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diff --git a/commons-math3-3.6.1/docs/apidocs/org/apache/commons/math3/ode/nonstiff/AdamsMoultonIntegrator.html b/commons-math3-3.6.1/docs/apidocs/org/apache/commons/math3/ode/nonstiff/AdamsMoultonIntegrator.html new file mode 100644 index 0000000..eeb438b --- /dev/null +++ b/commons-math3-3.6.1/docs/apidocs/org/apache/commons/math3/ode/nonstiff/AdamsMoultonIntegrator.html @@ -0,0 +1,555 @@ +<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd"> +<!-- NewPage --> +<html lang="en"> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> +<title>AdamsMoultonIntegrator (Apache Commons Math 3.6.1 API)</title> +<link rel="stylesheet" type="text/css" href="../../../../../../stylesheet.css" title="Style"> +</head> +<body> +<script type="text/javascript"><!-- + if (location.href.indexOf('is-external=true') == -1) { + parent.document.title="AdamsMoultonIntegrator (Apache Commons Math 3.6.1 API)"; + } +//--> +</script> +<noscript> +<div>JavaScript is disabled on your browser.</div> +</noscript> +<!-- ========= START OF TOP NAVBAR ======= --> +<div class="topNav"><a name="navbar_top"> +<!-- --> +</a><a href="#skip-navbar_top" title="Skip navigation links"></a><a name="navbar_top_firstrow"> +<!-- --> +</a> +<ul class="navList" title="Navigation"> +<li><a href="../../../../../../overview-summary.html">Overview</a></li> +<li><a href="package-summary.html">Package</a></li> +<li class="navBarCell1Rev">Class</li> +<li><a href="class-use/AdamsMoultonIntegrator.html">Use</a></li> +<li><a href="package-tree.html">Tree</a></li> +<li><a href="../../../../../../deprecated-list.html">Deprecated</a></li> +<li><a href="../../../../../../index-all.html">Index</a></li> +<li><a href="../../../../../../help-doc.html">Help</a></li> +</ul> +<div class="aboutLanguage"><em><script type="text/javascript" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script></em></div> +</div> +<div class="subNav"> +<ul class="navList"> +<li><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdamsMoultonFieldIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff"><span class="strong">Prev Class</span></a></li> +<li><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdamsNordsieckFieldTransformer.html" title="class in org.apache.commons.math3.ode.nonstiff"><span class="strong">Next Class</span></a></li> +</ul> +<ul class="navList"> +<li><a href="../../../../../../index.html?org/apache/commons/math3/ode/nonstiff/AdamsMoultonIntegrator.html" target="_top">Frames</a></li> +<li><a href="AdamsMoultonIntegrator.html" target="_top">No Frames</a></li> +</ul> +<ul class="navList" id="allclasses_navbar_top"> +<li><a href="../../../../../../allclasses-noframe.html">All Classes</a></li> +</ul> +<div> +<script type="text/javascript"><!-- + allClassesLink = document.getElementById("allclasses_navbar_top"); 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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>0</sub> (j+1) (-i)<sup>j</sup> s<sub>j+1</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+1) (-i)<sup>j</sup> terms with i being the row number starting from 1 and j being + the column number starting from 1: + <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></dl> +</li> +</ul> +</div> +<div class="summary"> +<ul class="blockList"> +<li class="blockList"> +<!-- ======== NESTED CLASS SUMMARY ======== --> +<ul class="blockList"> +<li class="blockList"><a name="nested_class_summary"> +<!-- --> +</a> +<h3>Nested Class Summary</h3> +<ul class="blockList"> +<li class="blockList"><a name="nested_classes_inherited_from_class_org.apache.commons.math3.ode.MultistepIntegrator"> +<!-- --> +</a> +<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> +</ul> +</li> +</ul> +<!-- =========== FIELD SUMMARY =========== --> +<ul class="blockList"> +<li class="blockList"><a name="field_summary"> +<!-- --> +</a> +<h3>Field Summary</h3> +<ul class="blockList"> +<li class="blockList"><a name="fields_inherited_from_class_org.apache.commons.math3.ode.MultistepIntegrator"> +<!-- --> +</a> +<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> +</ul> +<ul class="blockList"> +<li class="blockList"><a name="fields_inherited_from_class_org.apache.commons.math3.ode.nonstiff.AdaptiveStepsizeIntegrator"> +<!-- --> +</a> +<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> +</ul> +<ul class="blockList"> +<li class="blockList"><a name="fields_inherited_from_class_org.apache.commons.math3.ode.AbstractIntegrator"> +<!-- --> +</a> +<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> +</ul> +</li> +</ul> +<!-- ======== CONSTRUCTOR SUMMARY ======== --> +<ul class="blockList"> +<li class="blockList"><a name="constructor_summary"> +<!-- --> +</a> +<h3>Constructor Summary</h3> +<table class="overviewSummary" border="0" cellpadding="3" cellspacing="0" summary="Constructor Summary table, listing constructors, and an explanation"> +<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,%20double,%20double,%20double[],%20double[])">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,%20double,%20double,%20double,%20double)">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> +<!-- ========== METHOD SUMMARY =========== --> +<ul class="blockList"> +<li class="blockList"><a name="method_summary"> +<!-- --> +</a> +<h3>Method Summary</h3> +<table class="overviewSummary" border="0" cellpadding="3" cellspacing="0" summary="Method Summary table, listing methods, and an explanation"> +<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,%20double)">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,%20double[],%20double[][],%20double[][])">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[],%20double[],%20org.apache.commons.math3.linear.Array2DRowRealMatrix)">updateHighOrderDerivativesPhase2</a></code></li> +</ul> +<ul class="blockList"> +<li class="blockList"><a name="methods_inherited_from_class_org.apache.commons.math3.ode.MultistepIntegrator"> +<!-- --> +</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#getNSteps()">getNSteps</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,%20double[],%20double)">start</a></code></li> +</ul> +<ul class="blockList"> +<li class="blockList"><a name="methods_inherited_from_class_org.apache.commons.math3.ode.nonstiff.AdaptiveStepsizeIntegrator"> +<!-- --> +</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,%20boolean,%20boolean)">filterStep</a>, <a 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+ 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/7/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/7/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 ========== --> +<ul class="blockList"> +<li class="blockList"><a name="method_detail"> +<!-- --> +</a> +<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,%20double)">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> +</li> +</ul> +</li> +</ul> +</li> +</ul> +</div> +</div> +<!-- ========= END OF CLASS DATA ========= --> +<!-- ======= START OF BOTTOM NAVBAR ====== --> +<div class="bottomNav"><a name="navbar_bottom"> +<!-- --> +</a><a href="#skip-navbar_bottom" title="Skip navigation links"></a><a name="navbar_bottom_firstrow"> +<!-- --> +</a> +<ul class="navList" title="Navigation"> +<li><a href="../../../../../../overview-summary.html">Overview</a></li> +<li><a href="package-summary.html">Package</a></li> +<li class="navBarCell1Rev">Class</li> +<li><a href="class-use/AdamsMoultonIntegrator.html">Use</a></li> +<li><a href="package-tree.html">Tree</a></li> +<li><a href="../../../../../../deprecated-list.html">Deprecated</a></li> +<li><a href="../../../../../../index-all.html">Index</a></li> +<li><a href="../../../../../../help-doc.html">Help</a></li> +</ul> +<div class="aboutLanguage"><em><script type="text/javascript" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script></em></div> +</div> +<div class="subNav"> +<ul class="navList"> +<li><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdamsMoultonFieldIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff"><span class="strong">Prev Class</span></a></li> +<li><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdamsNordsieckFieldTransformer.html" title="class in org.apache.commons.math3.ode.nonstiff"><span class="strong">Next Class</span></a></li> +</ul> +<ul class="navList"> +<li><a href="../../../../../../index.html?org/apache/commons/math3/ode/nonstiff/AdamsMoultonIntegrator.html" target="_top">Frames</a></li> +<li><a href="AdamsMoultonIntegrator.html" target="_top">No Frames</a></li> +</ul> +<ul class="navList" id="allclasses_navbar_bottom"> +<li><a href="../../../../../../allclasses-noframe.html">All Classes</a></li> +</ul> +<div> +<script type="text/javascript"><!-- + allClassesLink = document.getElementById("allclasses_navbar_bottom"); 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