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class="title">Package org.apache.commons.math3.ode</h1> +<div class="docSummary"> +<div class="block"> + This package provides classes to solve Ordinary Differential Equations problems.</div> +</div> +<p>See: <a href="#package_description">Description</a></p> +</div> +<div class="contentContainer"> +<ul class="blockList"> +<li class="blockList"> +<table class="packageSummary" border="0" cellpadding="3" cellspacing="0" summary="Interface Summary table, listing interfaces, and an explanation"> +<caption><span>Interface Summary</span><span class="tabEnd"> </span></caption> +<tr> +<th class="colFirst" scope="col">Interface</th> +<th class="colLast" scope="col">Description</th> +</tr> +<tbody> +<tr class="altColor"> +<td class="colFirst"><a href="../../../../../org/apache/commons/math3/ode/FieldSecondaryEquations.html" title="interface in org.apache.commons.math3.ode">FieldSecondaryEquations</a><T extends <a href="../../../../../org/apache/commons/math3/RealFieldElement.html" title="interface in org.apache.commons.math3">RealFieldElement</a><T>></td> +<td class="colLast"> +<div class="block">This interface allows users to add secondary differential equations to a primary + set of differential equations.</div> +</td> +</tr> +<tr class="rowColor"> +<td class="colFirst"><a href="../../../../../org/apache/commons/math3/ode/FirstOrderDifferentialEquations.html" title="interface in org.apache.commons.math3.ode">FirstOrderDifferentialEquations</a></td> +<td class="colLast"> +<div class="block">This interface represents a first order differential equations set.</div> +</td> +</tr> +<tr class="altColor"> +<td class="colFirst"><a href="../../../../../org/apache/commons/math3/ode/FirstOrderFieldDifferentialEquations.html" title="interface in org.apache.commons.math3.ode">FirstOrderFieldDifferentialEquations</a><T extends <a href="../../../../../org/apache/commons/math3/RealFieldElement.html" title="interface in org.apache.commons.math3">RealFieldElement</a><T>></td> +<td class="colLast"> +<div class="block">This interface represents a first order differential equations set.</div> +</td> +</tr> +<tr class="rowColor"> +<td class="colFirst"><a href="../../../../../org/apache/commons/math3/ode/FirstOrderFieldIntegrator.html" title="interface in org.apache.commons.math3.ode">FirstOrderFieldIntegrator</a><T extends <a href="../../../../../org/apache/commons/math3/RealFieldElement.html" title="interface in org.apache.commons.math3">RealFieldElement</a><T>></td> +<td class="colLast"> +<div class="block">This interface represents a first order integrator for + differential equations.</div> +</td> +</tr> +<tr class="altColor"> +<td class="colFirst"><a href="../../../../../org/apache/commons/math3/ode/FirstOrderIntegrator.html" title="interface in org.apache.commons.math3.ode">FirstOrderIntegrator</a></td> +<td class="colLast"> +<div class="block">This interface represents a first order integrator for + differential equations.</div> +</td> +</tr> +<tr class="rowColor"> +<td class="colFirst"><a href="../../../../../org/apache/commons/math3/ode/MainStateJacobianProvider.html" title="interface in org.apache.commons.math3.ode">MainStateJacobianProvider</a></td> +<td class="colLast"> +<div class="block">Interface expanding <a href="../../../../../org/apache/commons/math3/ode/FirstOrderDifferentialEquations.html" title="interface in org.apache.commons.math3.ode"><code>first order + differential equations</code></a> in order to compute exactly the main state jacobian + matrix for <a href="../../../../../org/apache/commons/math3/ode/JacobianMatrices.html" title="class in org.apache.commons.math3.ode"><code>partial derivatives equations</code></a>.</div> +</td> +</tr> +<tr class="altColor"> +<td class="colFirst"><a href="../../../../../org/apache/commons/math3/ode/MultistepIntegrator.NordsieckTransformer.html" title="interface in org.apache.commons.math3.ode">MultistepIntegrator.NordsieckTransformer</a></td> +<td class="colLast">Deprecated +<div class="block"><i>as of 3.6 this unused interface is deprecated</i></div> +</td> +</tr> +<tr class="rowColor"> +<td class="colFirst"><a href="../../../../../org/apache/commons/math3/ode/ODEIntegrator.html" title="interface in org.apache.commons.math3.ode">ODEIntegrator</a></td> +<td class="colLast"> +<div class="block">This interface defines the common parts shared by integrators + for first and second order differential equations.</div> +</td> +</tr> +<tr class="altColor"> +<td class="colFirst"><a href="../../../../../org/apache/commons/math3/ode/Parameterizable.html" title="interface in org.apache.commons.math3.ode">Parameterizable</a></td> +<td class="colLast"> +<div class="block">This interface enables to process any parameterizable object.</div> +</td> +</tr> +<tr class="rowColor"> +<td class="colFirst"><a href="../../../../../org/apache/commons/math3/ode/ParameterizedODE.html" title="interface in org.apache.commons.math3.ode">ParameterizedODE</a></td> +<td class="colLast"> +<div class="block">Interface to compute by finite difference Jacobian matrix for some parameter + when computing <a href="../../../../../org/apache/commons/math3/ode/JacobianMatrices.html" title="class in org.apache.commons.math3.ode"><code>partial derivatives equations</code></a>.</div> +</td> +</tr> +<tr class="altColor"> +<td class="colFirst"><a href="../../../../../org/apache/commons/math3/ode/ParameterJacobianProvider.html" title="interface in org.apache.commons.math3.ode">ParameterJacobianProvider</a></td> +<td class="colLast"> +<div class="block">Interface to compute exactly Jacobian matrix for some parameter + when computing <a href="../../../../../org/apache/commons/math3/ode/JacobianMatrices.html" title="class in org.apache.commons.math3.ode"><code>partial derivatives equations</code></a>.</div> +</td> +</tr> +<tr class="rowColor"> +<td class="colFirst"><a href="../../../../../org/apache/commons/math3/ode/SecondaryEquations.html" title="interface in org.apache.commons.math3.ode">SecondaryEquations</a></td> +<td class="colLast"> +<div class="block">This interface allows users to add secondary differential equations to a primary + set of differential equations.</div> +</td> +</tr> +<tr class="altColor"> +<td class="colFirst"><a href="../../../../../org/apache/commons/math3/ode/SecondOrderDifferentialEquations.html" title="interface in org.apache.commons.math3.ode">SecondOrderDifferentialEquations</a></td> +<td class="colLast"> +<div class="block">This interface represents a second order differential equations set.</div> +</td> +</tr> +<tr class="rowColor"> +<td class="colFirst"><a href="../../../../../org/apache/commons/math3/ode/SecondOrderIntegrator.html" title="interface in org.apache.commons.math3.ode">SecondOrderIntegrator</a></td> +<td class="colLast"> +<div class="block">This interface represents a second order integrator for + differential equations.</div> +</td> +</tr> +</tbody> +</table> +</li> +<li class="blockList"> +<table class="packageSummary" border="0" cellpadding="3" cellspacing="0" summary="Class Summary table, listing classes, and an explanation"> +<caption><span>Class Summary</span><span class="tabEnd"> </span></caption> +<tr> +<th class="colFirst" scope="col">Class</th> +<th class="colLast" scope="col">Description</th> +</tr> +<tbody> +<tr class="altColor"> +<td class="colFirst"><a href="../../../../../org/apache/commons/math3/ode/AbstractFieldIntegrator.html" title="class in org.apache.commons.math3.ode">AbstractFieldIntegrator</a><T extends <a href="../../../../../org/apache/commons/math3/RealFieldElement.html" title="interface in org.apache.commons.math3">RealFieldElement</a><T>></td> +<td class="colLast"> +<div class="block">Base class managing common boilerplate for all integrators.</div> +</td> +</tr> +<tr class="rowColor"> +<td class="colFirst"><a href="../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html" title="class in org.apache.commons.math3.ode">AbstractIntegrator</a></td> +<td class="colLast"> +<div class="block">Base class managing common boilerplate for all integrators.</div> +</td> +</tr> +<tr class="altColor"> +<td class="colFirst"><a href="../../../../../org/apache/commons/math3/ode/AbstractParameterizable.html" title="class in org.apache.commons.math3.ode">AbstractParameterizable</a></td> +<td class="colLast"> +<div class="block">This abstract class provides boilerplate parameters list.</div> +</td> +</tr> +<tr class="rowColor"> +<td class="colFirst"><a href="../../../../../org/apache/commons/math3/ode/ContinuousOutputFieldModel.html" title="class in org.apache.commons.math3.ode">ContinuousOutputFieldModel</a><T extends <a href="../../../../../org/apache/commons/math3/RealFieldElement.html" title="interface in org.apache.commons.math3">RealFieldElement</a><T>></td> +<td class="colLast"> +<div class="block">This class stores all information provided by an ODE integrator + during the integration process and build a continuous model of the + solution from this.</div> +</td> +</tr> +<tr class="altColor"> +<td class="colFirst"><a href="../../../../../org/apache/commons/math3/ode/ContinuousOutputModel.html" title="class in org.apache.commons.math3.ode">ContinuousOutputModel</a></td> +<td class="colLast"> +<div class="block">This class stores all information provided by an ODE integrator + during the integration process and build a continuous model of the + solution from this.</div> +</td> +</tr> +<tr class="rowColor"> +<td class="colFirst"><a href="../../../../../org/apache/commons/math3/ode/EquationsMapper.html" title="class in org.apache.commons.math3.ode">EquationsMapper</a></td> +<td class="colLast"> +<div class="block">Class mapping the part of a complete state or derivative that pertains + to a specific differential equation.</div> +</td> +</tr> +<tr class="altColor"> +<td class="colFirst"><a href="../../../../../org/apache/commons/math3/ode/ExpandableStatefulODE.html" title="class in org.apache.commons.math3.ode">ExpandableStatefulODE</a></td> +<td class="colLast"> +<div class="block">This class represents a combined set of first order differential equations, + with at least a primary set of equations expandable by some sets of secondary + equations.</div> +</td> +</tr> +<tr class="rowColor"> +<td class="colFirst"><a href="../../../../../org/apache/commons/math3/ode/FieldEquationsMapper.html" title="class in org.apache.commons.math3.ode">FieldEquationsMapper</a><T extends <a href="../../../../../org/apache/commons/math3/RealFieldElement.html" title="interface in org.apache.commons.math3">RealFieldElement</a><T>></td> +<td class="colLast"> +<div class="block">Class mapping the part of a complete state or derivative that pertains + to a set of differential equations.</div> +</td> +</tr> +<tr class="altColor"> +<td class="colFirst"><a href="../../../../../org/apache/commons/math3/ode/FieldExpandableODE.html" title="class in org.apache.commons.math3.ode">FieldExpandableODE</a><T extends <a href="../../../../../org/apache/commons/math3/RealFieldElement.html" title="interface in org.apache.commons.math3">RealFieldElement</a><T>></td> +<td class="colLast"> +<div class="block">This class represents a combined set of first order differential equations, + with at least a primary set of equations expandable by some sets of secondary + equations.</div> +</td> +</tr> +<tr class="rowColor"> +<td class="colFirst"><a href="../../../../../org/apache/commons/math3/ode/FieldODEState.html" title="class in org.apache.commons.math3.ode">FieldODEState</a><T extends <a href="../../../../../org/apache/commons/math3/RealFieldElement.html" title="interface in org.apache.commons.math3">RealFieldElement</a><T>></td> +<td class="colLast"> +<div class="block">Container for time, main and secondary state vectors.</div> +</td> +</tr> +<tr class="altColor"> +<td class="colFirst"><a href="../../../../../org/apache/commons/math3/ode/FieldODEStateAndDerivative.html" title="class in org.apache.commons.math3.ode">FieldODEStateAndDerivative</a><T extends <a href="../../../../../org/apache/commons/math3/RealFieldElement.html" title="interface in org.apache.commons.math3">RealFieldElement</a><T>></td> +<td class="colLast"> +<div class="block">Container for time, main and secondary state vectors as well as their derivatives.</div> +</td> +</tr> +<tr class="rowColor"> +<td class="colFirst"><a href="../../../../../org/apache/commons/math3/ode/FirstOrderConverter.html" title="class in org.apache.commons.math3.ode">FirstOrderConverter</a></td> +<td class="colLast"> +<div class="block">This class converts second order differential equations to first + order ones.</div> +</td> +</tr> +<tr class="altColor"> +<td class="colFirst"><a href="../../../../../org/apache/commons/math3/ode/JacobianMatrices.html" title="class in org.apache.commons.math3.ode">JacobianMatrices</a></td> +<td class="colLast"> +<div class="block">This class defines a set of <a href="../../../../../org/apache/commons/math3/ode/SecondaryEquations.html" title="interface in org.apache.commons.math3.ode"><code>secondary equations</code></a> to + compute the Jacobian matrices with respect to the initial state vector and, if + any, to some parameters of the primary ODE set.</div> +</td> +</tr> +<tr class="rowColor"> +<td class="colFirst"><a href="../../../../../org/apache/commons/math3/ode/MultistepFieldIntegrator.html" title="class in org.apache.commons.math3.ode">MultistepFieldIntegrator</a><T extends <a href="../../../../../org/apache/commons/math3/RealFieldElement.html" title="interface in org.apache.commons.math3">RealFieldElement</a><T>></td> +<td class="colLast"> +<div class="block">This class is the base class for multistep integrators for Ordinary + Differential Equations.</div> +</td> +</tr> +<tr class="altColor"> +<td class="colFirst"><a href="../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html" title="class in org.apache.commons.math3.ode">MultistepIntegrator</a></td> +<td class="colLast"> +<div class="block">This class is the base class for multistep integrators for Ordinary + Differential Equations.</div> +</td> +</tr> +</tbody> +</table> +</li> +<li class="blockList"> +<table class="packageSummary" border="0" cellpadding="3" cellspacing="0" summary="Exception Summary table, listing exceptions, and an explanation"> +<caption><span>Exception Summary</span><span class="tabEnd"> </span></caption> +<tr> +<th class="colFirst" scope="col">Exception</th> +<th class="colLast" scope="col">Description</th> +</tr> +<tbody> +<tr class="altColor"> +<td class="colFirst"><a href="../../../../../org/apache/commons/math3/ode/JacobianMatrices.MismatchedEquations.html" title="class in org.apache.commons.math3.ode">JacobianMatrices.MismatchedEquations</a></td> +<td class="colLast"> +<div class="block">Special exception for equations mismatch.</div> +</td> +</tr> +<tr class="rowColor"> +<td class="colFirst"><a href="../../../../../org/apache/commons/math3/ode/UnknownParameterException.html" title="class in org.apache.commons.math3.ode">UnknownParameterException</a></td> +<td class="colLast"> +<div class="block">Exception to be thrown when a parameter is unknown.</div> +</td> +</tr> +</tbody> +</table> +</li> +</ul> +<a name="package_description"> +<!-- --> +</a> +<h2 title="Package org.apache.commons.math3.ode Description">Package org.apache.commons.math3.ode Description</h2> +<div class="block"><p> + This package provides classes to solve Ordinary Differential Equations problems. + </p> + + <p> + This package solves Initial Value Problems of the form + <code>y'=f(t,y)</code> with <code>t<sub>0</sub></code> and + <code>y(t<sub>0</sub>)=y<sub>0</sub></code> known. The provided + integrators compute an estimate of <code>y(t)</code> from + <code>t=t<sub>0</sub></code> to <code>t=t<sub>1</sub></code>. + It is also possible to get thederivatives with respect to the initial state + <code>dy(t)/dy(t<sub>0</sub>)</code> or the derivatives with + respect to some ODE parameters <code>dy(t)/dp</code>. + </p> + + <p> + All integrators provide dense output. This means that besides + computing the state vector at discrete times, they also provide a + cheap mean to get the state between the time steps. They do so through + classes extending the <a href="../../../../../org/apache/commons/math3/ode/sampling/StepInterpolator.html" title="interface in org.apache.commons.math3.ode.sampling"><code>StepInterpolator</code></a> + abstract class, which are made available to the user at the end of + each step. + </p> + + <p> + All integrators handle multiple discrete events detection based on switching + functions. This means that the integrator can be driven by user specified + discrete events. The steps are shortened as needed to ensure the events occur + at step boundaries (even if the integrator is a fixed-step + integrator). When the events are triggered, integration can be stopped + (this is called a G-stop facility), the state vector can be changed, + or integration can simply go on. The latter case is useful to handle + discontinuities in the differential equations gracefully and get + accurate dense output even close to the discontinuity. + </p> + + <p> + The user should describe his problem in his own classes + (<code>UserProblem</code> in the diagram below) which should implement + the <a href="../../../../../org/apache/commons/math3/ode/FirstOrderDifferentialEquations.html" title="interface in org.apache.commons.math3.ode"><code>FirstOrderDifferentialEquations</code></a> interface. Then he should pass it to + the integrator he prefers among all the classes that implement the + <a href="../../../../../org/apache/commons/math3/ode/FirstOrderIntegrator.html" title="interface in org.apache.commons.math3.ode"><code>FirstOrderIntegrator</code></a> interface. + </p> + + <p> + The solution of the integration problem is provided by two means. The + first one is aimed towards simple use: the state vector at the end of + the integration process is copied in the <code>y</code> array of the + <a href="../../../../../org/apache/commons/math3/ode/FirstOrderIntegrator.html#integrate(org.apache.commons.math3.ode.FirstOrderDifferentialEquations,%20double,%20double[],%20double,%20double[])"><code>FirstOrderIntegrator.integrate</code></a> method. The second one should be used + when more in-depth information is needed throughout the integration + process. The user can register an object implementing the <a href="../../../../../org/apache/commons/math3/ode/sampling/StepHandler.html" title="interface in org.apache.commons.math3.ode.sampling"><code>StepHandler</code></a> interface or a + <a href="../../../../../org/apache/commons/math3/ode/sampling/StepNormalizer.html" title="class in org.apache.commons.math3.ode.sampling"><code>StepNormalizer</code></a> + object wrapping a user-specified object implementing the <a href="../../../../../org/apache/commons/math3/ode/sampling/FixedStepHandler.html" title="interface in org.apache.commons.math3.ode.sampling"><code>FixedStepHandler</code></a> + interface into the integrator before calling the <a href="../../../../../org/apache/commons/math3/ode/FirstOrderIntegrator.html#integrate(org.apache.commons.math3.ode.FirstOrderDifferentialEquations,%20double,%20double[],%20double,%20double[])"><code>FirstOrderIntegrator.integrate</code></a> method. The user object will be called + appropriately during the integration process, allowing the user to + process intermediate results. The default step handler does nothing. + </p> + + <p> + <a href="../../../../../org/apache/commons/math3/ode/ContinuousOutputModel.html" title="class in org.apache.commons.math3.ode"><code>ContinuousOutputModel</code></a> is a special-purpose step handler that is able + to store all steps and to provide transparent access to any + intermediate result once the integration is over. An important feature + of this class is that it implements the <code>Serializable</code> + interface. This means that a complete continuous model of the + integrated function throughout the integration range can be serialized + and reused later (if stored into a persistent medium like a filesystem + or a database) or elsewhere (if sent to another application). Only the + result of the integration is stored, there is no reference to the + integrated problem by itself. + </p> + + <p> + Other default implementations of the <a href="../../../../../org/apache/commons/math3/ode/sampling/StepHandler.html" title="interface in org.apache.commons.math3.ode.sampling"><code>StepHandler</code></a> interface are + available for general needs (<a href="../../../../../org/apache/commons/math3/ode/sampling/DummyStepHandler.html" title="class in org.apache.commons.math3.ode.sampling"><code>DummyStepHandler</code></a>, <a href="../../../../../org/apache/commons/math3/ode/sampling/StepNormalizer.html" title="class in org.apache.commons.math3.ode.sampling"><code>StepNormalizer</code></a>) and custom + implementations can be developed for specific needs. As an example, + if an application is to be completely driven by the integration + process, then most of the application code will be run inside a step + handler specific to this application. + </p> + + <p> + Some integrators (the simple ones) use fixed steps that are set at + creation time. The more efficient integrators use variable steps that + are handled internally in order to control the integration error with + respect to a specified accuracy (these integrators extend the <a href="../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff"><code>AdaptiveStepsizeIntegrator</code></a> abstract class). In this case, the step + handler which is called after each successful step shows up the + variable stepsize. The <a href="../../../../../org/apache/commons/math3/ode/sampling/StepNormalizer.html" title="class in org.apache.commons.math3.ode.sampling"><code>StepNormalizer</code></a> class can + be used to convert the variable stepsize into a fixed stepsize that + can be handled by classes implementing the <a href="../../../../../org/apache/commons/math3/ode/sampling/FixedStepHandler.html" title="interface in org.apache.commons.math3.ode.sampling"><code>FixedStepHandler</code></a> + interface. Adaptive stepsize integrators can automatically compute the + initial stepsize by themselves, however the user can specify it if he + prefers to retain full control over the integration or if the + automatic guess is wrong. + </p> + + <p> + <table border="1" align="center"> + <tr BGCOLOR="#CCCCFF"><td colspan=2><font size="+2">Fixed Step Integrators</font></td></tr> + <tr BGCOLOR="#EEEEFF"><font size="+1"><td>Name</td><td>Order</td></font></tr> + <tr><td><a href="../../../../../org/apache/commons/math3/ode/nonstiff/EulerIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff"><code>Euler</code></a></td><td>1</td></tr> + <tr><td><a href="../../../../../org/apache/commons/math3/ode/nonstiff/MidpointIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff"><code>Midpoint</code></a></td><td>2</td></tr> + <tr><td><a href="../../../../../org/apache/commons/math3/ode/nonstiff/ClassicalRungeKuttaIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff"><code>Classical Runge-Kutta</code></a></td><td>4</td></tr> + <tr><td><a href="../../../../../org/apache/commons/math3/ode/nonstiff/GillIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff"><code>Gill</code></a></td><td>4</td></tr> + <tr><td><a href="../../../../../org/apache/commons/math3/ode/nonstiff/ThreeEighthesIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff"><code>3/8</code></a></td><td>4</td></tr> + <tr><td><a href="../../../../../org/apache/commons/math3/ode/nonstiff/LutherIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff"><code>Luther</code></a></td><td>6</td></tr> + </table> + </p> + + <table border="1" align="center"> + <tr BGCOLOR="#CCCCFF"><td colspan=3><font size="+2">Adaptive Stepsize Integrators</font></td></tr> + <tr BGCOLOR="#EEEEFF"><font size="+1"><td>Name</td><td>Integration Order</td><td>Error Estimation Order</td></font></tr> + <tr><td><a href="../../../../../org/apache/commons/math3/ode/nonstiff/HighamHall54Integrator.html" title="class in org.apache.commons.math3.ode.nonstiff"><code>Higham and Hall</code></a></td><td>5</td><td>4</td></tr> + <tr><td><a href="../../../../../org/apache/commons/math3/ode/nonstiff/DormandPrince54Integrator.html" title="class in org.apache.commons.math3.ode.nonstiff"><code>Dormand-Prince 5(4)</code></a></td><td>5</td><td>4</td></tr> + <tr><td><a href="../../../../../org/apache/commons/math3/ode/nonstiff/DormandPrince853Integrator.html" title="class in org.apache.commons.math3.ode.nonstiff"><code>Dormand-Prince 8(5,3)</code></a></td><td>8</td><td>5 and 3</td></tr> + <tr><td><a href="../../../../../org/apache/commons/math3/ode/nonstiff/GraggBulirschStoerIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff"><code>Gragg-Bulirsch-Stoer</code></a></td><td>variable (up to 18 by default)</td><td>variable</td></tr> + <tr><td><a href="../../../../../org/apache/commons/math3/ode/nonstiff/AdamsBashforthIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff"><code>Adams-Bashforth</code></a></td><td>variable</td><td>variable</td></tr> + <tr><td><a href="../../../../../org/apache/commons/math3/ode/nonstiff/AdamsMoultonIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff"><code>Adams-Moulton</code></a></td><td>variable</td><td>variable</td></tr> + </table> + </p> + + <p> + In the table above, the <a href="../../../../../org/apache/commons/math3/ode/nonstiff/AdamsBashforthIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff"><code>Adams-Bashforth</code></a> and <a href="../../../../../org/apache/commons/math3/ode/nonstiff/AdamsMoultonIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff"><code>Adams-Moulton</code></a> integrators appear as variable-step ones. This is an experimental extension + to the classical algorithms using the Nordsieck vector representation. + </p></div> +</div> +<!-- ======= 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 class="navBarCell1Rev">Package</li> +<li>Class</li> +<li><a href="package-use.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/ml/neuralnet/twod/util/package-summary.html">Prev Package</a></li> +<li><a href="../../../../../org/apache/commons/math3/ode/events/package-summary.html">Next Package</a></li> +</ul> +<ul class="navList"> +<li><a href="../../../../../index.html?org/apache/commons/math3/ode/package-summary.html" target="_top">Frames</a></li> +<li><a href="package-summary.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"); + if(window==top) { + allClassesLink.style.display = "block"; + } + else { + allClassesLink.style.display = "none"; + } + //--> +</script> +</div> +<a name="skip-navbar_bottom"> +<!-- --> +</a></div> +<!-- ======== END OF BOTTOM NAVBAR ======= --> +<p class="legalCopy"><small>Copyright © 2003–2016 <a href="http://www.apache.org/">The Apache Software Foundation</a>. 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