org.apache.commons.math3.ode.nonstiff

Class RungeKuttaIntegrator

java.lang.Object

org.apache.commons.math3.ode.AbstractIntegrator

org.apache.commons.math3.ode.nonstiff.RungeKuttaIntegrator

All Implemented Interfaces:

FirstOrderIntegrator, ODEIntegrator

Direct Known Subclasses:

ClassicalRungeKuttaIntegrator, EulerIntegrator, GillIntegrator, LutherIntegrator, MidpointIntegrator, ThreeEighthesIntegrator

public abstract class RungeKuttaIntegrator
extends AbstractIntegrator

This class implements the common part of all fixed step Runge-Kutta integrators for Ordinary Differential Equations.

These methods are explicit Runge-Kutta methods, their Butcher arrays are as follows :

    0  |
   c2  | a21
   c3  | a31  a32
   ... |        ...
   cs  | as1  as2  ...  ass-1
       |--------------------------
       |  b1   b2  ...   bs-1  bs
 

Since:

1.2

See Also:

EulerIntegrator, ClassicalRungeKuttaIntegrator, GillIntegrator, MidpointIntegrator

Method Summary

Modifier and Type	Method and Description
void	integrate(ExpandableStatefulODE equations, double t) Integrate a set of differential equations up to the given time.
double[]	singleStep(FirstOrderDifferentialEquations equations, double t0, double[] y0, double t) Fast computation of a single step of ODE integration.

Methods inherited from class org.apache.commons.math3.ode.AbstractIntegrator

addEventHandler, addEventHandler, addStepHandler, clearEventHandlers, clearStepHandlers, computeDerivatives, getCurrentSignedStepsize, getCurrentStepStart, getEvaluations, getEventHandlers, getMaxEvaluations, getName, getStepHandlers, integrate, setMaxEvaluations

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

integrate

public void integrate(ExpandableStatefulODE equations,
                      double t)
               throws NumberIsTooSmallException,
                      DimensionMismatchException,
                      MaxCountExceededException,
                      NoBracketingException

Integrate a set of differential equations up to the given time.

This method solves an Initial Value Problem (IVP).

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.

Since this method stores some internal state variables made available in its public interface during integration (AbstractIntegrator.getCurrentSignedStepsize()), it is not thread-safe.

Specified by:

integrate in class AbstractIntegrator

Parameters:

equations - complete set of differential equations to integrate

t - target time for the integration (can be set to a value smaller than t0 for backward integration)

Throws:

NumberIsTooSmallException - if integration step is too small

DimensionMismatchException - if the dimension of the complete state does not match the complete equations sets dimension

MaxCountExceededException - if the number of functions evaluations is exceeded

NoBracketingException - if the location of an event cannot be bracketed

singleStep

public double[] singleStep(FirstOrderDifferentialEquations equations,
                           double t0,
                           double[] y0,
                           double t)

Fast computation of a single step of ODE integration.

This method is intended for the limited use case of very fast computation of only one step without using any of the rich features of general integrators that may take some time to set up (i.e. no step handlers, no events handlers, no additional states, no interpolators, no error control, no evaluations count, no sanity checks ...). It handles the strict minimum of computation, so it can be embedded in outer loops.

This method is not used at all by the integrate(ExpandableStatefulODE, double) method. It also completely ignores the step set at construction time, and uses only a single step to go from t0 to t.

As this method does not use any of the state-dependent features of the integrator, it should be reasonably thread-safe if and only if the provided differential equations are themselves thread-safe.

Parameters:

equations - differential equations to integrate

t0 - initial time

y0 - initial value of the state vector at t0

t - target time for the integration (can be set to a value smaller than t0 for backward integration)

Returns:

state vector at t