Examples of ClassicalRungeKuttaIntegrator

org.apache.commons.math.ode.ClassicalRungeKuttaIntegrator
This class implements the classical fourth order Runge-Kutta integrator for Ordinary Differential Equations (it is the most often used Runge-Kutta method).
This method is an explicit Runge-Kutta method, its Butcher-array is the following one :
```
 0  |  0    0    0    0 1/2 | 1/2   0    0    0 1/2 |  0   1/2   0    0 1  |  0    0    1    0 |-------------------- | 1/6  1/3  1/3  1/6 
```
@see EulerIntegrator @see GillIntegrator @see MidpointIntegrator @see ThreeEighthesIntegrator @version $Revision: 620312 $ $Date: 2008-02-10 12:28:59 -0700 (Sun, 10 Feb 2008) $ @since 1.2
org.apache.commons.math.ode.nonstiff.ClassicalRungeKuttaIntegrator
This class implements the classical fourth order Runge-Kutta integrator for Ordinary Differential Equations (it is the most often used Runge-Kutta method).
This method is an explicit Runge-Kutta method, its Butcher-array is the following one :
```
 0  |  0    0    0    0 1/2 | 1/2   0    0    0 1/2 |  0   1/2   0    0 1  |  0    0    1    0 |-------------------- | 1/6  1/3  1/3  1/6 
```
@see EulerIntegrator @see GillIntegrator @see MidpointIntegrator @see ThreeEighthesIntegrator @version $Revision: 810196 $ $Date: 2009-09-01 21:47:46 +0200 (mar. 01 sept. 2009) $ @since 1.2
org.apache.commons.math3.ode.nonstiff.ClassicalRungeKuttaIntegrator
This class implements the classical fourth order Runge-Kutta integrator for Ordinary Differential Equations (it is the most often used Runge-Kutta method).
This method is an explicit Runge-Kutta method, its Butcher-array is the following one :
```
 0  |  0    0    0    0 1/2 | 1/2   0    0    0 1/2 |  0   1/2   0    0 1  |  0    0    1    0 |-------------------- | 1/6  1/3  1/3  1/6 
```
@see EulerIntegrator @see GillIntegrator @see MidpointIntegrator @see ThreeEighthesIntegrator @see LutherIntegrator @since 1.2

Examples of org.apache.commons.math.ode.nonstiff.ClassicalRungeKuttaIntegrator

    throws DerivativeException, IntegratorException {


    TestProblem5 pb = new TestProblem5();
    double step = Math.abs(pb.getFinalTime() - pb.getInitialTime()) * 0.001;


    FirstOrderIntegrator integ = new ClassicalRungeKuttaIntegrator(step);
    TestProblemHandler handler = new TestProblemHandler(pb, integ);
    integ.addStepHandler(handler);
    integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(),
                    pb.getFinalTime(), new double[pb.getDimension()]);


    assertTrue(handler.getLastError() < 5.0e-10);
    assertTrue(handler.getMaximalValueError() < 7.0e-10);
    assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
    assertEquals("classical Runge-Kutta", integ.getName());
  }

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Examples of org.apache.commons.math.ode.nonstiff.ClassicalRungeKuttaIntegrator

    throws DerivativeException, IntegratorException {


    final TestProblem3 pb  = new TestProblem3(0.9);
    double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.0003;


    FirstOrderIntegrator integ = new ClassicalRungeKuttaIntegrator(step);
    integ.addStepHandler(new KeplerHandler(pb));
    integ.integrate(pb,
                    pb.getInitialTime(), pb.getInitialState(),
                    pb.getFinalTime(), new double[pb.getDimension()]);
  }

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Examples of org.apache.commons.math.ode.nonstiff.ClassicalRungeKuttaIntegrator

  }


  public void testStepSize()
    throws DerivativeException, IntegratorException {
      final double step = 1.23456;
      FirstOrderIntegrator integ = new ClassicalRungeKuttaIntegrator(step);
      integ.addStepHandler(new StepHandler() {
          public void handleStep(StepInterpolator interpolator, boolean isLast) {
              if (! isLast) {
                  assertEquals(step,
                               interpolator.getCurrentTime() - interpolator.getPreviousTime(),
                               1.0e-12);
              }
          }
          public boolean requiresDenseOutput() {
              return false;
          }
          public void reset() {
          }          
      });
      integ.integrate(new FirstOrderDifferentialEquations() {
          private static final long serialVersionUID = 0L;
          public void computeDerivatives(double t, double[] y, double[] dot) {
              dot[0] = 1.0;
          }
          public int getDimension() {

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Examples of org.apache.commons.math3.ode.nonstiff.ClassicalRungeKuttaIntegrator

                                            double t0, double t,
                                            double step) throws DimensionMismatchException, NumberIsTooSmallException, MaxCountExceededException, NoBracketingException {
    double[] y0 = new double[2];
    y0[0] = FastMath.sin(omega * t0);
    y0[1] = omega * FastMath.cos(omega * t0);
    ClassicalRungeKuttaIntegrator i = new ClassicalRungeKuttaIntegrator(step);
    double[] y = new double[2];
    i.integrate(new FirstOrderConverter(new Equations(1, omega)), t0, y0, t, y);
    return y[0];
  }

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Examples of org.apache.commons.math3.ode.nonstiff.ClassicalRungeKuttaIntegrator

                                            double step)
  throws MathIllegalStateException, MathIllegalArgumentException {
    double[] y0 = new double[2];
    y0[0] = FastMath.sin(omega * t0);
    y0[1] = omega * FastMath.cos(omega * t0);
    ClassicalRungeKuttaIntegrator i = new ClassicalRungeKuttaIntegrator(step);
    double[] y = new double[2];
    i.integrate(new FirstOrderConverter(new Equations(1, omega)), t0, y0, t, y);
    return y[0];
  }

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