Class EulerIntegrator

  • All Implemented Interfaces:
    ButcherArrayProvider, ODEIntegrator

    public class EulerIntegrator
    extends RungeKuttaIntegrator
    This class implements a simple Euler integrator for Ordinary Differential Equations.

    The Euler algorithm is the simplest one that can be used to integrate ordinary differential equations. It is a simple inversion of the forward difference expression : f'=(f(t+h)-f(t))/h which leads to f(t+h)=f(t)+hf'. The interpolation scheme used for dense output is the linear scheme already used for integration.

    This algorithm looks cheap because it needs only one function evaluation per step. However, as it uses linear estimates, it needs very small steps to achieve high accuracy, and small steps lead to numerical errors and instabilities.

    This algorithm is almost never used and has been included in this package only as a comparison reference for more useful integrators.

    See Also:
    MidpointIntegrator, ClassicalRungeKuttaIntegrator, GillIntegrator, ThreeEighthesIntegrator, LutherIntegrator
    • Constructor Detail

      • EulerIntegrator

        public EulerIntegrator​(double step)
        Simple constructor. Build an Euler integrator with the given step.
        Parameters:
        step - integration step
    • Method Detail

      • getC

        public double[] getC()
        Get the time steps from Butcher array (without the first zero).
        Returns:
        time steps from Butcher array (without the first zero
      • getA

        public double[][] getA()
        Get the internal weights from Butcher array (without the first empty row).
        Returns:
        internal weights from Butcher array (without the first empty row)
      • getB

        public double[] getB()
        Get the external weights for the high order method from Butcher array.
        Returns:
        external weights for the high order method from Butcher array
      • createInterpolator

        protected org.hipparchus.ode.nonstiff.EulerStateInterpolator createInterpolator​(boolean forward,
                                                                                        double[][] yDotK,
                                                                                        ODEStateAndDerivative globalPreviousState,
                                                                                        ODEStateAndDerivative globalCurrentState,
                                                                                        EquationsMapper mapper)
        Create an interpolator.
        Specified by:
        createInterpolator in class RungeKuttaIntegrator
        Parameters:
        forward - integration direction indicator
        yDotK - slopes at the intermediate points
        globalPreviousState - start of the global step
        globalCurrentState - end of the global step
        mapper - equations mapper for the all equations
        Returns:
        external weights for the high order method from Butcher array