Class EulerIntegrator

  • All Implemented Interfaces:
    FirstOrderIntegrator, 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.

    Since:
    1.2
    See Also:
    MidpointIntegrator, ClassicalRungeKuttaIntegrator, GillIntegrator, ThreeEighthesIntegrator, LutherIntegrator
    • Field Detail

      • STATIC_C

        private static final double[] STATIC_C
        Time steps Butcher array.
      • STATIC_A

        private static final double[][] STATIC_A
        Internal weights Butcher array.
      • STATIC_B

        private static final double[] STATIC_B
        Propagation weights Butcher array.
    • Constructor Detail

      • EulerIntegrator

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