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package org.apache.commons.math3.ode.nonstiff;
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: Since: 1.2
/**
* This class implements a simple Euler integrator for Ordinary
* Differential Equations.
*
* <p>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 :
* <code>f'=(f(t+h)-f(t))/h</code> which leads to
* <code>f(t+h)=f(t)+hf'</code>. The interpolation scheme used for
* dense output is the linear scheme already used for integration.</p>
*
* <p>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.</p>
*
* <p>This algorithm is almost never used and has been included in
* this package only as a comparison reference for more useful
* integrators.</p>
*
* @see MidpointIntegrator
* @see ClassicalRungeKuttaIntegrator
* @see GillIntegrator
* @see ThreeEighthesIntegrator
* @see LutherIntegrator
* @since 1.2
*/
public class EulerIntegrator extends RungeKuttaIntegrator {
Time steps Butcher array. /** Time steps Butcher array. */
private static final double[] STATIC_C = {
};
Internal weights Butcher array. /** Internal weights Butcher array. */
private static final double[][] STATIC_A = {
};
Propagation weights Butcher array. /** Propagation weights Butcher array. */
private static final double[] STATIC_B = {
1.0
};
Simple constructor.
Build an Euler integrator with the given step.
Params: - step – integration step
/** Simple constructor.
* Build an Euler integrator with the given step.
* @param step integration step
*/
public EulerIntegrator(final double step) {
super("Euler", STATIC_C, STATIC_A, STATIC_B, new EulerStepInterpolator(), step);
}
}