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/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.commons.math3.ode.nonstiff;
/**
* 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. */
private static final double[] STATIC_C = {
};
/** Internal weights Butcher array. */
private static final double[][] STATIC_A = {
};
/** Propagation weights Butcher array. */
private static final double[] STATIC_B = {
1.0
};
/** 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);
}
}
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