/*
 * 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.math.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
 * @version $Revision$ $Date$
 * @since 1.2
 */

public class EulerIntegrator extends RungeKuttaIntegrator {

	/** Time steps Butcher array. */
	private static final double[] c = {};

	/** Internal weights Butcher array. */
	private static final double[][] a = {};

	/** Propagation weights Butcher array. */
	private static final double[] b = { 1.0 };

	/**
	 * Simple constructor. Build an Euler integrator with the given step.
	 * 
	 * @param step
	 *            integration step
	 */
	public EulerIntegrator(final double step) {
		super("Euler", c, a, b, new EulerStepInterpolator(), step);
	}

}
