001    /*
002     * Licensed to the Apache Software Foundation (ASF) under one or more
003     * contributor license agreements.  See the NOTICE file distributed with
004     * this work for additional information regarding copyright ownership.
005     * The ASF licenses this file to You under the Apache License, Version 2.0
006     * (the "License"); you may not use this file except in compliance with
007     * the License.  You may obtain a copy of the License at
008     *
009     *      http://www.apache.org/licenses/LICENSE-2.0
010     *
011     * Unless required by applicable law or agreed to in writing, software
012     * distributed under the License is distributed on an "AS IS" BASIS,
013     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014     * See the License for the specific language governing permissions and
015     * limitations under the License.
016     */
017    
018    package org.apache.commons.math3.ode.nonstiff;
019    
020    
021    /**
022     * This class implements a simple Euler integrator for Ordinary
023     * Differential Equations.
024     *
025     * <p>The Euler algorithm is the simplest one that can be used to
026     * integrate ordinary differential equations. It is a simple inversion
027     * of the forward difference expression :
028     * <code>f'=(f(t+h)-f(t))/h</code> which leads to
029     * <code>f(t+h)=f(t)+hf'</code>. The interpolation scheme used for
030     * dense output is the linear scheme already used for integration.</p>
031     *
032     * <p>This algorithm looks cheap because it needs only one function
033     * evaluation per step. However, as it uses linear estimates, it needs
034     * very small steps to achieve high accuracy, and small steps lead to
035     * numerical errors and instabilities.</p>
036     *
037     * <p>This algorithm is almost never used and has been included in
038     * this package only as a comparison reference for more useful
039     * integrators.</p>
040     *
041     * @see MidpointIntegrator
042     * @see ClassicalRungeKuttaIntegrator
043     * @see GillIntegrator
044     * @see ThreeEighthesIntegrator
045     * @version $Id: EulerIntegrator.java 1416643 2012-12-03 19:37:14Z tn $
046     * @since 1.2
047     */
048    
049    public class EulerIntegrator extends RungeKuttaIntegrator {
050    
051      /** Time steps Butcher array. */
052      private static final double[] STATIC_C = {
053      };
054    
055      /** Internal weights Butcher array. */
056      private static final double[][] STATIC_A = {
057      };
058    
059      /** Propagation weights Butcher array. */
060      private static final double[] STATIC_B = {
061        1.0
062      };
063    
064      /** Simple constructor.
065       * Build an Euler integrator with the given step.
066       * @param step integration step
067       */
068      public EulerIntegrator(final double step) {
069        super("Euler", STATIC_C, STATIC_A, STATIC_B, new EulerStepInterpolator(), step);
070      }
071    
072    }