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1   /*
2    * Licensed to the Apache Software Foundation (ASF) under one or more
3    * contributor license agreements.  See the NOTICE file distributed with
4    * this work for additional information regarding copyright ownership.
5    * The ASF licenses this file to You under the Apache License, Version 2.0
6    * (the "License"); you may not use this file except in compliance with
7    * the License.  You may obtain a copy of the License at
8    *
9    *      http://www.apache.org/licenses/LICENSE-2.0
10   *
11   * Unless required by applicable law or agreed to in writing, software
12   * distributed under the License is distributed on an "AS IS" BASIS,
13   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14   * See the License for the specific language governing permissions and
15   * limitations under the License.
16   */
17  
18  package org.apache.commons.math.ode;
19  
20  /**
21   * This class implements a simple Euler integrator for Ordinary
22   * Differential Equations.
23   *
24   * <p>The Euler algorithm is the simplest one that can be used to
25   * integrate ordinary differential equations. It is a simple inversion
26   * of the forward difference expression :
27   * <code>f'=(f(t+h)-f(t))/h</code> which leads to
28   * <code>f(t+h)=f(t)+hf'</code>. The interpolation scheme used for
29   * dense output is the linear scheme already used for integration.</p>
30   *
31   * <p>This algorithm looks cheap because it needs only one function
32   * evaluation per step. However, as it uses linear estimates, it needs
33   * very small steps to achieve high accuracy, and small steps lead to
34   * numerical errors and instabilities.</p>
35   *
36   * <p>This algorithm is almost never used and has been included in
37   * this package only as a comparison reference for more useful
38   * integrators.</p>
39   *
40   * @see MidpointIntegrator
41   * @see ClassicalRungeKuttaIntegrator
42   * @see GillIntegrator
43   * @see ThreeEighthesIntegrator
44   * @version $Revision: 620312 $ $Date: 2008-02-10 12:28:59 -0700 (Sun, 10 Feb 2008) $
45   * @since 1.2
46   */
47  
48  public class EulerIntegrator
49    extends RungeKuttaIntegrator {
50  
51    /** Integrator method name. */
52    private static final String methodName = "Euler";
53  
54    /** Time steps Butcher array. */
55    private static final double[] c = {
56    };
57  
58    /** Internal weights Butcher array. */
59    private static final double[][] a = {
60    };
61  
62    /** Propagation weights Butcher array. */
63    private static final double[] b = {
64      1.0
65    };
66  
67    /** Simple constructor.
68     * Build an Euler integrator with the given step.
69     * @param step integration step
70     */
71    public EulerIntegrator(double step) {
72      super(c, a, b, new EulerStepInterpolator(), step);
73    }
74  
75    /** Get the name of the method.
76     * @return name of the method
77     */
78    public String getName() {
79      return methodName;
80    }
81  
82  }