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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 the Gill fourth order Runge-Kutta
22   * integrator for Ordinary Differential Equations .
23  
24   * <p>This method is an explicit Runge-Kutta method, its Butcher-array
25   * is the following one :
26   * <pre>
27   *    0  |    0        0       0      0
28   *   1/2 |   1/2       0       0      0
29   *   1/2 | (q-1)/2  (2-q)/2    0      0
30   *    1  |    0       -q/2  (2+q)/2   0
31   *       |-------------------------------
32   *       |   1/6    (2-q)/6 (2+q)/6  1/6
33   * </pre>
34   * where q = sqrt(2)</p>
35   *
36   * @see EulerIntegrator
37   * @see ClassicalRungeKuttaIntegrator
38   * @see MidpointIntegrator
39   * @see ThreeEighthesIntegrator
40   * @version $Revision: 620312 $ $Date: 2008-02-10 12:28:59 -0700 (Sun, 10 Feb 2008) $
41   * @since 1.2
42   */
43  
44  public class GillIntegrator
45    extends RungeKuttaIntegrator {
46  
47    /** Integrator method name. */
48    private static final String methodName = "Gill";
49  
50    /** Time steps Butcher array. */
51    private static final double[] c = {
52      1.0 / 2.0, 1.0 / 2.0, 1.0
53    };
54  
55    /** Internal weights Butcher array. */
56    private static final double[][] a = {
57      { 1.0 / 2.0 },
58      { (Math.sqrt(2.0) - 1.0) / 2.0, (2.0 - Math.sqrt(2.0)) / 2.0 },
59      { 0.0, -Math.sqrt(2.0) / 2.0, (2.0 + Math.sqrt(2.0)) / 2.0 }
60    };
61  
62    /** Propagation weights Butcher array. */
63    private static final double[] b = {
64      1.0 / 6.0, (2.0 - Math.sqrt(2.0)) / 6.0, (2.0 + Math.sqrt(2.0)) / 6.0, 1.0 / 6.0
65    };
66  
67    /** Simple constructor.
68     * Build a fourth-order Gill integrator with the given step.
69     * @param step integration step
70     */
71    public GillIntegrator(double step) {
72      super(c, a, b, new GillStepInterpolator(), 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  }