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.nonstiff;
19
20
21 /**
22 * This class implements the Gill fourth order Runge-Kutta
23 * integrator for Ordinary Differential Equations .
24
25 * <p>This method is an explicit Runge-Kutta method, its Butcher-array
26 * is the following one :
27 * <pre>
28 * 0 | 0 0 0 0
29 * 1/2 | 1/2 0 0 0
30 * 1/2 | (q-1)/2 (2-q)/2 0 0
31 * 1 | 0 -q/2 (2+q)/2 0
32 * |-------------------------------
33 * | 1/6 (2-q)/6 (2+q)/6 1/6
34 * </pre>
35 * where q = sqrt(2)</p>
36 *
37 * @see EulerIntegrator
38 * @see ClassicalRungeKuttaIntegrator
39 * @see MidpointIntegrator
40 * @see ThreeEighthesIntegrator
41 * @version $Revision: 786881 $ $Date: 2009-06-20 14:53:08 -0400 (Sat, 20 Jun 2009) $
42 * @since 1.2
43 */
44
45 public class GillIntegrator extends RungeKuttaIntegrator {
46
47 /** Time steps Butcher array. */
48 private static final double[] c = {
49 1.0 / 2.0, 1.0 / 2.0, 1.0
50 };
51
52 /** Internal weights Butcher array. */
53 private static final double[][] a = {
54 { 1.0 / 2.0 },
55 { (Math.sqrt(2.0) - 1.0) / 2.0, (2.0 - Math.sqrt(2.0)) / 2.0 },
56 { 0.0, -Math.sqrt(2.0) / 2.0, (2.0 + Math.sqrt(2.0)) / 2.0 }
57 };
58
59 /** Propagation weights Butcher array. */
60 private static final double[] b = {
61 1.0 / 6.0, (2.0 - Math.sqrt(2.0)) / 6.0, (2.0 + Math.sqrt(2.0)) / 6.0, 1.0 / 6.0
62 };
63
64 /** Simple constructor.
65 * Build a fourth-order Gill integrator with the given step.
66 * @param step integration step
67 */
68 public GillIntegrator(final double step) {
69 super("Gill", c, a, b, new GillStepInterpolator(), step);
70 }
71
72 }