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.math4.legacy.ode.nonstiff;
19
20 import org.apache.commons.math4.core.jdkmath.JdkMath;
21
22
23 /**
24 * This class implements the Luther sixth order Runge-Kutta
25 * integrator for Ordinary Differential Equations.
26
27 * <p>
28 * This method is described in H. A. Luther 1968 paper <a
29 * href="http://www.ams.org/journals/mcom/1968-22-102/S0025-5718-68-99876-1/S0025-5718-68-99876-1.pdf">
30 * An explicit Sixth-Order Runge-Kutta Formula</a>.
31 * </p>
32
33 * <p>This method is an explicit Runge-Kutta method, its Butcher-array
34 * is the following one :
35 * <pre>
36 * 0 | 0 0 0 0 0 0
37 * 1 | 1 0 0 0 0 0
38 * 1/2 | 3/8 1/8 0 0 0 0
39 * 2/3 | 8/27 2/27 8/27 0 0 0
40 * (7-q)/14 | ( -21 + 9q)/392 ( -56 + 8q)/392 ( 336 - 48q)/392 ( -63 + 3q)/392 0 0
41 * (7+q)/14 | (-1155 - 255q)/1960 ( -280 - 40q)/1960 ( 0 - 320q)/1960 ( 63 + 363q)/1960 ( 2352 + 392q)/1960 0
42 * 1 | ( 330 + 105q)/180 ( 120 + 0q)/180 ( -200 + 280q)/180 ( 126 - 189q)/180 ( -686 - 126q)/180 ( 490 - 70q)/180
43 * |--------------------------------------------------------------------------------------------------------------------------------------------------
44 * | 1/20 0 16/45 0 49/180 49/180 1/20
45 * </pre>
46 * where q = √21
47 *
48 * @see EulerIntegrator
49 * @see ClassicalRungeKuttaIntegrator
50 * @see GillIntegrator
51 * @see MidpointIntegrator
52 * @see ThreeEighthesIntegrator
53 * @since 3.3
54 */
55
56 public class LutherIntegrator extends RungeKuttaIntegrator {
57
58 /** Square root. */
59 private static final double Q = JdkMath.sqrt(21);
60
61 /** Time steps Butcher array. */
62 private static final double[] STATIC_C = {
63 1.0, 1.0 / 2.0, 2.0 / 3.0, (7.0 - Q) / 14.0, (7.0 + Q) / 14.0, 1.0
64 };
65
66 /** Internal weights Butcher array. */
67 private static final double[][] STATIC_A = {
68 { 1.0 },
69 { 3.0 / 8.0, 1.0 / 8.0 },
70 { 8.0 / 27.0, 2.0 / 27.0, 8.0 / 27.0 },
71 { ( -21.0 + 9.0 * Q) / 392.0, ( -56.0 + 8.0 * Q) / 392.0, ( 336.0 - 48.0 * Q) / 392.0, (-63.0 + 3.0 * Q) / 392.0 },
72 { (-1155.0 - 255.0 * Q) / 1960.0, (-280.0 - 40.0 * Q) / 1960.0, ( 0.0 - 320.0 * Q) / 1960.0, ( 63.0 + 363.0 * Q) / 1960.0, (2352.0 + 392.0 * Q) / 1960.0 },
73 { ( 330.0 + 105.0 * Q) / 180.0, ( 120.0 + 0.0 * Q) / 180.0, (-200.0 + 280.0 * Q) / 180.0, (126.0 - 189.0 * Q) / 180.0, (-686.0 - 126.0 * Q) / 180.0, (490.0 - 70.0 * Q) / 180.0 }
74 };
75
76 /** Propagation weights Butcher array. */
77 private static final double[] STATIC_B = {
78 1.0 / 20.0, 0, 16.0 / 45.0, 0, 49.0 / 180.0, 49.0 / 180.0, 1.0 / 20.0
79 };
80
81 /** Simple constructor.
82 * Build a fourth-order Luther integrator with the given step.
83 * @param step integration step
84 */
85 public LutherIntegrator(final double step) {
86 super("Luther", STATIC_C, STATIC_A, STATIC_B, new LutherStepInterpolator(), step);
87 }
88 }