1 /*
2 * Licensed to the Hipparchus project 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 Hipparchus project 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 * https://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.hipparchus.ode.nonstiff;
19
20 import org.hipparchus.ode.EquationsMapper;
21 import org.hipparchus.ode.ODEStateAndDerivative;
22 import org.hipparchus.util.FastMath;
23
24
25 /**
26 * This class implements the Luther sixth order Runge-Kutta
27 * integrator for Ordinary Differential Equations.
28
29 * <p>
30 * This method is described in H. A. Luther 1968 paper <a
31 * href="http://www.ams.org/journals/mcom/1968-22-102/S0025-5718-68-99876-1/S0025-5718-68-99876-1.pdf">
32 * An explicit Sixth-Order Runge-Kutta Formula</a>.
33 * </p>
34
35 * <p>This method is an explicit Runge-Kutta method, its Butcher-array
36 * is the following one :</p>
37 * <pre>
38 * 0 | 0 0 0 0 0 0
39 * 1 | 1 0 0 0 0 0
40 * 1/2 | 3/8 1/8 0 0 0 0
41 * 2/3 | 8/27 2/27 8/27 0 0 0
42 * (7-q)/14 | ( -21 + 9q)/392 ( -56 + 8q)/392 ( 336 - 48q)/392 ( -63 + 3q)/392 0 0
43 * (7+q)/14 | (-1155 - 255q)/1960 ( -280 - 40q)/1960 ( 0 - 320q)/1960 ( 63 + 363q)/1960 ( 2352 + 392q)/1960 0
44 * 1 | ( 330 + 105q)/180 ( 120 + 0q)/180 ( -200 + 280q)/180 ( 126 - 189q)/180 ( -686 - 126q)/180 ( 490 - 70q)/180
45 * |--------------------------------------------------------------------------------------------------------------------------------------------------
46 * | 1/20 0 16/45 0 49/180 49/180 1/20
47 * </pre>
48 * <p>where q = √21</p>
49 *
50 * @see EulerIntegrator
51 * @see ClassicalRungeKuttaIntegrator
52 * @see GillIntegrator
53 * @see MidpointIntegrator
54 * @see ThreeEighthesIntegrator
55 */
56
57 public class LutherIntegrator extends RungeKuttaIntegrator {
58
59 /** Name of integration scheme. */
60 public static final String METHOD_NAME = "Luther";
61
62 /** Square root. */
63 private static final double Q = FastMath.sqrt(21);
64
65 /** Simple constructor.
66 * Build a fourth-order Luther integrator with the given step.
67 * @param step integration step
68 */
69 public LutherIntegrator(final double step) {
70 super(METHOD_NAME, step);
71 }
72
73 /** {@inheritDoc} */
74 @Override
75 public double[] getC() {
76 return new double[] {
77 1.0, 1.0 / 2.0, 2.0 / 3.0, (7.0 - Q) / 14.0, (7.0 + Q) / 14.0, 1.0
78 };
79 }
80
81 /** {@inheritDoc} */
82 @Override
83 public double[][] getA() {
84 return new double[][] {
85 { 1.0 },
86 { 3.0 / 8.0, 1.0 / 8.0 },
87 { 8.0 / 27.0, 2.0 / 27.0, 8.0 / 27.0 },
88 { ( -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 },
89 { (-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 },
90 { ( 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 }
91 };
92 }
93
94 /** {@inheritDoc} */
95 @Override
96 public double[] getB() {
97 return new double[] {
98 1.0 / 20.0, 0, 16.0 / 45.0, 0, 49.0 / 180.0, 49.0 / 180.0, 1.0 / 20.0
99 };
100 }
101
102 /** {@inheritDoc} */
103 @Override
104 protected LutherStateInterpolator
105 createInterpolator(final boolean forward, double[][] yDotK,
106 final ODEStateAndDerivative globalPreviousState,
107 final ODEStateAndDerivative globalCurrentState,
108 final EquationsMapper mapper) {
109 return new LutherStateInterpolator(forward, yDotK,
110 globalPreviousState, globalCurrentState,
111 globalPreviousState, globalCurrentState,
112 mapper);
113 }
114
115 }