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