1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
|
/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.commons.math3.ode.nonstiff;
import org.apache.commons.math3.Field;
import org.apache.commons.math3.RealFieldElement;
import org.apache.commons.math3.ode.FieldEquationsMapper;
import org.apache.commons.math3.ode.FieldODEStateAndDerivative;
import org.apache.commons.math3.util.MathArrays;
/**
* This class implements the Luther sixth order Runge-Kutta
* integrator for Ordinary Differential Equations.
* <p>
* This method is described in H. A. Luther 1968 paper <a
* href="http://www.ams.org/journals/mcom/1968-22-102/S0025-5718-68-99876-1/S0025-5718-68-99876-1.pdf">
* An explicit Sixth-Order Runge-Kutta Formula</a>.
* </p>
* <p>This method is an explicit Runge-Kutta method, its Butcher-array
* is the following one :
* <pre>
* 0 | 0 0 0 0 0 0
* 1 | 1 0 0 0 0 0
* 1/2 | 3/8 1/8 0 0 0 0
* 2/3 | 8/27 2/27 8/27 0 0 0
* (7-q)/14 | ( -21 + 9q)/392 ( -56 + 8q)/392 ( 336 - 48q)/392 ( -63 + 3q)/392 0 0
* (7+q)/14 | (-1155 - 255q)/1960 ( -280 - 40q)/1960 ( 0 - 320q)/1960 ( 63 + 363q)/1960 ( 2352 + 392q)/1960 0
* 1 | ( 330 + 105q)/180 ( 120 + 0q)/180 ( -200 + 280q)/180 ( 126 - 189q)/180 ( -686 - 126q)/180 ( 490 - 70q)/180
* |--------------------------------------------------------------------------------------------------------------------------------------------------
* | 1/20 0 16/45 0 49/180 49/180 1/20
* </pre>
* where q = √21</p>
*
* @see EulerFieldIntegrator
* @see ClassicalRungeKuttaFieldIntegrator
* @see GillFieldIntegrator
* @see MidpointFieldIntegrator
* @see ThreeEighthesFieldIntegrator
* @param <T> the type of the field elements
* @since 3.6
*/
public class LutherFieldIntegrator<T extends RealFieldElement<T>>
extends RungeKuttaFieldIntegrator<T> {
/** Simple constructor.
* Build a fourth-order Luther integrator with the given step.
* @param field field to which the time and state vector elements belong
* @param step integration step
*/
public LutherFieldIntegrator(final Field<T> field, final T step) {
super(field, "Luther", step);
}
/** {@inheritDoc} */
public T[] getC() {
final T q = getField().getZero().add(21).sqrt();
final T[] c = MathArrays.buildArray(getField(), 6);
c[0] = getField().getOne();
c[1] = fraction(1, 2);
c[2] = fraction(2, 3);
c[3] = q.subtract(7).divide(-14);
c[4] = q.add(7).divide(14);
c[5] = getField().getOne();
return c;
}
/** {@inheritDoc} */
public T[][] getA() {
final T q = getField().getZero().add(21).sqrt();
final T[][] a = MathArrays.buildArray(getField(), 6, -1);
for (int i = 0; i < a.length; ++i) {
a[i] = MathArrays.buildArray(getField(), i + 1);
}
a[0][0] = getField().getOne();
a[1][0] = fraction(3, 8);
a[1][1] = fraction(1, 8);
a[2][0] = fraction(8, 27);
a[2][1] = fraction(2, 27);
a[2][2] = a[2][0];
a[3][0] = q.multiply( 9).add( -21).divide( 392);
a[3][1] = q.multiply( 8).add( -56).divide( 392);
a[3][2] = q.multiply( -48).add( 336).divide( 392);
a[3][3] = q.multiply( 3).add( -63).divide( 392);
a[4][0] = q.multiply(-255).add(-1155).divide(1960);
a[4][1] = q.multiply( -40).add( -280).divide(1960);
a[4][2] = q.multiply(-320) .divide(1960);
a[4][3] = q.multiply( 363).add( 63).divide(1960);
a[4][4] = q.multiply( 392).add( 2352).divide(1960);
a[5][0] = q.multiply( 105).add( 330).divide( 180);
a[5][1] = fraction(2, 3);
a[5][2] = q.multiply( 280).add( -200).divide( 180);
a[5][3] = q.multiply(-189).add( 126).divide( 180);
a[5][4] = q.multiply(-126).add( -686).divide( 180);
a[5][5] = q.multiply( -70).add( 490).divide( 180);
return a;
}
/** {@inheritDoc} */
public T[] getB() {
final T[] b = MathArrays.buildArray(getField(), 7);
b[0] = fraction( 1, 20);
b[1] = getField().getZero();
b[2] = fraction(16, 45);
b[3] = getField().getZero();
b[4] = fraction(49, 180);
b[5] = b[4];
b[6] = b[0];
return b;
}
/** {@inheritDoc} */
@Override
protected LutherFieldStepInterpolator<T>
createInterpolator(final boolean forward, T[][] yDotK,
final FieldODEStateAndDerivative<T> globalPreviousState,
final FieldODEStateAndDerivative<T> globalCurrentState,
final FieldEquationsMapper<T> mapper) {
return new LutherFieldStepInterpolator<T>(getField(), forward, yDotK,
globalPreviousState, globalCurrentState,
globalPreviousState, globalCurrentState,
mapper);
}
}
|
