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.HighamHall54StateInterpolator;
23 import org.hipparchus.util.FastMath;
24
25
26 /**
27 * This class implements the 5(4) Higham and Hall integrator for
28 * Ordinary Differential Equations.
29 *
30 * <p>This integrator is an embedded Runge-Kutta integrator
31 * of order 5(4) used in local extrapolation mode (i.e. the solution
32 * is computed using the high order formula) with stepsize control
33 * (and automatic step initialization) and continuous output. This
34 * method uses 7 functions evaluations per step.</p>
35 *
36 */
37
38 public class HighamHall54Integrator extends EmbeddedRungeKuttaIntegrator {
39
40 /** Name of integration scheme. */
41 public static final String METHOD_NAME = "Higham-Hall 5(4)";
42
43 /** Error weights Butcher array. */
44 static final double[] STATIC_E = {
45 -1.0/20.0, 0.0, 81.0/160.0, -6.0/5.0, 25.0/32.0, 1.0/16.0, -1.0/10.0
46 };
47
48 /** Simple constructor.
49 * Build a fifth order Higham and Hall integrator with the given step bounds
50 * @param minStep minimal step (sign is irrelevant, regardless of
51 * integration direction, forward or backward), the last step can
52 * be smaller than this
53 * @param maxStep maximal step (sign is irrelevant, regardless of
54 * integration direction, forward or backward), the last step can
55 * be smaller than this
56 * @param scalAbsoluteTolerance allowed absolute error
57 * @param scalRelativeTolerance allowed relative error
58 */
59 public HighamHall54Integrator(final double minStep, final double maxStep,
60 final double scalAbsoluteTolerance,
61 final double scalRelativeTolerance) {
62 super(METHOD_NAME, -1,
63 minStep, maxStep, scalAbsoluteTolerance, scalRelativeTolerance);
64 }
65
66 /** Simple constructor.
67 * Build a fifth order Higham and Hall integrator with the given step bounds
68 * @param minStep minimal step (sign is irrelevant, regardless of
69 * integration direction, forward or backward), the last step can
70 * be smaller than this
71 * @param maxStep maximal step (sign is irrelevant, regardless of
72 * integration direction, forward or backward), the last step can
73 * be smaller than this
74 * @param vecAbsoluteTolerance allowed absolute error
75 * @param vecRelativeTolerance allowed relative error
76 */
77 public HighamHall54Integrator(final double minStep, final double maxStep,
78 final double[] vecAbsoluteTolerance,
79 final double[] vecRelativeTolerance) {
80 super(METHOD_NAME, -1,
81 minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance);
82 }
83
84 /** {@inheritDoc} */
85 @Override
86 public double[] getC() {
87 return new double[] {
88 2.0/9.0, 1.0/3.0, 1.0/2.0, 3.0/5.0, 1.0, 1.0
89 };
90 }
91
92 /** {@inheritDoc} */
93 @Override
94 public double[][] getA() {
95 return new double[][] {
96 {2.0/9.0},
97 {1.0/12.0, 1.0/4.0},
98 {1.0/8.0, 0.0, 3.0/8.0},
99 {91.0/500.0, -27.0/100.0, 78.0/125.0, 8.0/125.0},
100 {-11.0/20.0, 27.0/20.0, 12.0/5.0, -36.0/5.0, 5.0},
101 {1.0/12.0, 0.0, 27.0/32.0, -4.0/3.0, 125.0/96.0, 5.0/48.0}
102 };
103 }
104
105 /** {@inheritDoc} */
106 @Override
107 public double[] getB() {
108 return new double[] {
109 1.0/12.0, 0.0, 27.0/32.0, -4.0/3.0, 125.0/96.0, 5.0/48.0, 0.0
110 };
111 }
112
113 /** {@inheritDoc} */
114 @Override
115 protected HighamHall54StateInterpolator
116 createInterpolator(final boolean forward, double[][] yDotK,
117 final ODEStateAndDerivative globalPreviousState,
118 final ODEStateAndDerivative globalCurrentState,
119 final EquationsMapper mapper) {
120 return new HighamHall54StateInterpolator(forward, yDotK,
121 globalPreviousState, globalCurrentState,
122 globalPreviousState, globalCurrentState,
123 mapper);
124 }
125
126 /** {@inheritDoc} */
127 @Override
128 public int getOrder() {
129 return 5;
130 }
131
132 /** {@inheritDoc} */
133 @Override
134 protected double estimateError(final double[][] yDotK,
135 final double[] y0, final double[] y1,
136 final double h) {
137
138 final StepsizeHelper helper = getStepSizeHelper();
139 double error = 0;
140
141 for (int j = 0; j < helper.getMainSetDimension(); ++j) {
142 double errSum = STATIC_E[0] * yDotK[0][j];
143 for (int l = 1; l < STATIC_E.length; ++l) {
144 errSum += STATIC_E[l] * yDotK[l][j];
145 }
146
147 final double tol = helper.getTolerance(j, FastMath.max(FastMath.abs(y0[j]), FastMath.abs(y1[j])));
148 final double ratio = h * errSum / tol;
149 error += ratio * ratio;
150
151 }
152
153 return FastMath.sqrt(error / helper.getMainSetDimension());
154
155 }
156
157 }