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;
19
20 import org.apache.commons.math4.legacy.core.Field;
21 import org.apache.commons.math4.legacy.core.RealFieldElement;
22 import org.apache.commons.math4.legacy.core.MathArrays;
23
24 /**
25 * This class is used in the junit tests for the ODE integrators.
26
27 * <p>This specific problem is the following differential equation :
28 * <pre>
29 * y' = t^3 - t y
30 * </pre>
31 * with the initial condition y (0) = 0. The solution of this equation
32 * is the following function :
33 * <pre>
34 * y (t) = t^2 + 2 (exp (- t^2 / 2) - 1)
35 * </pre>
36 * </p>
37
38 * @param <T> the type of the field elements
39 */
40 public class TestFieldProblem2<T extends RealFieldElement<T>>
41 extends TestFieldProblemAbstract<T> {
42
43 /**
44 * Simple constructor.
45 * @param field field to which elements belong
46 */
47 public TestFieldProblem2(Field<T> field) {
48 super(field);
49 setInitialConditions(convert(0.0), convert(new double[] { 0.0 }));
50 setFinalConditions(convert(1.0));
51 setErrorScale(convert(new double[] { 1.0 }));
52 }
53
54 @Override
55 public T[] doComputeDerivatives(T t, T[] y) {
56
57 final T[] yDot = MathArrays.buildArray(getField(), getDimension());
58 // compute the derivatives
59 for (int i = 0; i < getDimension(); ++i) {
60 yDot[i] = t.multiply(t.multiply(t).subtract(y[i]));
61 }
62
63 return yDot;
64 }
65
66 @Override
67 public T[] computeTheoreticalState(T t) {
68 final T[] y = MathArrays.buildArray(getField(), getDimension());
69 T t2 = t.multiply(t);
70 T c = t2.add(t2.multiply(-0.5).exp().subtract(1).multiply(2));
71 for (int i = 0; i < getDimension(); ++i) {
72 y[i] = c;
73 }
74 return y;
75 }
76 }