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 * 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 /*
19 * This is not the original file distributed by the Apache Software Foundation
20 * It has been modified by the Hipparchus project
21 */
22
23 package org.hipparchus.ode;
24
25 import org.hipparchus.util.FastMath;
26
27 /**
28 * This class is used in the junit tests for the ODE integrators.
29
30 * <p>This specific problem is the following differential equation :
31 * <pre>
32 * y' = t^3 - t y
33 * </pre>
34 * with the initial condition y (0) = 0. The solution of this equation
35 * is the following function :
36 * <pre>
37 * y (t) = t^2 + 2 (exp (- t^2 / 2) - 1)
38 * </pre>
39 * </p>
40
41 */
42 public class TestProblem2 extends TestProblemAbstract {
43
44 /**
45 * Simple constructor.
46 */
47 public TestProblem2() {
48 super(0.0, new double[] { 0.0 }, 1.0, new double[] { 1.0 });
49 }
50
51 @Override
52 public double[] doComputeDerivatives(double t, double[] y) {
53
54 // compute the derivatives
55 final double[] yDot = new double[getDimension()];
56 for (int i = 0; i < getDimension(); ++i) {
57 yDot[i] = t * (t * t - y[i]);
58 }
59 return yDot;
60
61 }
62
63 @Override
64 public double[] computeTheoreticalState(double t) {
65 final double[] y = new double[getDimension()];
66 double t2 = t * t;
67 double c = t2 + 2 * (FastMath.exp (-0.5 * t2) - 1);
68 for (int i = 0; i < getDimension(); ++i) {
69 y[i] = c;
70 }
71 return y;
72 }
73
74 }