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.math.ode;
19  
20  /**
21   * This class is used in the junit tests for the ODE integrators.
22  
23   * <p>This specific problem is the following differential equation :
24   * <pre>
25   *    y' = t^3 - t y
26   * </pre>
27   * with the initial condition y (0) = 0. The solution of this equation
28   * is the following function :
29   * <pre>
30   *   y (t) = t^2 + 2 (ext (- t^2 / 2) - 1)
31   * </pre>
32   * </p>
33  
34   */
35  class TestProblem2
36    extends TestProblemAbstract {
37  
38    /** theoretical state */
39    private double[] y;
40  
41    /**
42     * Simple constructor.
43     */
44    public TestProblem2() {
45      super();
46      double[] y0 = { 0.0 };
47      setInitialConditions(0.0, y0);
48      setFinalConditions(1.0);
49      double[] errorScale = { 1.0 };
50      setErrorScale(errorScale);
51      y = new double[y0.length];
52    }
53   
54    /**
55     * Copy constructor.
56     * @param problem problem to copy
57     */
58    public TestProblem2(TestProblem2 problem) {
59      super(problem);
60      y = (double[]) problem.y.clone();
61    }
62  
63    /**
64     * Clone operation.
65     * @return a copy of the instance
66     */
67    public Object clone() {
68      return new TestProblem2(this);
69    }
70  
71    public void doComputeDerivatives(double t, double[] y, double[] yDot) {
72  
73      // compute the derivatives
74      for (int i = 0; i < n; ++i)
75        yDot[i] = t * (t * t - y[i]);
76  
77    }
78  
79    public double[] computeTheoreticalState(double t) {
80      double t2 = t * t;
81      double c = t2 + 2 * (Math.exp (-0.5 * t2) - 1);
82      for (int i = 0; i < n; ++i) {
83        y[i] = c;
84      }
85      return y;
86    }
87  
88  }