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.nonstiff;
19
20
21 /**
22 * This class implements a simple Euler integrator for Ordinary
23 * Differential Equations.
24 *
25 * <p>The Euler algorithm is the simplest one that can be used to
26 * integrate ordinary differential equations. It is a simple inversion
27 * of the forward difference expression :
28 * <code>f'=(f(t+h)-f(t))/h</code> which leads to
29 * <code>f(t+h)=f(t)+hf'</code>. The interpolation scheme used for
30 * dense output is the linear scheme already used for integration.</p>
31 *
32 * <p>This algorithm looks cheap because it needs only one function
33 * evaluation per step. However, as it uses linear estimates, it needs
34 * very small steps to achieve high accuracy, and small steps lead to
35 * numerical errors and instabilities.</p>
36 *
37 * <p>This algorithm is almost never used and has been included in
38 * this package only as a comparison reference for more useful
39 * integrators.</p>
40 *
41 * @see MidpointIntegrator
42 * @see ClassicalRungeKuttaIntegrator
43 * @see GillIntegrator
44 * @see ThreeEighthesIntegrator
45 * @see LutherIntegrator
46 * @since 1.2
47 */
48
49 public class EulerIntegrator extends RungeKuttaIntegrator {
50
51 /** Time steps Butcher array. */
52 private static final double[] STATIC_C = {
53 };
54
55 /** Internal weights Butcher array. */
56 private static final double[][] STATIC_A = {
57 };
58
59 /** Propagation weights Butcher array. */
60 private static final double[] STATIC_B = {
61 1.0
62 };
63
64 /** Simple constructor.
65 * Build an Euler integrator with the given step.
66 * @param step integration step
67 */
68 public EulerIntegrator(final double step) {
69 super("Euler", STATIC_C, STATIC_A, STATIC_B, new EulerStepInterpolator(), step);
70 }
71 }