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
23 /**
24 * This class implements a simple Euler integrator for Ordinary
25 * Differential Equations.
26 *
27 * <p>The Euler algorithm is the simplest one that can be used to
28 * integrate ordinary differential equations. It is a simple inversion
29 * of the forward difference expression :
30 * <code>f'=(f(t+h)-f(t))/h</code> which leads to
31 * <code>f(t+h)=f(t)+hf'</code>. The interpolation scheme used for
32 * dense output is the linear scheme already used for integration.</p>
33 *
34 * <p>This algorithm looks cheap because it needs only one function
35 * evaluation per step. However, as it uses linear estimates, it needs
36 * very small steps to achieve high accuracy, and small steps lead to
37 * numerical errors and instabilities.</p>
38 *
39 * <p>This algorithm is almost never used and has been included in
40 * this package only as a comparison reference for more useful
41 * integrators.</p>
42 *
43 * @see MidpointIntegrator
44 * @see ClassicalRungeKuttaIntegrator
45 * @see GillIntegrator
46 * @see ThreeEighthesIntegrator
47 * @see LutherIntegrator
48 */
49
50 public class EulerIntegrator extends RungeKuttaIntegrator {
51
52 /** Name of integration scheme. */
53 public static final String METHOD_NAME = "Euler";
54
55 /** Simple constructor.
56 * Build an Euler integrator with the given step.
57 * @param step integration step
58 */
59 public EulerIntegrator(final double step) {
60 super(METHOD_NAME, step);
61 }
62
63 /** {@inheritDoc} */
64 @Override
65 public double[] getC() {
66 return new double[0];
67 }
68
69 /** {@inheritDoc} */
70 @Override
71 public double[][] getA() {
72 return new double[0][];
73 }
74
75 /** {@inheritDoc} */
76 @Override
77 public double[] getB() {
78 return new double[] { 1 };
79 }
80
81 /** {@inheritDoc} */
82 @Override
83 protected EulerStateInterpolator
84 createInterpolator(final boolean forward, double[][] yDotK,
85 final ODEStateAndDerivative globalPreviousState,
86 final ODEStateAndDerivative globalCurrentState,
87 final EquationsMapper mapper) {
88 return new EulerStateInterpolator(forward, yDotK,
89 globalPreviousState, globalCurrentState,
90 globalPreviousState, globalCurrentState,
91 mapper);
92 }
93
94 }