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.nonstiff;
24
25 import org.hipparchus.CalculusFieldElement;
26 import org.hipparchus.Field;
27 import org.hipparchus.ode.FieldEquationsMapper;
28 import org.hipparchus.ode.FieldODEStateAndDerivative;
29 import org.hipparchus.util.MathArrays;
30
31 /**
32 * This class implements a simple Euler integrator for Ordinary
33 * Differential Equations.
34 *
35 * <p>The Euler algorithm is the simplest one that can be used to
36 * integrate ordinary differential equations. It is a simple inversion
37 * of the forward difference expression :
38 * <code>f'=(f(t+h)-f(t))/h</code> which leads to
39 * <code>f(t+h)=f(t)+hf'</code>. The interpolation scheme used for
40 * dense output is the linear scheme already used for integration.</p>
41 *
42 * <p>This algorithm looks cheap because it needs only one function
43 * evaluation per step. However, as it uses linear estimates, it needs
44 * very small steps to achieve high accuracy, and small steps lead to
45 * numerical errors and instabilities.</p>
46 *
47 * <p>This algorithm is almost never used and has been included in
48 * this package only as a comparison reference for more useful
49 * integrators.</p>
50 *
51 * @see MidpointFieldIntegrator
52 * @see ClassicalRungeKuttaFieldIntegrator
53 * @see GillFieldIntegrator
54 * @see ThreeEighthesFieldIntegrator
55 * @see LutherFieldIntegrator
56 * @param <T> the type of the field elements
57 */
58
59 public class EulerFieldIntegrator<T extends CalculusFieldElement<T>> extends RungeKuttaFieldIntegrator<T> {
60
61 /** Name of integration scheme. */
62 public static final String METHOD_NAME = EulerIntegrator.METHOD_NAME;
63
64 /** Simple constructor.
65 * Build an Euler integrator with the given step.
66 * @param field field to which the time and state vector elements belong
67 * @param step integration step
68 */
69 public EulerFieldIntegrator(final Field<T> field, final T step) {
70 super(field, METHOD_NAME, step);
71 }
72
73 /** {@inheritDoc} */
74 @Override
75 public T[] getC() {
76 return MathArrays.buildArray(getField(), 0);
77 }
78
79 /** {@inheritDoc} */
80 @Override
81 public T[][] getA() {
82 return MathArrays.buildArray(getField(), 0, 0);
83 }
84
85 /** {@inheritDoc} */
86 @Override
87 public T[] getB() {
88 final T[] b = MathArrays.buildArray(getField(), 1);
89 b[0] = getField().getOne();
90 return b;
91 }
92
93 /** {@inheritDoc} */
94 @Override
95 protected EulerFieldStateInterpolator<T>
96 createInterpolator(final boolean forward, T[][] yDotK,
97 final FieldODEStateAndDerivative<T> globalPreviousState,
98 final FieldODEStateAndDerivative<T> globalCurrentState,
99 final FieldEquationsMapper<T> mapper) {
100 return new EulerFieldStateInterpolator<T>(getField(), forward, yDotK,
101 globalPreviousState, globalCurrentState,
102 globalPreviousState, globalCurrentState,
103 mapper);
104 }
105
106 }