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.ode.nonstiff.interpolators.EulerFieldStateInterpolator;
30 import org.hipparchus.util.MathArrays;
31
32 /**
33 * This class implements a simple Euler integrator for Ordinary
34 * Differential Equations.
35 *
36 * <p>The Euler algorithm is the simplest one that can be used to
37 * integrate ordinary differential equations. It is a simple inversion
38 * of the forward difference expression :
39 * <code>f'=(f(t+h)-f(t))/h</code> which leads to
40 * <code>f(t+h)=f(t)+hf'</code>. The interpolation scheme used for
41 * dense output is the linear scheme already used for integration.</p>
42 *
43 * <p>This algorithm looks cheap because it needs only one function
44 * evaluation per step. However, as it uses linear estimates, it needs
45 * very small steps to achieve high accuracy, and small steps lead to
46 * numerical errors and instabilities.</p>
47 *
48 * <p>This algorithm is almost never used and has been included in
49 * this package only as a comparison reference for more useful
50 * integrators.</p>
51 *
52 * @see MidpointFieldIntegrator
53 * @see ClassicalRungeKuttaFieldIntegrator
54 * @see GillFieldIntegrator
55 * @see ThreeEighthesFieldIntegrator
56 * @see LutherFieldIntegrator
57 * @param <T> the type of the field elements
58 */
59
60 public class EulerFieldIntegrator<T extends CalculusFieldElement<T>> extends FixedStepRungeKuttaFieldIntegrator<T> {
61
62 /** Name of integration scheme. */
63 public static final String METHOD_NAME = EulerIntegrator.METHOD_NAME;
64
65 /** Simple constructor.
66 * Build an Euler integrator with the given step.
67 * @param field field to which the time and state vector elements belong
68 * @param step integration step
69 */
70 public EulerFieldIntegrator(final Field<T> field, final T step) {
71 super(field, METHOD_NAME, step);
72 }
73
74 /** {@inheritDoc} */
75 @Override
76 public T[] getC() {
77 return MathArrays.buildArray(getField(), 0);
78 }
79
80 /** {@inheritDoc} */
81 @Override
82 public T[][] getA() {
83 return MathArrays.buildArray(getField(), 0, 0);
84 }
85
86 /** {@inheritDoc} */
87 @Override
88 public T[] getB() {
89 final T[] b = MathArrays.buildArray(getField(), 1);
90 b[0] = getField().getOne();
91 return b;
92 }
93
94 /** {@inheritDoc} */
95 @Override
96 protected EulerFieldStateInterpolator<T>
97 createInterpolator(final boolean forward, T[][] yDotK,
98 final FieldODEStateAndDerivative<T> globalPreviousState,
99 final FieldODEStateAndDerivative<T> globalCurrentState,
100 final FieldEquationsMapper<T> mapper) {
101 return new EulerFieldStateInterpolator<>(getField(), forward, yDotK,
102 globalPreviousState, globalCurrentState,
103 globalPreviousState, globalCurrentState,
104 mapper);
105 }
106
107 }