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/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.commons.math3.ode.nonstiff;
import org.apache.commons.math3.Field;
import org.apache.commons.math3.RealFieldElement;
import org.apache.commons.math3.ode.FieldEquationsMapper;
import org.apache.commons.math3.ode.FieldODEStateAndDerivative;
import org.apache.commons.math3.util.MathArrays;
/**
* This class implements a simple Euler integrator for Ordinary
* Differential Equations.
*
* <p>The Euler algorithm is the simplest one that can be used to
* integrate ordinary differential equations. It is a simple inversion
* of the forward difference expression :
* <code>f'=(f(t+h)-f(t))/h</code> which leads to
* <code>f(t+h)=f(t)+hf'</code>. The interpolation scheme used for
* dense output is the linear scheme already used for integration.</p>
*
* <p>This algorithm looks cheap because it needs only one function
* evaluation per step. However, as it uses linear estimates, it needs
* very small steps to achieve high accuracy, and small steps lead to
* numerical errors and instabilities.</p>
*
* <p>This algorithm is almost never used and has been included in
* this package only as a comparison reference for more useful
* integrators.</p>
*
* @see MidpointFieldIntegrator
* @see ClassicalRungeKuttaFieldIntegrator
* @see GillFieldIntegrator
* @see ThreeEighthesFieldIntegrator
* @see LutherFieldIntegrator
* @param <T> the type of the field elements
* @since 3.6
*/
public class EulerFieldIntegrator<T extends RealFieldElement<T>> extends RungeKuttaFieldIntegrator<T> {
/** Simple constructor.
* Build an Euler integrator with the given step.
* @param field field to which the time and state vector elements belong
* @param step integration step
*/
public EulerFieldIntegrator(final Field<T> field, final T step) {
super(field, "Euler", step);
}
/** {@inheritDoc} */
public T[] getC() {
return MathArrays.buildArray(getField(), 0);
}
/** {@inheritDoc} */
public T[][] getA() {
return MathArrays.buildArray(getField(), 0, 0);
}
/** {@inheritDoc} */
public T[] getB() {
final T[] b = MathArrays.buildArray(getField(), 1);
b[0] = getField().getOne();
return b;
}
/** {@inheritDoc} */
@Override
protected EulerFieldStepInterpolator<T>
createInterpolator(final boolean forward, T[][] yDotK,
final FieldODEStateAndDerivative<T> globalPreviousState,
final FieldODEStateAndDerivative<T> globalCurrentState,
final FieldEquationsMapper<T> mapper) {
return new EulerFieldStepInterpolator<T>(getField(), forward, yDotK,
globalPreviousState, globalCurrentState,
globalPreviousState, globalCurrentState,
mapper);
}
}
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