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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
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 * 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
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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.
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 :
f'=(f(t+h)-f(t))/h which leads to
f(t+h)=f(t)+hf'. The interpolation scheme used for
dense output is the linear scheme already used for integration.
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.
This algorithm is almost never used and has been included in
this package only as a comparison reference for more useful
integrators.
Type parameters:
<T> – the type of the field elements
See Also:
MidpointFieldIntegrator
ClassicalRungeKuttaFieldIntegrator
GillFieldIntegrator
ThreeEighthesFieldIntegrator
LutherFieldIntegrator
Since:
3.6/**
 * 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.
Params:
field – field to which the time and state vector elements belong
step – integration step/** 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} /** {@inheritDoc} */
    public T[] getC() {
        return MathArrays.buildArray(getField(), 0);
    }

    
{@inheritDoc} /** {@inheritDoc} */
    public T[][] getA() {
        return MathArrays.buildArray(getField(), 0, 0);
    }

    
{@inheritDoc} /** {@inheritDoc} */
    public T[] getB() {
        final T[] b = MathArrays.buildArray(getField(), 1);
        b[0] = getField().getOne();
        return b;
    }

    
{@inheritDoc} /** {@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);
    }

}