EulerIntegrator.java

/*
 * Licensed to the Hipparchus project under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The Hipparchus project 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
 *
 *      https://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.hipparchus.ode.nonstiff;

import org.hipparchus.ode.EquationsMapper;
import org.hipparchus.ode.ODEStateAndDerivative;
import org.hipparchus.ode.nonstiff.interpolators.EulerStateInterpolator;

/**
 * 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 MidpointIntegrator
 * @see ClassicalRungeKuttaIntegrator
 * @see GillIntegrator
 * @see ThreeEighthesIntegrator
 * @see LutherIntegrator
 */

public class EulerIntegrator extends FixedStepRungeKuttaIntegrator {

    /** Name of integration scheme. */
    public static final String METHOD_NAME = "Euler";

    /** Simple constructor.
     * Build an Euler integrator with the given step.
     * @param step integration step
     */
    public EulerIntegrator(final double step) {
        super(METHOD_NAME, step);
    }

    /** {@inheritDoc} */
    @Override
    public double[] getC() {
        return new double[0];
    }

    /** {@inheritDoc} */
    @Override
    public double[][] getA() {
        return new double[0][];
    }

    /** {@inheritDoc} */
    @Override
    public double[] getB() {
        return new double[] { 1 };
    }

    /** {@inheritDoc} */
    @Override
    protected EulerStateInterpolator createInterpolator(final boolean forward, final double[][] yDotK,
                                                        final ODEStateAndDerivative globalPreviousState,
                                                        final ODEStateAndDerivative globalCurrentState,
                                                        final EquationsMapper mapper) {
        return new EulerStateInterpolator(forward, yDotK, globalPreviousState, globalCurrentState,
                                         globalPreviousState, globalCurrentState, mapper);
    }

}