/* * 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; /** * 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 RungeKuttaIntegrator { /** 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, double[][] yDotK, final ODEStateAndDerivative globalPreviousState, final ODEStateAndDerivative globalCurrentState, final EquationsMapper mapper) { return new EulerStateInterpolator(forward, yDotK, globalPreviousState, globalCurrentState, globalPreviousState, globalCurrentState, mapper); } }