| /* |
| * 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.math4.legacy.ode.nonstiff; |
| |
| |
| /** |
| * 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 |
| * @since 1.2 |
| */ |
| |
| public class EulerIntegrator extends RungeKuttaIntegrator { |
| |
| /** Time steps Butcher array. */ |
| private static final double[] STATIC_C = { |
| }; |
| |
| /** Internal weights Butcher array. */ |
| private static final double[][] STATIC_A = { |
| }; |
| |
| /** Propagation weights Butcher array. */ |
| private static final double[] STATIC_B = { |
| 1.0 |
| }; |
| |
| /** Simple constructor. |
| * Build an Euler integrator with the given step. |
| * @param step integration step |
| */ |
| public EulerIntegrator(final double step) { |
| super("Euler", STATIC_C, STATIC_A, STATIC_B, new EulerStepInterpolator(), step); |
| } |
| |
| } |