| /* |
| * 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; |
| |
| import org.apache.commons.math4.legacy.core.Field; |
| import org.apache.commons.math4.legacy.core.RealFieldElement; |
| import org.apache.commons.math4.legacy.ode.FieldEquationsMapper; |
| import org.apache.commons.math4.legacy.ode.FieldODEStateAndDerivative; |
| import org.apache.commons.math4.legacy.core.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} */ |
| @Override |
| public T[] getC() { |
| return MathArrays.buildArray(getField(), 0); |
| } |
| |
| /** {@inheritDoc} */ |
| @Override |
| public T[][] getA() { |
| return MathArrays.buildArray(getField(), 0, 0); |
| } |
| |
| /** {@inheritDoc} */ |
| @Override |
| 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<>(getField(), forward, yDotK, |
| globalPreviousState, globalCurrentState, |
| globalPreviousState, globalCurrentState, |
| mapper); |
| } |
| |
| } |