001 /*
002 * Licensed to the Apache Software Foundation (ASF) under one or more
003 * contributor license agreements. See the NOTICE file distributed with
004 * this work for additional information regarding copyright ownership.
005 * The ASF licenses this file to You under the Apache License, Version 2.0
006 * (the "License"); you may not use this file except in compliance with
007 * the License. You may obtain a copy of the License at
008 *
009 * http://www.apache.org/licenses/LICENSE-2.0
010 *
011 * Unless required by applicable law or agreed to in writing, software
012 * distributed under the License is distributed on an "AS IS" BASIS,
013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014 * See the License for the specific language governing permissions and
015 * limitations under the License.
016 */
017
018 package org.apache.commons.math.ode.nonstiff;
019
020 import org.apache.commons.math.util.FastMath;
021
022
023 /**
024 * This class implements the Gill fourth order Runge-Kutta
025 * integrator for Ordinary Differential Equations .
026
027 * <p>This method is an explicit Runge-Kutta method, its Butcher-array
028 * is the following one :
029 * <pre>
030 * 0 | 0 0 0 0
031 * 1/2 | 1/2 0 0 0
032 * 1/2 | (q-1)/2 (2-q)/2 0 0
033 * 1 | 0 -q/2 (2+q)/2 0
034 * |-------------------------------
035 * | 1/6 (2-q)/6 (2+q)/6 1/6
036 * </pre>
037 * where q = sqrt(2)</p>
038 *
039 * @see EulerIntegrator
040 * @see ClassicalRungeKuttaIntegrator
041 * @see MidpointIntegrator
042 * @see ThreeEighthesIntegrator
043 * @version $Revision: 990655 $ $Date: 2010-08-29 23:49:40 +0200 (dim. 29 ao??t 2010) $
044 * @since 1.2
045 */
046
047 public class GillIntegrator extends RungeKuttaIntegrator {
048
049 /** Time steps Butcher array. */
050 private static final double[] STATIC_C = {
051 1.0 / 2.0, 1.0 / 2.0, 1.0
052 };
053
054 /** Internal weights Butcher array. */
055 private static final double[][] STATIC_A = {
056 { 1.0 / 2.0 },
057 { (FastMath.sqrt(2.0) - 1.0) / 2.0, (2.0 - FastMath.sqrt(2.0)) / 2.0 },
058 { 0.0, -FastMath.sqrt(2.0) / 2.0, (2.0 + FastMath.sqrt(2.0)) / 2.0 }
059 };
060
061 /** Propagation weights Butcher array. */
062 private static final double[] STATIC_B = {
063 1.0 / 6.0, (2.0 - FastMath.sqrt(2.0)) / 6.0, (2.0 + FastMath.sqrt(2.0)) / 6.0, 1.0 / 6.0
064 };
065
066 /** Simple constructor.
067 * Build a fourth-order Gill integrator with the given step.
068 * @param step integration step
069 */
070 public GillIntegrator(final double step) {
071 super("Gill", STATIC_C, STATIC_A, STATIC_B, new GillStepInterpolator(), step);
072 }
073
074 }