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    
021    /**
022     * This class implements the Gill fourth order Runge-Kutta
023     * integrator for Ordinary Differential Equations .
024    
025     * <p>This method is an explicit Runge-Kutta method, its Butcher-array
026     * is the following one :
027     * <pre>
028     *    0  |    0        0       0      0
029     *   1/2 |   1/2       0       0      0
030     *   1/2 | (q-1)/2  (2-q)/2    0      0
031     *    1  |    0       -q/2  (2+q)/2   0
032     *       |-------------------------------
033     *       |   1/6    (2-q)/6 (2+q)/6  1/6
034     * </pre>
035     * where q = sqrt(2)</p>
036     *
037     * @see EulerIntegrator
038     * @see ClassicalRungeKuttaIntegrator
039     * @see MidpointIntegrator
040     * @see ThreeEighthesIntegrator
041     * @version $Revision: 786881 $ $Date: 2009-06-20 14:53:08 -0400 (Sat, 20 Jun 2009) $
042     * @since 1.2
043     */
044    
045    public class GillIntegrator extends RungeKuttaIntegrator {
046    
047      /** Time steps Butcher array. */
048      private static final double[] c = {
049        1.0 / 2.0, 1.0 / 2.0, 1.0
050      };
051    
052      /** Internal weights Butcher array. */
053      private static final double[][] a = {
054        { 1.0 / 2.0 },
055        { (Math.sqrt(2.0) - 1.0) / 2.0, (2.0 - Math.sqrt(2.0)) / 2.0 },
056        { 0.0, -Math.sqrt(2.0) / 2.0, (2.0 + Math.sqrt(2.0)) / 2.0 }
057      };
058    
059      /** Propagation weights Butcher array. */
060      private static final double[] b = {
061        1.0 / 6.0, (2.0 - Math.sqrt(2.0)) / 6.0, (2.0 + Math.sqrt(2.0)) / 6.0, 1.0 / 6.0
062      };
063    
064      /** Simple constructor.
065       * Build a fourth-order Gill integrator with the given step.
066       * @param step integration step
067       */
068      public GillIntegrator(final double step) {
069        super("Gill", c, a, b, new GillStepInterpolator(), step);
070      }
071    
072    }