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.math3.ode.nonstiff;
019    
020    import org.apache.commons.math3.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 $Id: GillIntegrator.java 1416643 2012-12-03 19:37:14Z tn $
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    }