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      1 /*
      2  * Licensed to the Apache Software Foundation (ASF) under one or more
      3  * contributor license agreements.  See the NOTICE file distributed with
      4  * this work for additional information regarding copyright ownership.
      5  * The ASF licenses this file to You under the Apache License, Version 2.0
      6  * (the "License"); you may not use this file except in compliance with
      7  * the License.  You may obtain a copy of the License at
      8  *
      9  *      http://www.apache.org/licenses/LICENSE-2.0
     10  *
     11  * Unless required by applicable law or agreed to in writing, software
     12  * distributed under the License is distributed on an "AS IS" BASIS,
     13  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
     14  * See the License for the specific language governing permissions and
     15  * limitations under the License.
     16  */
     17 
     18 package org.apache.commons.math.ode.nonstiff;
     19 
     20 import org.apache.commons.math.util.FastMath;
     21 
     22 
     23 /**
     24  * This class implements the Gill fourth order Runge-Kutta
     25  * integrator for Ordinary Differential Equations .
     26 
     27  * <p>This method is an explicit Runge-Kutta method, its Butcher-array
     28  * is the following one :
     29  * <pre>
     30  *    0  |    0        0       0      0
     31  *   1/2 |   1/2       0       0      0
     32  *   1/2 | (q-1)/2  (2-q)/2    0      0
     33  *    1  |    0       -q/2  (2+q)/2   0
     34  *       |-------------------------------
     35  *       |   1/6    (2-q)/6 (2+q)/6  1/6
     36  * </pre>
     37  * where q = sqrt(2)</p>
     38  *
     39  * @see EulerIntegrator
     40  * @see ClassicalRungeKuttaIntegrator
     41  * @see MidpointIntegrator
     42  * @see ThreeEighthesIntegrator
     43  * @version $Revision: 990655 $ $Date: 2010-08-29 23:49:40 +0200 (dim. 29 aot 2010) $
     44  * @since 1.2
     45  */
     46 
     47 public class GillIntegrator extends RungeKuttaIntegrator {
     48 
     49   /** Time steps Butcher array. */
     50   private static final double[] STATIC_C = {
     51     1.0 / 2.0, 1.0 / 2.0, 1.0
     52   };
     53 
     54   /** Internal weights Butcher array. */
     55   private static final double[][] STATIC_A = {
     56     { 1.0 / 2.0 },
     57     { (FastMath.sqrt(2.0) - 1.0) / 2.0, (2.0 - FastMath.sqrt(2.0)) / 2.0 },
     58     { 0.0, -FastMath.sqrt(2.0) / 2.0, (2.0 + FastMath.sqrt(2.0)) / 2.0 }
     59   };
     60 
     61   /** Propagation weights Butcher array. */
     62   private static final double[] STATIC_B = {
     63     1.0 / 6.0, (2.0 - FastMath.sqrt(2.0)) / 6.0, (2.0 + FastMath.sqrt(2.0)) / 6.0, 1.0 / 6.0
     64   };
     65 
     66   /** Simple constructor.
     67    * Build a fourth-order Gill integrator with the given step.
     68    * @param step integration step
     69    */
     70   public GillIntegrator(final double step) {
     71     super("Gill", STATIC_C, STATIC_A, STATIC_B, new GillStepInterpolator(), step);
     72   }
     73 
     74 }
     75