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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 
     21 /**
     22  * This class implements the classical fourth order Runge-Kutta
     23  * integrator for Ordinary Differential Equations (it is the most
     24  * often used Runge-Kutta method).
     25  *
     26  * <p>This method is an explicit Runge-Kutta method, its Butcher-array
     27  * is the following one :
     28  * <pre>
     29  *    0  |  0    0    0    0
     30  *   1/2 | 1/2   0    0    0
     31  *   1/2 |  0   1/2   0    0
     32  *    1  |  0    0    1    0
     33  *       |--------------------
     34  *       | 1/6  1/3  1/3  1/6
     35  * </pre>
     36  * </p>
     37  *
     38  * @see EulerIntegrator
     39  * @see GillIntegrator
     40  * @see MidpointIntegrator
     41  * @see ThreeEighthesIntegrator
     42  * @version $Revision: 810196 $ $Date: 2009-09-01 21:47:46 +0200 (mar. 01 sept. 2009) $
     43  * @since 1.2
     44  */
     45 
     46 public class ClassicalRungeKuttaIntegrator extends RungeKuttaIntegrator {
     47 
     48   /** Time steps Butcher array. */
     49   private static final double[] STATIC_C = {
     50     1.0 / 2.0, 1.0 / 2.0, 1.0
     51   };
     52 
     53   /** Internal weights Butcher array. */
     54   private static final double[][] STATIC_A = {
     55     { 1.0 / 2.0 },
     56     { 0.0, 1.0 / 2.0 },
     57     { 0.0, 0.0, 1.0 }
     58   };
     59 
     60   /** Propagation weights Butcher array. */
     61   private static final double[] STATIC_B = {
     62     1.0 / 6.0, 1.0 / 3.0, 1.0 / 3.0, 1.0 / 6.0
     63   };
     64 
     65   /** Simple constructor.
     66    * Build a fourth-order Runge-Kutta integrator with the given
     67    * step.
     68    * @param step integration step
     69    */
     70   public ClassicalRungeKuttaIntegrator(final double step) {
     71     super("classical Runge-Kutta", STATIC_C, STATIC_A, STATIC_B,
     72           new ClassicalRungeKuttaStepInterpolator(), step);
     73   }
     74 
     75 }
     76