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: 810196 $ $Date: 2009-09-01 15:47:46 -0400 (Tue, 01 Sep 2009) $ 042 * @since 1.2 043 */ 044 045 public class GillIntegrator extends RungeKuttaIntegrator { 046 047 /** Time steps Butcher array. */ 048 private static final double[] STATIC_C = { 049 1.0 / 2.0, 1.0 / 2.0, 1.0 050 }; 051 052 /** Internal weights Butcher array. */ 053 private static final double[][] STATIC_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[] STATIC_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", STATIC_C, STATIC_A, STATIC_B, new GillStepInterpolator(), step); 070 } 071 072 }