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 018package org.apache.commons.math3.ode.nonstiff; 019 020import 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 * @see LutherIntegrator 044 * @since 1.2 045 */ 046 047public 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}