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/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.commons.math3.ode.nonstiff;
import org.apache.commons.math3.util.FastMath;
/**
* This class implements the Gill fourth order Runge-Kutta
* integrator for Ordinary Differential Equations .
* <p>This method is an explicit Runge-Kutta method, its Butcher-array
* is the following one :
* <pre>
* 0 | 0 0 0 0
* 1/2 | 1/2 0 0 0
* 1/2 | (q-1)/2 (2-q)/2 0 0
* 1 | 0 -q/2 (2+q)/2 0
* |-------------------------------
* | 1/6 (2-q)/6 (2+q)/6 1/6
* </pre>
* where q = sqrt(2)</p>
*
* @see EulerIntegrator
* @see ClassicalRungeKuttaIntegrator
* @see MidpointIntegrator
* @see ThreeEighthesIntegrator
* @see LutherIntegrator
* @since 1.2
*/
public class GillIntegrator extends RungeKuttaIntegrator {
/** Time steps Butcher array. */
private static final double[] STATIC_C = {
1.0 / 2.0, 1.0 / 2.0, 1.0
};
/** Internal weights Butcher array. */
private static final double[][] STATIC_A = {
{ 1.0 / 2.0 },
{ (FastMath.sqrt(2.0) - 1.0) / 2.0, (2.0 - FastMath.sqrt(2.0)) / 2.0 },
{ 0.0, -FastMath.sqrt(2.0) / 2.0, (2.0 + FastMath.sqrt(2.0)) / 2.0 }
};
/** Propagation weights Butcher array. */
private static final double[] STATIC_B = {
1.0 / 6.0, (2.0 - FastMath.sqrt(2.0)) / 6.0, (2.0 + FastMath.sqrt(2.0)) / 6.0, 1.0 / 6.0
};
/** Simple constructor.
* Build a fourth-order Gill integrator with the given step.
* @param step integration step
*/
public GillIntegrator(final double step) {
super("Gill", STATIC_C, STATIC_A, STATIC_B, new GillStepInterpolator(), step);
}
}
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