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 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
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 *      http://www.apache.org/licenses/LICENSE-2.0
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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 .
This method is an explicit Runge-Kutta method, its Butcher-array
is the following one :
   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

where q = sqrt(2)

See Also:
EulerIntegrator
ClassicalRungeKuttaIntegrator
MidpointIntegrator
ThreeEighthesIntegrator
LutherIntegrator
Since:
1.2/**
 * 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. /** Time steps Butcher array. */
  private static final double[] STATIC_C = {
    1.0 / 2.0, 1.0 / 2.0, 1.0
  };

  
Internal weights Butcher array. /** 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. /** 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.
Params:
step – integration step/** 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);
  }

}