GillIntegrator.java

/*
 * Licensed to the Hipparchus project under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The Hipparchus project 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
 *
 *      https://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.hipparchus.ode.nonstiff;

import org.hipparchus.ode.EquationsMapper;
import org.hipparchus.ode.ODEStateAndDerivative;
import org.hipparchus.ode.nonstiff.interpolators.GillStateInterpolator;
import org.hipparchus.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 :</p>
 * <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>
 * <p>where q = sqrt(2)</p>
 *
 * @see EulerIntegrator
 * @see ClassicalRungeKuttaIntegrator
 * @see MidpointIntegrator
 * @see ThreeEighthesIntegrator
 * @see LutherIntegrator
 */

public class GillIntegrator extends FixedStepRungeKuttaIntegrator {

    /** Name of integration scheme. */
    public static final String METHOD_NAME = "Gill";

    /** Simple constructor.
     * Build a fourth-order Gill integrator with the given step.
     * @param step integration step
     */
    public GillIntegrator(final double step) {
        super(METHOD_NAME, step);
    }

    /** {@inheritDoc} */
    @Override
    public double[] getC() {
        return new double[] {
            1.0 / 2.0, 1.0 / 2.0, 1.0
        };
    }

    /** {@inheritDoc} */
    @Override
    public double[][] getA() {
        return new double[][] {
            { 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 }
        };
    }

    /** {@inheritDoc} */
    @Override
    public double[] getB() {
        return new double[] {
            1.0 / 6.0, (2.0 - FastMath.sqrt(2.0)) / 6.0, (2.0 + FastMath.sqrt(2.0)) / 6.0, 1.0 / 6.0
        };
    }

    /** {@inheritDoc} */
    @Override
    protected GillStateInterpolator createInterpolator(final boolean forward, final double[][] yDotK,
                                                       final ODEStateAndDerivative globalPreviousState,
                                                       final ODEStateAndDerivative globalCurrentState,
                                                       final EquationsMapper mapper) {
        return new GillStateInterpolator(forward, yDotK, globalPreviousState, globalCurrentState,
                                        globalPreviousState, globalCurrentState, mapper);
    }

}