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With inspiration from other libraries
/*
* 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.Field;
import org.apache.commons.math3.RealFieldElement;
import org.apache.commons.math3.ode.FieldEquationsMapper;
import org.apache.commons.math3.ode.FieldODEStateAndDerivative;
import org.apache.commons.math3.util.MathArrays;
/**
* 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 EulerFieldIntegrator
* @see ClassicalRungeKuttaFieldIntegrator
* @see MidpointFieldIntegrator
* @see ThreeEighthesFieldIntegrator
* @see LutherFieldIntegrator
* @param the type of the field elements
* @since 3.6
*/
public class GillFieldIntegrator>
extends RungeKuttaFieldIntegrator {
/** Simple constructor.
* Build a fourth-order Gill integrator with the given step.
* @param field field to which the time and state vector elements belong
* @param step integration step
*/
public GillFieldIntegrator(final Field field, final T step) {
super(field, "Gill", step);
}
/** {@inheritDoc} */
public T[] getC() {
final T[] c = MathArrays.buildArray(getField(), 3);
c[0] = fraction(1, 2);
c[1] = c[0];
c[2] = getField().getOne();
return c;
}
/** {@inheritDoc} */
public T[][] getA() {
final T two = getField().getZero().add(2);
final T sqrtTwo = two.sqrt();
final T[][] a = MathArrays.buildArray(getField(), 3, -1);
for (int i = 0; i < a.length; ++i) {
a[i] = MathArrays.buildArray(getField(), i + 1);
}
a[0][0] = fraction(1, 2);
a[1][0] = sqrtTwo.subtract(1).multiply(0.5);
a[1][1] = sqrtTwo.subtract(2).multiply(-0.5);
a[2][0] = getField().getZero();
a[2][1] = sqrtTwo.multiply(-0.5);
a[2][2] = sqrtTwo.add(2).multiply(0.5);
return a;
}
/** {@inheritDoc} */
public T[] getB() {
final T two = getField().getZero().add(2);
final T sqrtTwo = two.sqrt();
final T[] b = MathArrays.buildArray(getField(), 4);
b[0] = fraction(1, 6);
b[1] = sqrtTwo.subtract(2).divide(-6);
b[2] = sqrtTwo.add(2).divide(6);
b[3] = b[0];
return b;
}
/** {@inheritDoc} */
@Override
protected GillFieldStepInterpolator
createInterpolator(final boolean forward, T[][] yDotK,
final FieldODEStateAndDerivative globalPreviousState,
final FieldODEStateAndDerivative globalCurrentState,
final FieldEquationsMapper mapper) {
return new GillFieldStepInterpolator(getField(), forward, yDotK,
globalPreviousState, globalCurrentState,
globalPreviousState, globalCurrentState,
mapper);
}
}