DormandPrince54Integrator.java
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* this work for additional information regarding copyright ownership.
* The Hipparchus project licenses this file to You under the Apache License, Version 2.0
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*
* 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,
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package org.hipparchus.ode.nonstiff;
import org.hipparchus.ode.EquationsMapper;
import org.hipparchus.ode.ODEStateAndDerivative;
import org.hipparchus.util.FastMath;
/**
* This class implements the 5(4) Dormand-Prince integrator for Ordinary
* Differential Equations.
* <p>This integrator is an embedded Runge-Kutta integrator
* of order 5(4) used in local extrapolation mode (i.e. the solution
* is computed using the high order formula) with stepsize control
* (and automatic step initialization) and continuous output. This
* method uses 7 functions evaluations per step. However, since this
* is an <i>fsal</i>, the last evaluation of one step is the same as
* the first evaluation of the next step and hence can be avoided. So
* the cost is really 6 functions evaluations per step.</p>
*
* <p>This method has been published (whithout the continuous output
* that was added by Shampine in 1986) in the following article :</p>
* <pre>
* A family of embedded Runge-Kutta formulae
* J. R. Dormand and P. J. Prince
* Journal of Computational and Applied Mathematics
* volume 6, no 1, 1980, pp. 19-26
* </pre>
*
*/
public class DormandPrince54Integrator extends EmbeddedRungeKuttaIntegrator {
/** Name of integration scheme. */
public static final String METHOD_NAME = "Dormand-Prince 5 (4)";
/** Error array, element 1. */
static final double E1 = 71.0 / 57600.0;
// element 2 is zero, so it is neither stored nor used
/** Error array, element 3. */
static final double E3 = -71.0 / 16695.0;
/** Error array, element 4. */
static final double E4 = 71.0 / 1920.0;
/** Error array, element 5. */
static final double E5 = -17253.0 / 339200.0;
/** Error array, element 6. */
static final double E6 = 22.0 / 525.0;
/** Error array, element 7. */
static final double E7 = -1.0 / 40.0;
/** Simple constructor.
* Build a fifth order Dormand-Prince integrator with the given step bounds
* @param minStep minimal step (sign is irrelevant, regardless of
* integration direction, forward or backward), the last step can
* be smaller than this
* @param maxStep maximal step (sign is irrelevant, regardless of
* integration direction, forward or backward), the last step can
* be smaller than this
* @param scalAbsoluteTolerance allowed absolute error
* @param scalRelativeTolerance allowed relative error
*/
public DormandPrince54Integrator(final double minStep, final double maxStep,
final double scalAbsoluteTolerance,
final double scalRelativeTolerance) {
super(METHOD_NAME, 6,
minStep, maxStep, scalAbsoluteTolerance, scalRelativeTolerance);
}
/** Simple constructor.
* Build a fifth order Dormand-Prince integrator with the given step bounds
* @param minStep minimal step (sign is irrelevant, regardless of
* integration direction, forward or backward), the last step can
* be smaller than this
* @param maxStep maximal step (sign is irrelevant, regardless of
* integration direction, forward or backward), the last step can
* be smaller than this
* @param vecAbsoluteTolerance allowed absolute error
* @param vecRelativeTolerance allowed relative error
*/
public DormandPrince54Integrator(final double minStep, final double maxStep,
final double[] vecAbsoluteTolerance,
final double[] vecRelativeTolerance) {
super(METHOD_NAME, 6,
minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance);
}
/** {@inheritDoc} */
@Override
public double[] getC() {
return new double[] {
1.0 / 5.0, 3.0 / 10.0, 4.0 / 5.0, 8.0 / 9.0, 1.0, 1.0
};
}
/** {@inheritDoc} */
@Override
public double[][] getA() {
return new double[][] {
{ 1.0 / 5.0 },
{ 3.0 / 40.0, 9.0 / 40.0 },
{ 44.0 / 45.0, -56.0 / 15.0, 32.0 / 9.0 },
{ 19372.0 / 6561.0, -25360.0 / 2187.0, 64448.0 / 6561.0, -212.0 / 729.0 },
{ 9017.0 / 3168.0, -355.0 / 33.0, 46732.0 / 5247.0, 49.0 / 176.0, -5103.0 / 18656.0 },
{ 35.0 / 384.0, 0.0, 500.0 / 1113.0, 125.0 / 192.0, -2187.0 / 6784.0, 11.0 / 84.0 }
};
}
/** {@inheritDoc} */
@Override
public double[] getB() {
return new double[] {
35.0 / 384.0, 0.0, 500.0 / 1113.0, 125.0 / 192.0, -2187.0 / 6784.0, 11.0 / 84.0, 0.0
};
}
/** {@inheritDoc} */
@Override
protected DormandPrince54StateInterpolator
createInterpolator(final boolean forward, double[][] yDotK,
final ODEStateAndDerivative globalPreviousState,
final ODEStateAndDerivative globalCurrentState,
final EquationsMapper mapper) {
return new DormandPrince54StateInterpolator(forward, yDotK,
globalPreviousState, globalCurrentState,
globalPreviousState, globalCurrentState,
mapper);
}
/** {@inheritDoc} */
@Override
public int getOrder() {
return 5;
}
/** {@inheritDoc} */
@Override
protected double estimateError(final double[][] yDotK,
final double[] y0, final double[] y1,
final double h) {
final StepsizeHelper helper = getStepSizeHelper();
double error = 0;
for (int j = 0; j < helper.getMainSetDimension(); ++j) {
final double errSum = E1 * yDotK[0][j] + E3 * yDotK[2][j] +
E4 * yDotK[3][j] + E5 * yDotK[4][j] +
E6 * yDotK[5][j] + E7 * yDotK[6][j];
final double tol = helper.getTolerance(j, FastMath.max(FastMath.abs(y0[j]), FastMath.abs(y1[j])));
final double ratio = h * errSum / tol;
error += ratio * ratio;
}
return FastMath.sqrt(error / helper.getMainSetDimension());
}
}