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https://issues.apache.org/jira/browse/MATH-338?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel
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Phil Steitz closed MATH-338.
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> Wrong parameter for first step size guess for Embedded Runge Kutta methods
> --------------------------------------------------------------------------
>
> Key: MATH-338
> URL: https://issues.apache.org/jira/browse/MATH-338
> Project: Commons Math
> Issue Type: Bug
> Affects Versions: 2.0
> Environment: Eclipse sous Red Hat 5
> Reporter: Morand Vincent
> Fix For: 2.1
>
>
> In a space application using DOP853 i detected what seems to be a bad
> parameter in the call to the method initializeStep of class
> AdaptiveStepsizeIntegrator.
> Here, DormandPrince853Integrator is a subclass for
> EmbeddedRungeKuttaIntegrator which perform the call to initializeStep at the
> beginning of its method integrate(...)
> The problem comes from the array "scale" that is used as a parameter in the
> call off initializeStep(..)
> Following the theory described by Hairer in his book "Solving Ordinary
> Differential Equations 1 : Nonstiff Problems", the scaling should be :
> sci = Atol i + |y0i| * Rtoli
> Whereas EmbeddedRungeKuttaIntegrator uses : sci = Atoli
> Note that the Gragg-Bulirsch-Stoer integrator uses the good implementation
> "sci = Atol i + |y0i| * Rtoli " when he performs the call to the same method
> initializeStep(..)
> In the method initializeStep, the error leads to a wrong step size h used to
> perform an Euler step. Most of the time it is unvisible for the user.
> But in my space application the Euler step with this wrong step size h (much
> bigger than it should be) makes an exception occur (my satellite hits the
> ground...)
> To fix the bug, one should use the same algorithm as in the rescale method in
> GraggBulirschStoerIntegrator
> For exemple :
> final double[] scale= new double[y0.length];;
>
> if (vecAbsoluteTolerance == null) {
> for (int i = 0; i < scale.length; ++i) {
> final double yi = Math.max(Math.abs(y0[i]), Math.abs(y0[i]));
> scale[i] = scalAbsoluteTolerance + scalRelativeTolerance * yi;
> }
> } else {
> for (int i = 0; i < scale.length; ++i) {
> final double yi = Math.max(Math.abs(y0[i]), Math.abs(y0[i]));
> scale[i] = vecAbsoluteTolerance[i] + vecRelativeTolerance[i]
> * yi;
> }
> }
>
> hNew = initializeStep(equations, forward, getOrder(), scale,
> stepStart, y, yDotK[0], yTmp, yDotK[1]);
> Sorry for the length of this message, looking forward to hearing from you soon
> Vincent Morand
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