Phillip Helbig wrote:
> I once had an application where Bulirsch-Stoer turned out to be much
> quicker than Runge-Kutta. It depends on the problem.
Phillip is right. The performance of an initial-value problem integrator
depends on the problem.
It also depends on the implementation. No matter what formula is
used, one needs to do a good job of error control and stepsize selection.
For Adams-type methods, one also needs to do a good job of order
selection. If one does not carefully consider the interaction of
truncation (of the approximation) error, round-off error, stability,
stepsize and order, the usual outcome is a slow and poor-quality
procedure.
When comparing different methods to solve any problem, one should
always compare the best available implementations of those methods.
Frequently, this set doesn't include anything from Numerical Recipes.
Best regards,
Van Snyder
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