Re: fixed classic rk4 step actually returns result for two half steps

[Tuomo Keskitalo]

Hi,

if I remember correctly, all steppers that use step doubling for error
estimates return the more accurate value from two half steps. At this point
I think it is best to just document this behavior, I can update docs this
week. Thanks for mentioning this issue!

BR,
Tuomo


On Tue, Oct 6, 2020 at 11:27 PM Krishna Myneni <krishna.myneni@ccreweb.org>
wrote:

> The function gsl_odeiv2_driver_apply_fixed_step() function in GSL 2.5,
> using the rk4 step method actually returns the result for two half-
> steps instead of the result for a single step. The attached code shows
> the result for integrating the Lorenz system of ODEs with given
> parameters and initial conditions, after 1 step at dt = 1e-4:
>
> $ ./bench_gsl_rk4
> 1.59864268529822870e-03  9.99903676398808394e-01  7.99388902928489989e-
> 08
>
> The above result for y[0] only has 12 significant digits in comparison
> to the double precision result for a single step of the classical RK4
> estimate for the step size used. Of course it is more accurate, but the
> point is that it is not giving the expected result for 1 classical RK4
> step. The problem appears to be with rk4_apply() which is using both
> single step and two half steps for estimating the error. It leaves the
> output state to be the result of the two half steps.
>
> Perhaps this is by design, but it will cause confusion when comparing
> with other rk4 fixed step solutions.
>
> Krishna Myneni
>
>

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