Grid Independence of Series approximation

Question

I'm working on a project where I need to write out in MatLab an application of the Runge-Kutta formula to approximate the Bessel function. One part of the problem says

Try step size r=0.2 and then use step-size halving to evaluate whether the numerical
solution is grid independent. 

What does the term "grid independent" mean in this context?

Answer 1

grid dependent usually means: the finer/coarser is your grid the better/worst is the approximate of your solution.

So I can imagine that grid independent means that the "quality" (in the sense of precision) of the approximate solution do not depend on how fine is your grid (i.e. how small is the step size).