I am going to calculate a trajectory, by using a pre-calculated vector field. The values of the field are known on a grid which is quadratic in the horizontal direction, un-evenly spaced in the vertical, and evenly spaced in time.
I'm planning to use a 4th order Runge-Kutta integrator, and my question is if I should simply select my time step such that the three different times in the Runge-Kutta calculation exactly matches three consecutive time steps in the data, or if I will gain anything by implementing some kind of interpolation scheme to allow using a shorter time step in the integrator.
The spatial and temporal resolution of the pre-calculated dataset is such that the trajectory will seldom move further than the spatial step during one time step.