How can I integrate discrete data without an analytical function?

[avas]

I have a grid and on each point on the grid I have discrete velocity data. I however don't have anyalytical function. I need to integrate the points and check where in space they will be after some time. I know it very easy to do it with runge-kutta if i have the analytical function for velocity but how can i do it just using the discrete data??

 

[HallsofIvy]

"Runge-Kutta", or any numerical integration method, sums values of f at discrete points: f(x+ nh, y+ mk), for example. Just use the given function values, choosing $\Delta x$, $\Delta y$ as the distances between the given x and y values rather than a fixed step like "x+ nh" or "y+ mk".

 

[avas]

Thanks