I have a numerical ODE simulation that I computed at fixed time step $h$ using a 4-th order Runge-Kutta method (
RK4), producing a series of results $(x_1,y_1), (x_2,y_2), (x_3,y_3) \dots (x_N,y_N)$.
If I want to find an approximate solution $y$ at a location $x$ in between my intervals, I could use
- linear interpolation (just kidding, I wouldn't use this)
- cubic splines (current solution, whats my error estimate ?)
- a new
RK4step with $h=x-x_i$ (is error still $O(h^4)$ ?)
- some other appropriate method
What are the recommended methods for interpolating Runge-Kutta results and what is their error order?