Let's say I want to obtain the finite difference representation of the differential operator $(dU/dx)_j$ at the nodal point $j$ (or $j\Delta x$). I'm also interested in the mentioned finite difference operator at the nodal points at $(j-1)$, $j$, $(j+1)$ and $(j+2)$, which is not symmetrical about the nodal point $j$. This is because I want to implement the boundary conditions involving $(dU/dx)_j$ at the boundary in which a symmetrical finite difference representation would create additional fictitious nodal points outside the computational domain of interest. So, in the derivation, I want to obtain the finite difference operator of $(dU/dx)_j$ at the nodal points at $(j-1)$, $j$, $(j+1)$ and $(j+2)$, also determine the order of accuracy of the representation.
What are some of the simple ways of obtaining the finite difference representation aside from Implicit Runge Kutta method?