Given nodal points of i-1, i, i+1 and i+2 , we want to derive the finite difference discretization for (dy/dx)i . Hint: would be good to establish a statement stating the representation of (dy/dx)i at the above-mentioned nodal points on the LHS and equating to the order of the representation on the RHS, and hence a table with the appropriate Taylor series expansions equating the LHS = RHS.)
Subsequently, I need to obtain the order of accuracy for the derived finite difference operator, question is where can I start?