Numerical analysis problem.
I am experiencing difficulty in solving the following numerical analysis problem:
I need to find the coefficients of the estimation formula
F''(0) ~ A F(-h) + B F(0) + C F(h)by making it exact for the functions:
F(x) = cos(x) , F(x) = sin(x) , F(x) = 1I also need to find an expression for the truncation error for this formula in a form of power series of h, this is to be used to estimate the order of the error after one step of Richardson extrapolation.
It seems easy to find the coefficients, but I have no idea how to find the error, since the interpolating functions are not polynomials.
Some hints or advises would be appreciated.
Thanks in advance.