Answer to Question #8035 in Quantitative Methods for ahmad

Question

Consider the scheme
yn+1 −2yn +yn−1 =h^2 4 (fn+1 +2fn +fn−1)
where fn = f(xn,yn) etc. is used to solve the initial value problem
y′′ = f(x, y), y(x0) = y0, y′(x0) = y0′
(a) Show that the method has the global error of order 2 when applied to IVP
(b) Show that this method is stable for any value of hk when applied to
y′′=−k^2y k>0