Show that the fourth centered divided difference approaching to 

d'u A) Show that the fourth centered divided difference approaching to dx* Where x is a point belonging to a uniform mesh of size h, it is given by Uk-2 -Aux-1 +6U AUx+1 +UK+2 +0(h) - B) Apply the Backward-Euler method to the following ordinary differential equation to obtain the approximations at t= 0.1 and t= 0.2. Compare your results with those of the exact solution u(t)= # 1+t du t u(t); u(0) = 1 dt 1+t =