4 (a) Use a Taylor series approach to show that the second derivative of a function F(x) can be approximated by F(x + h) - 2F(x) + F(x -h) F" (x) =- h2 (3) (b) Hence, discretise the following Partial Differential Equation, for the function U(x, t) au at Pax2 Expressing your result in terms of a time-stepping formula for U,/+1- Assuming a rectangular grid with spacings Ax and At and U (X, + (Ax, to + jAt) = Up. You may assume the result in (a) and also assume that a first order derivative can be approximated by F(x + h) - F(x) F'(x)