3. A thin rod of length, L = 12 cm, was made from a material with a thermal conductivity, k = 1 cm²/s. The temperature distribution in terms of the time, t and the position, x is denoted by T(t, x). The following initial and boundary conditions are considered: T(0, x) = f(x), T(t, 0) = f(0) and T(t, 12) = f(12) where f(x) is a continuous and non-monotonic function that satisfies either f(20) > ƒ(0)>0 or ƒ (0) > ƒ(20) > 0. By using a suitable function f(x) and, the values of Ax = 2 cm and At = 1 s, consider two (2) different finite-difference methods to investigate the temperature distribution T(t, x) over the time interval [0,2] and discuss your findings. [40 marks]