Question 4 (13 marks) a) Consider the following parabolic heat conduction equation JT (x,t) at a²T(x,t) = α дх² i) ii) Write the finite different approximation of this equation using the Forward-Time, Central-Space (FTCS) scheme and rearrange it to be solved by an explicit method. What is the stability condition for the numerical solution of this equation using an explicit method? b) The initial temperature of a metal rod of length 1m is given by T(x, 0) = 2 sin(x), 0<x<1 The temperatures of the rod at x = 0 and x = 1 are given by Using a = 0.5, Ax T(0,t) = 0, T(1,t) = 0, t>0 0.25 and At = 0.02, determine the temperature distribution in the rod at t = 0.04 using the explicit method by numerically solving the parabolic heat conduction equation in (a). c) If the calculations in part (b) were repeated with Ax = 0.1 to reduce the error and At remains as 0.02, what difficulty would be encountered? Do not repeat the finite difference calculations to determine your answer.