In this Matlab exercise sheet, we consider the heat equation of the form du 0u = Oz u(a,t) = u(b, t) = 0, u(x,0) = f(x). 0t 10. Use the backward difference code BD heat to solve the heat equation with the following initial conditions. In each case, choose k in a way that would result in the instability of the forward difference scheme: 1. L= 4T, N = 40, a = 0, f(z) = u(z,0) = sin z 2. a=-10, b=10, h = 0.25, f(z)= u(z,0) = sechz, 3. L=10, b = L/2, N=20, f(x) = u(x,0)=