Problem (10 Marks: Given the following partial differential equation below: ди ди =8 0<x<1, and t>0 at dx23 1. Write down the Crank-Nicolson finite difference scheme. 2. What order approximation is this in time and in space? 3. Discuss the stability of this finite difference scheme using the von Neumann stability criterion. 4. Use the Crank-Nicolson finite difference scheme with Ax = 0.25, At = 0.0625 to solve numerically the given problem for two steps in t-direction, where u(x, 0)=sin(x), 0<x<1 u(0,t) = u(1,t) = 0, t>0