EXAMPLE 6.8 OF THE GOCKENBACH TEXT PRESENTS THE SOLUTION FOR THE FOLLOWING TRANSIENT HEAT CONDUCTION PROBLEM USING FEM AND THE METHOD OF LINES. PC = f(x, ?), 0 0 w(x,0) = 0, 0 0 u (100, z) = 0, t >0 f (x t) =10-Box (100 - x)= W/cm: Constants: p = 7.88, c = 0.437, K - 0.836, PROBLEM 14.1 (10 POINTS) Set up the comparable problem using the first central difference approximation for fx . L.e. derive the arrays M and K in the system of equations represented by dr This is the implicit Euler algorithm