Qu PROBLEM 4 (20 points) Consider a linear convection equation: au +c at Ox 0. where c > 0 for 00 And u(t,0) = Qu(tl) = R as boundary conditions The implicit FTCS approximation of the above equation is given by: t 24x (up - u-1) Assume the grid is constructed of N equally spaced points. i=l i=2 i=N-1 i=N X=0 XEL Problem 4-1) show that the resulting finite difference equation for this approximation has the following form, Ax = 6 where, X is the vector of unknown u values at each node, * = [uz, uz, uz....., UN-1, UNIT And A is a matrix of the form, Y 0 ' Y 0 0 0 BY 0 A= 0 0 ve 0 0 I Problem 4-2) Determine the values of & Randy in the matrix A Problem 4-3) Determine the vector 6 Qu PROBLEM 4 (20 points) Consider a linear convection equation: au +c at Ox 0. where c > 0 for 00 And u(t,0) = Qu(tl) = R as boundary conditions The implicit FTCS approximation of the above equation is given by: t 24x (up - u-1) Assume the grid is constructed of N equally spaced points. i=l i=2 i=N-1 i=N X=0 XEL Problem 4-1) show that the resulting finite difference equation for this approximation has the following form, Ax = 6 where, X is the vector of unknown u values at each node, * = [uz, uz, uz....., UN-1, UNIT And A is a matrix of the form, Y 0 ' Y 0 0 0 BY 0 A= 0 0 ve 0 0 I Problem 4-2) Determine the values of & Randy in the matrix A Problem 4-3) Determine the vector 6