1. (20 pts) For the 1D explicit finite difference model of flow and decay uk+1 = duk-1 +aut, i = 1, ,n-I,0, 1, . . . , mark-1, where d = ! and a = 1-d-t, assume that the decay rate is a function of the spatial variable x, say (x) = 0.1 + 0.02e- (a) Change the finite difference model above to account for this (b) Modify the Matlab code flowld2.m and use it to study this case for L-5,n 100,T 15. mark = 450, u 0.2 and with the initial condition u(z,0) = 0.2 + 1 sin T I if x e l0. and u(z,0-0.2 if x E (, L] and the upwind boundary condition u(0,t) = 0.2. Plot your result in the (r, t, u) space. (c) Compare the result obtained in (b) with the results for the constant decay rates of = 0.1 and = 0.12, and explain what you have noticed from the comparison. 1. (20 pts) For the 1D explicit finite difference model of flow and decay uk+1 = duk-1 +aut, i = 1, ,n-I,0, 1, . . . , mark-1, where d = ! and a = 1-d-t, assume that the decay rate is a function of the spatial variable x, say (x) = 0.1 + 0.02e- (a) Change the finite difference model above to account for this (b) Modify the Matlab code flowld2.m and use it to study this case for L-5,n 100,T 15. mark = 450, u 0.2 and with the initial condition u(z,0) = 0.2 + 1 sin T I if x e l0. and u(z,0-0.2 if x E (, L] and the upwind boundary condition u(0,t) = 0.2. Plot your result in the (r, t, u) space. (c) Compare the result obtained in (b) with the results for the constant decay rates of = 0.1 and = 0.12, and explain what you have noticed from the comparison