Axial dispersion in a chemical tubular reactor is modeled using the following equation: d2d2ddkm=0;0xL Subject to boundary conditions: (=0)=0.8 and (n=0.3)=0.4 Consider L=0.3,k=3, and =0.1, where is a dimensionless tubular axis, and is is a dimensionless concentration. Using the finite difference method, answer the following questions: (Part A) Consider the value m=1.0 : a) Transform the BVP to a system of linear equations in the form of Ax=b. Discretize the above equation into 3 equal sized intervals. ( 30 points) b) USe LU decomposition method to solve the system of lineat equations. (10 points) (Part B) Consider the value m=1.5 : c) Transform the BVP to a system of nonlinear equations. ( 5 points) d) To be able to solve the system of equations derived in part (c) using the Nevton's method, arrange the equations in the form of: (10 points) I(xi)(xf+1xi)=F(xi)(Donotsolvethesystem). e) Explain briefly how to solve the system above. You may describe the process a a lit steps. (5 points)