Please solve all parts

Problem 2 (40 points) Axial dispersion in a chemical tubular reactor is modeled using the following equation: d2d2ddkm=0;0xL Subject to boundary conditions: (=0)=0.8 and (=0.3)=0.4 Consider L=0.3,k=3, and =0.1, where is a dimensionless tubular axis, and 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. ( 10 points) b) Use LU decomposition method to solve the system of linear 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 Newton's method, arrange the equations in the form of: (10 points) J(Xi)(Xi+1Xi)=F(Xi)(Donotsolvethesystem). e) Explain briefly how to solve the system above. You may describe the process as a list of steps. (5 points)