Please solve the following questions

Problem 4 ( 20 points) The outflow concentration (c) from a reactor is measured at a number of times over a 24-hr period: The volume flow rate (Q) for the outflow in (m3/hr), can be computed with the following equation: Q(t)=20+10sin(242(t10)) Use the composite Simpson's 1/3 method to determine the flow-weighted average concentration leaving the reactor over the 24 -hr period, c=0tQ(t)dt0tQ(t)c(t)dt (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). Problem 3 (20 points) Consider the following differential equation: dx2d2y0.05dxdy+0.15y=0 with the condition: y(x=0)=1 and dxdyx=0=0 Solve the system using 4th order Runge-Kutta method with a step size of 1.0 and estimate y(1.0). Note: use four decimal digits in your calculations 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) e) Explain briefly how to solve the system above. You may describe the process as a list of steps. (5 points) b) Use LU decomposition method to solve the system of linear equations. (10 points)