4. Modeling and Computing. (35 marks) Consider a substance M in a tube. At x=0, there is a large source of M at a concentration of 0.1 mol. (1) If the concentration distribution is described by ax -pc, where p is a constant 2.5/m. What is the maximum timestep that can be used to solve this equation with Euler's method? (5 marks) (2) Solve the above equation using Euler's method with a step size of 0.1 m. Show your calculations for the first four steps and summarize the data in a table. (10 marks) *(m) c(mol) Ca(mol) Ca-c Jeal (%) ac (3) If M can diffuse, the equation governing the concentration is D dx2 = kc, where D is the diffusion constant, 2x10-8 m/s, and k=5x107/s. Convert the differential equation to two first-order equations. (10 marks) (4) Solve the equations in (3) with Euler's method with a step size of 0.1 m. Show your calculations for the first three steps and summarize the data in a table. Suppose that dc/dx=0 at x-0. (10 marks) *(m) c(mol)