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 ac -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) x (m) c (mol) Ca(mol) Ca-c Jeal (%) (3) If M can diffuse, the equation governing the concentration is Done = kc, where D is the diffusion constant, 2x10-8 m+/s, and k=5x10-7/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 de dr=0 at x=0.(10 marks) x (m) c (mol) 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 ac -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) x (m) c (mol) Ca(mol) Ca-c Jeal (%) (3) If M can diffuse, the equation governing the concentration is Done = kc, where D is the diffusion constant, 2x10-8 m+/s, and k=5x10-7/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 de dr=0 at x=0.(10 marks) x (m) c (mol)