Further study in the numerical solution of BVPs

For a BVP in a simple geometry, it is fairly straightforward to discretize the system oneself using finite differences. For 1-D BVPs with equations of parabolic and elhptic type, pdepe can be used instead. For BVPs in a complex domain in two dimensions, the PDE toolkit 

Use finite differences to discretize the following BVP in three dimensions  

Solve the system Ax = b that discretizes the BVP of problem 6.A.1 without storing the matrix A in memory. Supply a routine that returns zln for input v. 

You are conducting the enzymatic conversion of a substrate S into a product P, with fhe micromoles of S converted per minute per milhgram of enzyme being described by Michaelis Menten kinetics, 

You use an inunobilized enzyme system in which the enzyme is encapsulated in beads of radius of a polymer hydrogel at a mass loading density /Oe = 10 mg /ml of gel. The substrate diffiisivity in the hydrogel is 10 cm /s. The bulk substrate concentration is 1 M. Neglect external mass transfer resistance. Define an internal effectiveness factor, and compute its value as a function of in the range fO fO m. Since the enzyme is expensive, what radins wonld yon use, and why  

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