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Exercise 31: Developing a system of FDEs for an elliptic BVP.

As t approaches infinity the solution to the IBVP of Exercise 5 approaches the solution of the following elliptic BVP:

(a) Beginning with the solution of Exercise 5, develop a system of 16 FDEs for this BVP. (b) Use a conservation law argument to develop the same system of FDEs for this BVP. (c) Use centered difference formulas for and to develop the system of FDEs found in parts (a) and (b).