| Project 4 Partner: Lado Tonia
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Division of Labor: ...
Project B
Warm-up exercise: Computer Problem 8.3.5.
Hydrostatic pressure can be expressed as a hydraulic head, defined as the equivalent height u of a column of water exerting
that pressure. In an underground resevoir, the steady-state grondwater flow satisfies the Laplace equation Δu=0. Assume that the
resevoir has dimensions 2km x 1km, and water table heights:
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Exercise 4
4. Prove that the functions (a) u(x, y) = e-xy
, (b) u(x, y) = (x2 + y 2)3/2
are solutions of the
specified Poisson equation with the given boundary conditions
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Part 3
Main problem: Begin with Computer
Problem 8.3.8, but use sparse matrix methods to extend p as large as possible.
8. For the Poisson equations in Exercise 4, make a table of the finite difference approximation
and error at (x, y) = (1/4,3/4) as a function of step sizes h = k = 2-p for p = 2, . . . , 5
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