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Under a number of simplifying assumptions, the steadystate height of the water table in a one-dimensional, unconfined groundwater aquifer (Fig. P28.30) can be modeled with the following second-order ODE,
Where x = distance (m), K = hydraulic conductivity (m/d), h = height of the water table (m), h = the average height of the water table (m), and N = infiltration rate (m/d). Solve for the height of the water table for x = 0 to 1000 m where h(0) = 10 m and h(1000) = 5 m. Use the following parameters for the calculation: K = 1 m/d and N = 0.0001 m/d. Set the average height of the water table as the average of the boundary conditions. Obtain your solution with
(a) The shooting method and
(b) The finite difference method. |
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