For the same parameters in the example problem presented under the discussion section:

Recall the problem involved a one-dimensional confined aquifer, with a constant initial head across its length. Then instantly drop the head on the right end of the aquifer while maintaining a constant head on the left side.


we defined a grid on it, one unit thickness into the computer screen


initial head will be the same for each cell

cell 5 will be a constant head equal to the initial head, H_L

cell 1 will be defined as a constant head equal to the head, H_R that begins the stress on the right



for this exercise, let:

y = 3 ft
b = 3 ft
H_L = h₁ = 8.2 ft
H_R = h₅ = 3.6 ft
K = 0.02 ft/day T= 0.06 ft²/day
s = 0.00033 ft^-1 S = 0.001

initially, h₁ = h₂ = h₃ = h₄ = h₅ = 8.2 ft

for t>0 h₅ = 3.6 ft

1. Calculate h₄ @ 0.07 day increments to 0.7 days using the implicit approach

2. Repeat #1 @ 0.14 day increments to 0.7 days using the implicit approach

3. Compare the mass balance at each step for the 0.07 and the 0.14 day time steps.

4. Graph your results as head Vs time

5. Compare your result to those from the explicit method


Answer to the Implicit Solutions