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The solution to the finite difference scheme is obtained through
recursive backsubstitution.
Equation 31  is solved by,
 

 (43) 
The solution for a fixed number j in range obtained through,
 
(44) 
where,
Equation 32  is solved by,
 

 (45) 
The solution for a fixed j in range is obtained
through,
 
(46) 
where,
Equation 33  is solved by,
 

 (47) 
The solution for a fixed i in the range is
obtained
through,
 
(48) 
where,
Equation 34  is solved by,
 

 (49) 
The solution for a fixed i in the range is
obtained through,
 
(50) 
where,
An approximate solution of the equations 19 will be
found at some large time T_{N} that satisfies,
 
(51) 
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Stanford Exploration Project
4/5/2006