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III. THE NUMERICAL SOLUTION 
27. The numerical method, as applied to this problem, 
is described in reference (1). Briefly, the method is 
as follows: If the initial distributionsof pressure and 
of velocity are given, then the initial values of P and @ 
can be found from equations (14.6), (14.7), (14.3), and 
(14.8). If P and Q are known at any time t, they can be 
found at the later time t + A&t since P moves with the 
velocity c + u, and Q moves with the velocity c - u, 
according to (14.4) and (14.5). These new values may be 
found by a simple deformation of the P,x and Q,x curves. 
This process is carried out in both regions, Hi and Moe 
On the M, side of the shock P, and Q, are always known. 
On the M side, however, Q travels away from the shock, and 
so a gap in the Q distribution develops after each deforma- 
tion. Since Py, Q,,and P are known, by means of the shock 
equations one can fill the gap, and determine the shock 
velocity at each step. Similarly at the wall a gap appears 
in the P curve, and this has to be filled by the retation 
; (wall) = & (wall) 
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