where 



a m+l/2 = A m + a m-l/2 S m-1 



m ~ Tl Q m Tl 



» i B i /o + a Q 



m+1 „ m+1/2 m in 



m T2 m T2 



Tl = 1 + a . ,„R , 

 m-1/2 m-1 



(51) 



T2 = a , /0 + a P 

 m+1/2 m m 



38. Since in FORTRAN computer language fractional indices are not 



possible, a new integer index system is adopted in the program. Thus all the 



variables defined at the center and the faces m+1/2 and n+1/2 of a cell 



n,m will be designated by the integer indices N,M . The only exceptions are 



the expansion coefficients \i and \i which are defined at cell centers and 



x y 



faces. For these the following index system is adopted. For example, u 

 at the center of cell n,m is designated by the index 2M-1 , whereas p at 

 the face m+1/2 is denoted by the index 2M , and similarly for \i . Using 

 this new notation, the expanded form of the recursion coefficients for the 

 a 1 (x)-sweep may be written as follows: 



P Nil! (52) 



M " ( ^x ) 2M-l A0 l T1 



At5 N,M-l 

 A„ + 



M ( V2M-l Aa i "- 1 



S, = Tl (53) 



R M = , N S At = (54) 



M W. 



2M 



30 



Act T2 



