B M + EAt 



M (v \ Aa, X M 



1 



where 



S M " T2 (55) 



■m i At d N,M-l D 



Tl = 1 + -7 r ! — ; R u , (56) 



(» ) Ao^ M-l 

 V '2M-1 



2At c< 

 T2 = 1 + 



orb 



N,M gAt 



— — + —, — r^- 



P» (57) 



7JTT Aol *M 

 d N,M V^ 2M 1 



Using the same notation, the solution (Equations 49 and 50) may be written as 



^N.M - - P M U N/i + % (58) 



«N!Ll = - R M-1^N,M + S M-1 (59) 



For any given N , the recursion coefficients P , Q , R , and S are com- 

 puted, using Equations 52-57, in succession between the boundaries in the 

 direction of increasing a..(x) . The values of these coefficients at the 

 boundaries depend on the types of boundary conditions encountered. Once all 

 the coefficients for a given N have been determined, the values of n* 

 and U r+ for all the cells in the column are computed, using Equations 58 

 and 59, in the direction of decreasing a, (x) . By continuing to progress to 

 the next higher value of N , the whole grid is swept in the a.(x)- 

 direction. 



39. The development of the finite difference equations and the recursion 

 relations for the cx„(y) sweep is similar to that for the ol (x) sweep. In 

 this case, using the same notation as before, the recursion coefficients may 

 be written as 



31 



