D = 



D^° 



R^O 













B^^ 



D^l 



B^l 















b" 



d" 



b" 







_iiJ ni3 



,0 -B -^ D 

 



-B^J+l 



SlJ 



0. 



ij+1 -ij+1 



0. 



(47) 



The system of linear equations then can be written in the form 



DX = C 



(48a) 



where X = (x ) and C = (c ) for y = 1, . . . ,3(M+1) , where the components 

 X of the vector X are defined by 



3k+K 



i+1 k 



K 



(48b) 



where K = 1,2,3 and the components c of the vector C are defined by 



:;ik 



'3k+K K 



(48c) 



Gaussian reduction is used to solve Equation (48) . The 3x3 sub- 

 matrices of D have been inverted explicitly so that the Gaussian reduction 

 of Equation (48) is very fast on the computer. Back substitution is used 

 to obtain the vector X. 



COMPUTATIONAL RESULTS AND DISCUSSION 

 Some sample computational results of the boundary layer on two double 

 ship models are presented in this section. The first sample, computational 



25 



