G - -|Vs| cos 9 (20) 



These substitutions result in the following equation in which the sine of the 

 local wave angle at the location i— 1 , j is the quantity to be determined, 

 thus 



sin 9 



•14= T^~i M^sl . , . sin 9. , , + (1 - 2a) Ivsl . , sin 9. , 



1-1, J l Vs li-i,jL\' ' i, J+1 i,J+i ' 'i,j i,j 



+ a Ivsl . . . sin 8. , . ) - ttt— ( Ivsl . . , . cos 9. . . , 

 1 'iJ-1 i, j-1 / 2Ay \l li-1,j + 1 i-1, j+1 



(21) 



-lvs| . , . , cos 9. . . ,) - d - W)A» /| | cos 9. , . 

 1 i-1, j-1 1-1, j-V 2Ay V 'i, j+1 i, j+1 



- vs . , . cos 9 . . . \"1 

 1 'if J-1 ^J -1 )] 



22. Similarly, using the substitutions 



F = a 2 A (22) 



G = a 2 B (23) 



where 



A = cc | Vs | cos 9 (24) 



B = cc | Vs | sin 9 (25) 



the finite difference form of Equation 9 becomes 



Ik 



