2y . .Aol 

 x;i,j 1 



cos 8 + 



sin 9 (U sin 9 - V cos 9) 



Ji,3 



i,j+l i,j-l 

 2u . .Aot„ 



cos 9 (U sin 9 - V cos 9) 



i.3 



i.3 



9V • *\ ( 



17 sin j , ifo - 



Uk cos 9 - Vk sin 9 



A sinh (2kd) 



3d 



-s— - sin 



°y • • !»j 



3U . 3V 

 t— cos 9 + -t— si 

 3x 3x 



ln 6 ) | ("o - 



Uk cos 9 - Vk sin 



A sinh (2kd) 



= 



i.3 



(24) 



where Aa.. and Aa„ are the constant grid spacings in a. , cu space. 



All values of d , U , and V are known at the start of computation for 



9 . If all values of 9 on rows i and i+1 are known, then Equation 24 



can be solved for all values on row i-1 . When this has been done, the next 



row can be solved. To find 9. , . it is first necessary to find k. • . 



i-l, 3 i'J 



Since 9. . is already known, Equation 12 can be solved by Newton-Raphson 



iteration for k. • . 

 1 » J 



19. Substitution of Equations 3 and 5 into Equation 19 yields 



H. . . - H. , 



2\i . .Aol 

 x;i,j 1 



L U + C cos 

 \ 8 



i.3 



H. . . - H. . , 



i.j+1 i,3-l 



2y . . Aou 



y;i,3 2 



V + C sin 



i.3 



§ |- (U + C cos 9) + -J |- (V + C sin 9) 



2 3x g 2 3y g 



H [- 3U - 3U - 3V - 3V] 



2 \ xx 3x yx 3y xy 3x yy 3y/ 



-I i,3 



(25) 



At this point in the computation, all values of U , V , d and 9 are 

 known, making possible the calculation of all values of k , n , ~a , and 

 C as well. If all of the values of H in rows i and i+1 are known, 

 then all values of H in row i-1 can be found, which then allows the 

 determination of values of H in the next row. The values of H in the two 



15 



