6a ol 



a 2 + 

 " 6 a ol + a o2 



6 + 1 l 



6(6 + 1) 



.2 



o a , 

 ol 



A 2 



-o a , + a 

 ol oz 



(6 + l) 2 



(6 + l) 2 



(93) 



(94) 



85. If a „ is zero, the expressions on the right side reduce to those 

 o2 ° 



on the left side. As can be seen from Equations 81 and 82, even though the 

 description involves only two solution areas, the governing equation is 

 already quite complex. Generalization to an arbitrary number of solution 

 areas is straightforward, in which case the situation is mathematically ex- 

 pressed for the i area as follows (see Figure 41): 



.2 



9 y ± zy ± 



x < x < x. . , (95) 



i 2 at 1 _ _ i+1 



3x 



ix~ = °oi " ~2 a oi+l + 72 IF - x = x i+l (96) 



3y i-i l i 9y i 



ax — = a oi-i - ~r~ a oi + -j- ^r x = x i (97) 



6 i-i 6 i-i 



y i = y i+ i x = x i+ i (98 > 



where 



.2 %i_ 



65 



(99) 



