n-1 

 P(n+1) = A -^-r- + B P(n) + E P(n-l) 



D O 



where 



A = 



(n-2) a 



(2n-3) b 

 (n-2) a 



E = - 



(n-1) c 

 (n-2) a 



n > 3 



The integration with respect to $ is performed using the trapezoidal rule. Then the 

 integral equation can be represented as a system of linear, simultaneous equations 

 for the unknown coefficients a.., b.., and a. 



1 J 



zz 



i=l j=l 



a ij £m(ij) 



P Q 



ZZ 



p=l q=l 



pq &m(pq) 



z 



k=l 



a k\m(k) 



2V V 2 V V V 



on the blade plane 



(36) 



V 

 a _s 



2 V 



on the cavity plane 



where the A n are the integrations of the double integrals of source distribution in 

 x-m 



Equations (18), (20), (27)- (29) both on the blade and the cavity planes at the £th 

 collocation point, and m(ij) is the index corresponding to the coefficient a.. . 



By the least-squares method of solving simultaneous equations, a square matrix 

 (B ) is made out of the generally nonsquare matrix (A..) where 



pq 



z 



A £p A Jlq 



(37) 



15 



