A q j+l x j+l _ - q 3+l x 3+l , . q 3 x 3+l , _ - q j x j+l , 6 j 



A.,,e -B.,,e J =6.A.e JJ - 6 . B . e JJ 

 3+1 3+1 J 3 3 2 



q j+ l S 



(E12) 



where 



5 . = a ... - 6 .a . 

 3 oj+1 j oj 



(E13) 



3. Equations similar to E9 to E13 may be written from solution area 2 

 to solution area N-l . In the first and last solution areas, two other con- 

 ditions prevail at the outer boundaries, namely, no sand transport in the 

 first solution area (area 1) and no shoreline change as x->°° in the last 

 solution area (area N) . The Laplace transforms of these boundary conditions 

 are 



dyj 

 dx 



= tan a 



ol 



x = 



(E14) 



% = 



(E15) 



A. Equation E15 implies that the constant A^ is zero. The resulting 

 system of equations to be solved in order to determine the value of the con- 

 stants is conveniently written in matrix form. A general system of N solu- 

 tion areas gives rise to 2N - 1 equations as follows: 



4 1"2 ''2*2 



q N-l x N , q N-l x N ~ q N*N 

 6 6 N-l e 









— — 





A l 





tan a ol 



q,s 





B l 











A 2 





8 1 

 q 2 s 





B 2 









x 





° 







V-i 





B N-2 





V-i 











B N 





%-l 

 q N S 



(E16) 



E3 



