where 



6 - ^SJ- (E6) 



The solution to the ordinary linear differential Equation El is 



q.x -q .x 



y. = A.e - 1 +B.e J (E7) 



J 3 3 



where. 



q? = f- (E8) 



J 3 



in which A. and B. are constants to be determined through the boundary 



3 J 

 conditions. Since the shoreline evolution in each solution area is connected 



via the boundary conditions with the neighboring areas, an equation system 



with 2N unknowns (two constants for every solution area) is obtained. The 



boundary conditions E2 and E3 give the following relationships: 



q.x. -q.x. q. .x. -q._.x. 



A.e J J + B.e J J = A. , e 3 J + B. . e 3 J (E9) 



J 3 3-1 J-l 



A.e^ 1 + B.e"^ 1 = A.,/*^ 1 + B^.^ 1 ^ 1 (E10) 

 J J j+1 3+1 



2. Furthermore, Equations E4 and E5 give 



q.x. -q.x qi-l x i " q i-l X i B i-1 



A 4 e J J - B.e J 2 = 6. ,A. ,e 2 l J - 6. ,B. ,e J 2 + - 2 - 1 (Ell) 



j j 3-1 J-l 3-1 3-1 q^s 



E2 



