In a particular scheme for numerically modeling one-dimensional fluid flow, the successive values, u n , of the solution are connected for n ≥ 1 by the difference equation
c ( un+1 - un-1 ) = d ( un+1 - 2un + un-1 ) ,
where c and d are positive constants. The boundary conditions are u0 = 0 and uM = 1. Find the solution to the equation, and show that successive values of u n will have alternating signs if c > d .