ABSTRACT
The asymptotic behavior of the solution to problems such as (1-2) is well studied; see Eckhaus and deJager [11] or Vishik and Liusternik [29]. For the sake of discussion, let us assume that f( 0) -=1 0 and f( 1) -=I 0 and that f or f' is discontinuous at a point y0 such that 0 < yo < 1. (In computations we usually may ignore any milder singularities.) On 0 < y < Yo and Yo < y < 1 we require f to be in C 2• It is then natural to introduce a domain decomposition as shown in Fig. 2, and the motivation is as follows. The reduced equation obtained by formally setting E = 0 is
where
X ( . )- (exp{snx}-exp{sn-rn(1-x)})f n X, E - { ( )} n, 1 - exp - r n - Sn
fn1l" ~ 1.
