ABSTRACT

Indeed, the polynomials qn given by ( 48-49) do exhibit these behaviors in the following sense. We can immediately read off the following results from ( 48-49) as b -+ 0, that as a first approximation we have

2n + 1 = 2q~(l), (51) and

(52) These equations describe the set of orthonormal Legendre polynomials. Similarly, as b -+ oo we have approximately

(53) and

(54)

0.6

0.2

0.0 0 20 40 60 80 100

In closing, we note that a successful computer implementation of domain decomposition methods induced by asymptotic analysis will require close cooperation and interaction between physical scientists, engineers, applied mathematicians, and computer scientists.