ISSN:
0945-3245
Keywords:
AMS: 30C30, 65H10, 65R20
;
CR: 5.15, 5.18
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary Discretization of the Theodorsen integral equation (T) yields the discrete Theodorsen-equation (T d ), a system of 2N nonlinear equations. A so-called ε-condition may be fulfilled. It is known that (T) has exactly one continuous solution. This solution gives the boundary correspondence of the normalized conformal map of the unit disc onto a given domainG. It is also known that (T d ) has one and only one solution if ε〈1 and at least one solution if ε≧1. We show here that for every ε≧1 and N∈ℕ\ {1} there is a domainG satisfying an ε-condition such that (T d ) has an infinite number of solutions. Moreover, givenK〉0 and any domainG that fulfills an ε-condition, we will construct a domainG 1 in the neighbourhood ofG that fulfills a max (1, ε+K)-condition such that (T d ) forG 1 has an infinite number of solutions. The underlying idea of the construction of those domains allows also to give important new facts about iterative methods for the solution of (T d ), even in the case ε〈1.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01408693
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