Abstract

Entire domain series expansions used in the method of collocation can give rise to unbalanced system matrices. By studying the asymptotic properties of the expansion functions the numerically ill-behaved part of the functions can be factored out. A well-behaved function can then be obtained by suitable normalization. However, the ill-behaved factor is a function of the coordinates and therefore the normalization factor can be considered constant only over small regions. Hence, the normalization process gives rise to a well-behaved set of subdomain basis functions instead of entire domain functions.

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