Subdomain basis functions from entire domain basis functions for a certain class of problems

摘要

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.