Another look at admissible functions

Problems associated with using global admissible functions in boundary value problems are discussed. It is shown that if care is not taken, it is possible to construct sets of trial functions that yield inaccurate results which take too long to converge. The concept of complementary boundary conditions is introduced, and their existence is established. Complementary boundary conditions indicate that the solution to the boundary value problem cannot take certain values at the boundaries. It is shown that trial functions that yield incorrect or very slowly converging results are those that violate the complementary boundary conditions. A revision for the definition of admissible and comparison functions is proposed that takes the complementary boundary conditions into consideration.