Base functions for projective methods in the hydrodynamics

Abstract

The paper constructs a family of harmonic functions which are furthermore
adopted as a functional basis of a projective method in the hydrodyna-
mics of a limited liquid volume. To get these functions, the Whittecker
representation is utilised. Exact and recurrence formulas are derived to
compute the harmonic functions and their derivatives. The harmonic
functions are analytical in the closed domain of definition but their analyti-
cal continuation has a jump along a ray going from the domain corner poi-
nts. Employing the functional set improves the precision of the projective
method and makes it possible to get extra 2-3 significant figures of the
approximate solution.