A numerical implementation of the variational method for solving certain problems in hydrodynamics

The variational method is applied to a hydrodynamic boundary value problem relating to the free-surface oscillations of an ideal incompressible fluid contained in an axisymmetric cavity and subjected to the effect of a uniform field of body forces. The ways to standardize computer programs and to achieve computer time savings in solving problems of this class are discussed. It is shown that the computational accuracy and speed can be increased by introducing an optimal parameter into the coordinate functions of the Ritz series.